As a game developer, if the thought of hand crafting a level does not appeal to you, then you may consider looking into procedural generation for your next project. Even using procedural generation, however, you still need to be able to turn your generated map arrays into a tilemap with clean, contiguous walls, and sprites that match up cleanly, as if it was drawn by hand. This is where a technique called auto-tiling can come into play to help determine which tiles should be drawn in which locations on your tilemap.

In this article, I will explain the concept of auto-tiling, Wang Tiles, binary and bitmasks, and then walk through the process and algorithms associated with using this tool in a project.

What is auto-tiling​

Auto-tiling converts a matrix or array of information about a map and assigns the corresponding tile texture to each tile in a manner that makes sense visually for the tilemap level. This uses a tile's position, relative to its neighbor tiles to determine which tile sprite should be used. Today we will focus on bitmask encoding neighbor data, although there are other techniques that can be used to accomplish this.

One can get exposed to auto-tiling in different implementations. If you're using a game engine like Unity or Godot, there are features automatically built into those packages to enabling auto-tiling as you draw and create your levels. Also, there are software tools like Tiled, LDTK, and Sprite Fusion, that are a little more tilemap specific and give you native tools for auto-tiling.

Auto-tiling has provided the most benefit when we think about how we can pivot from tilemap matrices or flat indexes representing the state of a tilemap, to a rendered map on the screen. Let us say you have a tilemap in the form of a 2d matrix with 1's and 0's in it representing the 'walkable' state of a tile. Let us assign a tile as a floor (0) piece or a wall (1) piece. Now, one can simply use two different tiles, for example:

a grass tile and a dirt path tile

We could take a tilemap matrix like this:

and use these two tiles to assign the grass to the 1's and the 0's to the path tile. It would look like this:

This is technically a tile-map which has been auto-tiled, but we can do a little better.

What are Wang tiles?​

Wang tiles do not belong or associate with game development or tile-sets specifically, but come from mathematics. So, why are we talking about them? The purpose of the Wang tiles within the scope of game development is to have a series of tile edges that create matching patterns to other tiles. We control which tiles are used by assigning a unique set of bitmasks to each tile that allows us reference them later.

Wang tiles themselves are a class of system which can be modeled visually by square tiles with a color on each side. The tiles can be copied and arranged side by side with matching edges to form a pattern. Wang tile-sets or Wang 'Blob' tiles are named after Hao Wang, a mathematician in the 1960's who theorized that a finite set of tiles, whose sides matched up with other tiles, would ultimately form a repeating or periodic pattern. This was later to be proven false by one of his students. This is a massive oversimplification of Wang's work, for more information on the backstory of Wang tiles you can be read here: Wang Tiles.

This concept of matching tile edges to a pattern can be used for a game's tilemap. One way we can implement Wang tiles in game development is to create levels from the tiles. We start with a tile-set that represents all the possible edge outcomes for any tile.

These tile assets can be found here: Wang Tile Set

The numbers on each tile represents the bitmask value for that particular permutation of tile design. We then can see how you can swap these tiles for a separate texture below. In the image above, there are a couple duplicate tile configurations, and they are shown in white font.

The magic of Wang tiles is that it can be extended out and create unique patterns that visually work. For example:

A bitmask is a binary representation of some pattern. In the scope of this conversation, we will use a bitmask to represent the 8 neighbors tiles of an given tile on a tilemap.

What is a bitmask?​

A bitmask is a binary representation of some pattern. In the scope of this conversation, we will use a bitmask to represent the 8 neighbors tiles of an given tile on a tilemap.

Quick crash course on Binary​

So our normal counting format is designed as base-10. This means that each digit in our number system represents digits 0-9 (10 digits), and the value of each place value increases in power of base 10.

So in the number '42', the 2 represents - (2 * 10⁰) which is added to the 4 in the 'tens' place, which is (4 * 10¹), which equals 42.

(2 * 1) + (4 * 10) = 42
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(2 * 1) + (4 * 10) = 42
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T This in binary looks different, as binary is base-2, which means that each digit position has digits 0 and 1, (2 digits). This is the counting system and 'language' of computers and processors.

Quickly, let's re-assess the previous example of '42'. 42 in binary is 101010. Let's break this down in similar fashion.

Starting from the right placeholder and working our way left... The 0 in the right most digit represents 0 * 2⁰. The next digit represents 1 * 2¹... and on for each digit and the exponent increases each placeholder.

   0         1         0         1         0          1
_________________________________________________________________
(0 * 1) + (1 * 2) + (0 * 4) + (1 * 8) + (0 * 16) + (1 * 32) = 42
2 + 8 + 32 = 42
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   0         1         0         1         0          1
_________________________________________________________________
(0 * 1) + (1 * 2) + (0 * 4) + (1 * 8) + (0 * 16) + (1 * 32) = 42
2 + 8 + 32 = 42
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Bits, Bytes, and Bitmasks​

That is how information in computers is encoded. We can use this 'encoding' scheme to easily represent binary information, like 'on' or 'off', or in this discussion, walkable tile or not walkable. This is why in the tile-set matrix example above, we can flag non-walkable tiles as '1', and walkable tiles as '0'. This is now binary encoded.

A bit is one of these placeholders, or one digit. 8 of this bits together is a byte. Computers and processors, at a minimum, read at least a byte at a time.

We can use this binary encoding for the auto-tiling by representing the state of each of a tile's neighbors into 8 bits, one for each neighbor. This means that the condition and status of each neighbor for a tile can be encoded into one byte of data (8 bits) and CAN be represented with a decimal value, see my earlier explanation about how the number 42 is represented in binary.

So the whole point of this section is to get to this example: we are going to encode the neighbor's data for an example tile.

Quick Demonstration​

Now the tile we are assigning the bitmask to is the green, center tile. This tile has 8 neighbors. If I start reading the 1's and 0's from the top left and reading right, then down, I can get the value: 101 (top row) - 01 (middle row) - 101 (bottom row). Remember to skip the green tile.

All together, this is 10101101, which can be stored as a binary value, which can be converted to a decimal value: 173. Remember to start at the rightmost bit when converting.

   1         0         1         1         0          1          0          1
__________________________________________________________________________________
(1 * 1) + (0 * 2) + (1 * 4) + (1 * 8) + (0 * 16) + (1 * 32) + (0 * 64) + (1 * 128)
1 + 4 + 8 + 32 + 128 = 173
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   1         0         1         1         0          1          0          1
__________________________________________________________________________________
(1 * 1) + (0 * 2) + (1 * 4) + (1 * 8) + (0 * 16) + (1 * 32) + (0 * 64) + (1 * 128)
1 + 4 + 8 + 32 + 128 = 173
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Now we can use that decimal value of 173 to represent the neighbor pattern for that tile. Every tile in a tilemap, can be encoded with their 'neighbors' bitmasks.

As you saw earlier, the wang tiles had bitmask values assigned to them. This is how we know which tile to substitute for each bitmask.

The Process​

We have already covered the hard part. In this section we are pulling it all together in a walkthrough of the overall high level process.

Here are the steps we are covering:

Find or create a tile-set spritesheet that you would like to use Create your tilemap data, however you like. Loop through each index of tile, and evaluate the neighbor tiles, and assign bitmask Map the bitmap values to the 'appropriate' tile in your tile-set (this is the long/boring part IMO) Iterate over each tile and assign the correct image that matches the bitmask value Draw your tilemap in your game Creating a tile-set Here is an example of a tile-set that I drew for the demo project.

These 47 tiles represent all the different 'wall' formations that would be required. I kept my floor tiles separate in a different file so that it is easier to swap out. The floor is drawn as a separate tile underneath the wall. Each tile represented in the grid is designed to match up with a specific group of neighbor patterns. Let's take the top-left tile:

This tile is intended to be mapped to a tile where there are walled neighbors on the right, below, and bottom right of the tile in question. There maybe a few neighbor combinations ultimately that may be mapped to this tile, in my project I found 7 combinations that this tile configuration would be mapped to.

If you look through each tile you can see how it 'matches' up with another mating tile or tiles in the map. For my implementation, I spent time testing out each configuration visually to see which tile different bitmasks needed to be mapped to.

Create your tilemap data​

Now we will use either a 2d matrix or a flat array in your codebase, with each index representing a tile. I use a flat array, with a tilemap width and height parameter. It is simply preference.

You can manually set these values in your array, or you can use a procedural generation algorithm to determine what your wall and floor tiles. I can recommend my Cellular Automata aarticle that I wrote earlier if you are interested in generating the tilemap procedurally. When this is completed, you'll have a data set that will look something like this.

Loop through tilemap and assign bitmasks​

For each index of your array, you will need to capture all the states of the neighbor tiles for each tile, and record that value on each tile. I would refer to the previous section regarding how to calculate the bitmasks.

ts
    // This loops through each tile in the tilemap
    private createTileMapBitmasks(map: TileMap): number[] {
        // create the array of bitmasks, the indexes of this array will match up to the index
        // of the tilemap
        let bitmask: number[] = new Array(map.columns * map.rows).fill(0);
        let tileIndex = 0;
        // for each tile in the map, add the bitmask to the array
        for (let tile of map.tiles) {
            bitmask[tileIndex] = this._getBitmask(map, tileIndex, 1);
            tileIndex++;
        }
        return bitmask;
  }
  // setting up neighbor offsets indexes /
    const neighborOffsets = [
        [1, 1],
        [0, 1],
        [-1, 1],
        [1, 0],
        [-1, 0],
        [1, -1],
        [0, -1],
        [-1, -1],
    ];
  // iterate through each neighbor tile and get the bitmask based on if the tile is solid
    private _getBitmask(map: TileMap, index: number, outofbound: number): number {
        let bitmask = 0;
        // find the coordinates of current tile
        const width = map.columns;
        const height = map.rows;
        let y = Math.floor(index / width);
        let x = index % width;
        // loop through each neighbor offset, and 'collect' their state
        for (let i = 0; i < neighborOffsets.length; i++) {
            const [dx, dy] = neighborOffsets[i];
            const nx = x + dx;
            const ny = y + dy;
            //convert back to index
            const altIndex = nx + ny * width;
            // check if the neighbor tile is out of bounds, else if tile is a wall ('solid') shift in the bitmask
            if (ny < 0 || ny >= height || nx < 0 || nx >= width) bitmask |= outofbound << i;
            else if (map.tiles[altIndex].data.get("solid") === true) bitmask |= 1 << i;
        }
        return bitmask;
    }
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ts
    // This loops through each tile in the tilemap
    private createTileMapBitmasks(map: TileMap): number[] {
        // create the array of bitmasks, the indexes of this array will match up to the index
        // of the tilemap
        let bitmask: number[] = new Array(map.columns * map.rows).fill(0);
        let tileIndex = 0;
        // for each tile in the map, add the bitmask to the array
        for (let tile of map.tiles) {
            bitmask[tileIndex] = this._getBitmask(map, tileIndex, 1);
            tileIndex++;
        }
        return bitmask;
  }
  // setting up neighbor offsets indexes /
    const neighborOffsets = [
        [1, 1],
        [0, 1],
        [-1, 1],
        [1, 0],
        [-1, 0],
        [1, -1],
        [0, -1],
        [-1, -1],
    ];
  // iterate through each neighbor tile and get the bitmask based on if the tile is solid
    private _getBitmask(map: TileMap, index: number, outofbound: number): number {
        let bitmask = 0;
        // find the coordinates of current tile
        const width = map.columns;
        const height = map.rows;
        let y = Math.floor(index / width);
        let x = index % width;
        // loop through each neighbor offset, and 'collect' their state
        for (let i = 0; i < neighborOffsets.length; i++) {
            const [dx, dy] = neighborOffsets[i];
            const nx = x + dx;
            const ny = y + dy;
            //convert back to index
            const altIndex = nx + ny * width;
            // check if the neighbor tile is out of bounds, else if tile is a wall ('solid') shift in the bitmask
            if (ny < 0 || ny >= height || nx < 0 || nx >= width) bitmask |= outofbound << i;
            else if (map.tiles[altIndex].data.get("solid") === true) bitmask |= 1 << i;
        }
        return bitmask;
    }
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Map bitmask values to each tile sprite in spritesheet​

Here is the monotonous part. For a byte, or an 8-bit word, the amount of permutations of tile patterns is 256. That's a lot of mappings. Now I did mine the hard way, manually, one by one. But there may be easier ways to do this. I use Typescript, so I will share a bit of what my mappings look like. Each number key in the object is the bitmask value, and its mapped to a coordinate array [x, y] for my spritesheet that I shared earlier in the article. Now, I could have put them in order, but that does not really serve any benefit.

ts
export const tilebitmask: Record<number, Array<number>> = {
  0: [3, 3],
  1: [3, 3],
  4: [3, 3],
  128: [3, 3],
  32: [3, 3],
  11: [0, 0],
  175: [0, 0],
  15: [0, 0],
  47: [0, 0],
  207: [0, 5],
  203: [0, 5],
  124: [3, 5],
  43: [0, 0],
  ...
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ts
export const tilebitmask: Record<number, Array<number>> = {
  0: [3, 3],
  1: [3, 3],
  4: [3, 3],
  128: [3, 3],
  32: [3, 3],
  11: [0, 0],
  175: [0, 0],
  15: [0, 0],
  47: [0, 0],
  207: [0, 5],
  203: [0, 5],
  124: [3, 5],
  43: [0, 0],
  ...
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Iterate over the tiles and assign tile sprite​

The last two steps we'll do together. Now we simply need to iterate over our tilemap, assign the appropriate sprite tiles. I'm using Excalibur.js for my game engine, and the code is in Typescript, but you can use whichever tool you would prefer.

ts
draw(): TileMap {
    // call the method that loops through and configures all the bitmasks
    let bitmask = this.createTileMapBitmasks(this.map);
    let tileindex = 0;
    for (const tile of this.map.tiles) {
      tile.clearGraphics();
      // if the tile is solid, draw the base tile first, THEN the foreground tile
      if (tile.data.get("solid") === true) {
        // add floor tile
        tile.addGraphic(this.baseTile);
        // using the tile's index grab the bitmask value
        let thisTileBitmask = bitmask[tileindex];
        // this is the magic... grab the coordinates of the tile sprite from tilebitmask, and provide that to Excalibur
        let sprite: Sprite;
        sprite = this.spriteSheet.getSprite(tilebitmask[thisTileBitmask][0], tilebitmask[thisTileBitmask][1]);
        //add the wall sprite to the tile
        tile.addGraphic(sprite);
      } else {
        // if the tile is not solid, just draw the base tile
        tile.addGraphic(this.baseTile);
      }
      tileindex++;
    }
    return this.map;
  }
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ts
draw(): TileMap {
    // call the method that loops through and configures all the bitmasks
    let bitmask = this.createTileMapBitmasks(this.map);
    let tileindex = 0;
    for (const tile of this.map.tiles) {
      tile.clearGraphics();
      // if the tile is solid, draw the base tile first, THEN the foreground tile
      if (tile.data.get("solid") === true) {
        // add floor tile
        tile.addGraphic(this.baseTile);
        // using the tile's index grab the bitmask value
        let thisTileBitmask = bitmask[tileindex];
        // this is the magic... grab the coordinates of the tile sprite from tilebitmask, and provide that to Excalibur
        let sprite: Sprite;
        sprite = this.spriteSheet.getSprite(tilebitmask[thisTileBitmask][0], tilebitmask[thisTileBitmask][1]);
        //add the wall sprite to the tile
        tile.addGraphic(sprite);
      } else {
        // if the tile is not solid, just draw the base tile
        tile.addGraphic(this.baseTile);
      }
      tileindex++;
    }
    return this.map;
  }
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Demo Application​

Link to Demo

Link to Repo

In this demo application, I'm using Excalibur.js engine to show how auto-tiling can work, and its benefits in game development. The user can click on the tilemap to draw walkable paths onto the canvas. As the walkable paths are drawn, the auto-tiling algorithm will automatically place the correct tile in its position based on the neighbor tile's walkable status.

There are some controls at the top of this app, a button to reset the tilemap settings back to not walkable, so one can start over. Also, two drop downs that let the user swap out tile-sets for different styles. This shows the benefits of having standardized Wang tiles for your tile-sets. For example, in this demo, we have three Wang tile-sets. When you swap them out, it can automatically draw them correctly into your tilemap.

Grass

Snow

and Rock

Why Excalibur

Small Plug...

ExcaliburJS is a friendly, TypeScript 2D game engine that can produce games for the web. It is free and open source (FOSS), well documented, and has a growing, healthy community of gamedevs working with it and supporting each other. There is a great discord channel for it JOIN HERE, for questions and inquiries. Check it out!!!

Conclusions

TThat was quite a bit, no? We covered the concept of Autotiling as a tool you can use in game developement. We discussed the benefits of Wang tiles for your projects and that they allow for the auto selection of the correct tile sprites to use based off of bitmask assignments. We dug into bitmask and base-2 binary encoding a little bit just to show how we were encoding the neighbor tile information into a decimal value so we could map the tile sprites appropriately. We finished this portion by doing an example tile encoding of neighbors to demonstrate the process.

We went step by step throught he process of autotiling, looking at tilesets, looking at code snippets, and finishing at the demo application on itch. I hope you enjoyed this take on autotiling, as mentioned above, this is NOT the only way to do this, there are other ways of accomplishing the same effect. You also can tweak this to your own liking, for instance, you can introduce varying tiles so you can use different floor tiles, or adding decord on to walls to add additional variety and add a feeling of greater immersion into the worlds your building. Have fun!

I love procedural generation. As a hobbyist game developer, it is the concept and technique that I keep reaching for in my games. This article is about Cellular Automata, which follows suit of my previous articles regarding other procedural generation strategies for game development. In my last article, we studied the Wave Function Collapse Algorithm. Staying within that topical thread of procedural algorithms which can be leveraged in game development, let's turn our focus to Cellular Automata.

What is Cellular Automata​

Cellular Automata, or CA for short, is an algorithm which has some key potential benefits within the field of game development. You may have seen in certain games, for example Dwarf Fortress or Terraria for example, where organic looking caves are generated, or some map patterns that look naturally grown. Essentially, it uses a grid based data set, and for each discrete unit in that grid, uses the state of all its neighbors to determine the end state of that cell in the ending simulation result.

History of Cellular Automata​

Background​

The early beginnings of the algorithm originated in the 1940's while scientists were studying crystal growth. That study, plus others including self-replicating robot experiments led to the realization of using a method of treating a system as a collection of discrete units (cells), and calculating their behavior based on the influence of each cell's neighbors. For more details on this: Cellular Automata

The Game of Life​

In the 1970's, James Conway famously created a simulation called the Game of Life. This very simple simulation, which had only four rules, created a very dynamic and varied group of results that bounced between appearing random and controlled order. The rules determined each cell's future state as classified as dying due to underpopulation or overpopulation, creating a new living unit due to reproduction, or just continuing to exist with the correct balance of population around that unit.

Uses in Game Development​

There are some common implementations of using Cellular Automata in game development. The classic trope is using the CA algorithm for generating tilemaps of organic looking areas or cave systems.

Another application is simulating the spread of fire across an area. Brogue is a good example of how this can be used.

Other aspects is simulating gas expansion in an area, or the spread of a virus, or enemy reproduction simulations for generating new enemies.

The Algorithm​

For explaining the CA algorithm, we will demonstrate code snippets that demonstrate TypeScript and using Excalibur.js, but this can be done in any languages and framework of your choice.

Initialization​

We start with a grid of tiles that are randomly filled with ones and zeroes.

ts
const tiles:number[]=new Array(49);
// define the blue and white tiles for the TileMap
export const blueTile = new Rectangle({ width: 16, height: 16, color: Color.fromRGB(0, 0, 255, 1) });
export const whiteTile = new Rectangle({ width: 16, height: 16, color: Color.fromRGB(255, 255, 255, 1) });
//Utilizing PerlinNoise plug-in for Excalibur
generator = new PerlinGenerator({
    seed: Date.now(), // random seed
    octaves: 2, 
    frequency: 24, 
    amplitude: 0.91, 
    persistance: 0.95, 
  });
// This uses the TileMap object from Excalibur
export const tmap = new TileMap({
  tileWidth: 16,
  tileHeight: 16,
  columns: 7,
  rows: 7,
});
// Using the Perlin Noise Field, fill the Tilemap and tiles array with data
let tileIndex = 0;
for (const tile of tmap.tiles) {
  const noise = generator.noise(tile.x / tmap.columns, tile.y / tmap.rows);
  if (noise > 0.5) {
    tiles[tileIndex] = 1;
    tile.addGraphic(blueTile);
  } else {
    tiles[tileIndex] = 0;
    tile.addGraphic(whiteTile);
  }
  tileIndex++;
}
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ts
const tiles:number[]=new Array(49);
// define the blue and white tiles for the TileMap
export const blueTile = new Rectangle({ width: 16, height: 16, color: Color.fromRGB(0, 0, 255, 1) });
export const whiteTile = new Rectangle({ width: 16, height: 16, color: Color.fromRGB(255, 255, 255, 1) });
//Utilizing PerlinNoise plug-in for Excalibur
generator = new PerlinGenerator({
    seed: Date.now(), // random seed
    octaves: 2, 
    frequency: 24, 
    amplitude: 0.91, 
    persistance: 0.95, 
  });
// This uses the TileMap object from Excalibur
export const tmap = new TileMap({
  tileWidth: 16,
  tileHeight: 16,
  columns: 7,
  rows: 7,
});
// Using the Perlin Noise Field, fill the Tilemap and tiles array with data
let tileIndex = 0;
for (const tile of tmap.tiles) {
  const noise = generator.noise(tile.x / tmap.columns, tile.y / tmap.rows);
  if (noise > 0.5) {
    tiles[tileIndex] = 1;
    tile.addGraphic(blueTile);
  } else {
    tiles[tileIndex] = 0;
    tile.addGraphic(whiteTile);
  }
  tileIndex++;
}
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The algorithm will have us walk through the grid tile by tile and we will either leave the one or zero in place, or we will flip that value to the opposite, meaning a zero will become a one, and vice versa. The results of this assessment needs to be kept in a new or cloned array, as to not overwrite the starting array's values as you iterate over the tiles.

The Rules​

The rules around flipping the values in each cell will depend on each implementation of the CA algorithm. These can be variable rules, each implementation can be unique in that instance. This gives you some agency and control over how you want your simulation to run. I've tailored this function with the flexibility to pass in the rules on each iteration. The rules are regarding how to handle out of bounds indexes, and what cutoff points are being used.

ts
// Defining our CA function, passing in the grid, dimensions, and rules for OOB indexes and cutoff points
export function applyCellularAutomataRules(
  map: number[],
  width: number,
  height: number,
  oob: string | undefined,
  cutoff0: number | undefined,
  cutoff1: number | undefined
): number[] {
  const newMap = new Array(width * height).fill(0);
  let zeroLimit = 4;
  if (cutoff0) zeroLimit = cutoff0 + 1; //this creates the less than effect
  let oneLimit = 5;
  if (cutoff1) oneLimit = cutoff1;  // this creates the greater than or equalto
  for (let i = 0; i < height * width; i++) {
    for (let x = 0; x < width; x++) {
      const wallCount = countAdjacentWalls(map, width, height, i, oob); //counts walls in neighbors
      if (map[i] === 1) {
        if (wallCount < zeroLimit) {
          newMap[i] = 0; // Change to floor if there are less than cuttoff0 adjacent walls
        } else {
          newMap[i] = 1; // Remain wall
        }
      } else {
        if (wallCount >= oneLimit) {
          newMap[i] = 1; // Change to wall if there are cutoff1 or more adjacent walls
        } else {
          newMap[i] = 0; // Remain floor
        }
      }
    }
  }
  return newMap;
}
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ts
// Defining our CA function, passing in the grid, dimensions, and rules for OOB indexes and cutoff points
export function applyCellularAutomataRules(
  map: number[],
  width: number,
  height: number,
  oob: string | undefined,
  cutoff0: number | undefined,
  cutoff1: number | undefined
): number[] {
  const newMap = new Array(width * height).fill(0);
  let zeroLimit = 4;
  if (cutoff0) zeroLimit = cutoff0 + 1; //this creates the less than effect
  let oneLimit = 5;
  if (cutoff1) oneLimit = cutoff1;  // this creates the greater than or equalto
  for (let i = 0; i < height * width; i++) {
    for (let x = 0; x < width; x++) {
      const wallCount = countAdjacentWalls(map, width, height, i, oob); //counts walls in neighbors
      if (map[i] === 1) {
        if (wallCount < zeroLimit) {
          newMap[i] = 0; // Change to floor if there are less than cuttoff0 adjacent walls
        } else {
          newMap[i] = 1; // Remain wall
        }
      } else {
        if (wallCount >= oneLimit) {
          newMap[i] = 1; // Change to wall if there are cutoff1 or more adjacent walls
        } else {
          newMap[i] = 0; // Remain floor
        }
      }
    }
  }
  return newMap;
}
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To note, this approach to the CA algorithm is for the sake of THIS article. Other approaches can be implemented. Let's define our rules for the scope of this article.

• If the starting value for a tile is a zero, then to flip it to a one, the neighbors must have five or more ones surrounding the starting tile.
• If the starting value for a tile is a one, then to flip it to a zero, the neighbors must have three or fewer ones surrounding the starting tile.
• For tiles on the edges of the grid, which will not have 8 neighbors, out of bound regions will be treated as ones or 'walls'

ts
tiles = applyCellularAutomataRules(tiles, 7, 7, 'walls', 3, 5);
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ts
tiles = applyCellularAutomataRules(tiles, 7, 7, 'walls', 3, 5);
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With these rules in place, which can be modified and tailored to your liking, we can use them to determine the next iteration of the grid by going tile by tile and setting the new grid's values based on each tile's neighbors.

Counting Walls​

For the rule on out of bound neighbors, you can use a variety of different rules to your liking. You can treat them as constants, like in this instance, we treat them as walls. You can have them be treated as floors, which will change how your simulation runs, producing a more 'open' result. You can also have the out of bound tiles mirror the value of the starting value, i.e. if your starting tile on the edge is a one, then out of bound tiles are all ones, and vice versa.

ts
// This function takes in the grid and dims, which index is being inspected, and the rules on OOB tiles
function countAdjacentWalls(map: number[], width: number, height: number, index: number, oob: string | undefined): number {
  let count = 0;
  const y = Math.floor(index / width);
  const x = index % width;
  for (let i = -1; i <= 1; i++) {
    for (let j = -1; j <= 1; j++) {
      if (i === 0 && j === 0) continue;
      
      const newY = y + i;
      const newX = x + j;
      if (newY >= 0 && newY < height && newX >= 0 && newX < width) {
        const adjacentIndex = newY * width + newX;
        if (map[adjacentIndex] === 1) count++;
      } else {
        switch (oob) {
          // The 4 types of rules provided are for constant values, floor and wall, random
          // , and mirror
          case "floor":
            break;
          case "wall":
            count++;
            break;
          case "random":
            let coinflip = Math.random();
            if (coinflip > 0.5) count++;
            break;
          case "mirror":
            if (map[index]==1) count++;
            break;
          default:
            count++; // Perceive out of bounds as wall
            break;
        }
      }
    }
  }
  return count;
}
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ts
// This function takes in the grid and dims, which index is being inspected, and the rules on OOB tiles
function countAdjacentWalls(map: number[], width: number, height: number, index: number, oob: string | undefined): number {
  let count = 0;
  const y = Math.floor(index / width);
  const x = index % width;
  for (let i = -1; i <= 1; i++) {
    for (let j = -1; j <= 1; j++) {
      if (i === 0 && j === 0) continue;
      
      const newY = y + i;
      const newX = x + j;
      if (newY >= 0 && newY < height && newX >= 0 && newX < width) {
        const adjacentIndex = newY * width + newX;
        if (map[adjacentIndex] === 1) count++;
      } else {
        switch (oob) {
          // The 4 types of rules provided are for constant values, floor and wall, random
          // , and mirror
          case "floor":
            break;
          case "wall":
            count++;
            break;
          case "random":
            let coinflip = Math.random();
            if (coinflip > 0.5) count++;
            break;
          case "mirror":
            if (map[index]==1) count++;
            break;
          default:
            count++; // Perceive out of bounds as wall
            break;
        }
      }
    }
  }
  return count;
}
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So starting at the first tile of the grid, you will look at the eight neighbors of the tile, in this instance, five of them are out of bound indexes. You add all the walls up in the neighbors,since the starting value is a zero, if the value is greater or equal to five, in the new grid/array, you will place a one in index zero for the new grid. This is how you flip the values. If, for instance, there would be less than five walls for the neighbors of this index, the value would have remained zero. You repeat this process for each tile in the grid/array.

Redraw your tiles​

At the end, when you have completely iterated over each tile, you will have a new grid of tiles that are now set to zeroes or ones, based on that starting array. You can use this new grid as a completed result, or you can re-run the same simulation using this new grid as your 'new' starting array of data.

ts
// function that clears out the existing Tilemap and redraws it based on the new returned tile array
function redrawTilemap(map: number[], tilemap: TileMap, game: Engine) {
  game.remove(game.currentScene.tileMaps[0]);
  let tileIndex = 0;
  for (const tile of tilemap.tiles) {
    const value = map[tileIndex];
    if (value == 1) {
      tile.addGraphic(blueTile);
    } else {
      tile.addGraphic(whiteTile);
    }
    tileIndex++;
  }
  game.add(tilemap);
}
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ts
// function that clears out the existing Tilemap and redraws it based on the new returned tile array
function redrawTilemap(map: number[], tilemap: TileMap, game: Engine) {
  game.remove(game.currentScene.tileMaps[0]);
  let tileIndex = 0;
  for (const tile of tilemap.tiles) {
    const value = map[tileIndex];
    if (value == 1) {
      tile.addGraphic(blueTile);
    } else {
      tile.addGraphic(whiteTile);
    }
    tileIndex++;
  }
  game.add(tilemap);
}
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Walkthrough of the Algorithm​

This walkthrough will simply use an array of numbers. With this array of numbers we will use a noise field, to represent random starting values, and then we will utilize the CA algorithm over multiple steps to highlight how it can be utilized.

Starting Point​

Let's start with an empty array of numbers. We will represent the flat array as a two dimensional grid, with x and y coordinates. This is a 7 x 7 grid, which will be an array of forty-nine cells. As we process throught he CA algorithm, we will be recording our results into a new array, as to not overwrite the input array while we are iterating over the indexes.

For the CA algorithm, it is suggested to fill the initial array with random ones and zeroes. You can use a Perlin noise field, or a Simplex noise field or just use your languages built in random function to fill the field. Here is ours:

Now we start the process of looping through each index and either leave them alone of flip the value between 0 and 1 based on the values of the neighbors. For this simulation we treat out of bound indexes as walls.

The first index​

The first index of the array is the top left corner of the grid. This is relatively unique in the sense that this index only has three real neighbors. But as we mentioned before, out of bound (OOB) indexes will be treated as walls. If we count up each neighbor index, plus the OOB indexes, we get a value of seven. Since this count is higher than four, we will flip this indexes value to one in the new array we are creating.

Iterating​

The second index of the array is a one. Now this index only has three OOB indexes that will count as walls.

This index only has one addition one in its neighbors, and if that's added to the three OOB index values, that puts our value to four. In our algorithm we are using today, the value that is required to change a one to a zero is if it has less than four walls as neighbors. With that, we will leave this one in place and insert this value in the new array.

We will follow this process for each index with the given rules below:

• If the original value is one in the starting index, to be set to zero in the new array, the neighbor values have to be less than four.
• If the original value is zero in the starting index, to be set to one in the new array, the neighbor values need to be five or higher.

Let's speed this process along a bit.

Finishing the first row.

Generating the 2nd row.

Generating the 3rd row.

Generating the 4th row.

Generating the 5th row.

Generating the 6th row.

Generating the Final row.

Now we have a completed array of new values. The thing about the CA algorithm that is favorable is that you can reuse the algorithm again on the new set of values to generate deeper levels of generation on the initial data set.

Let's run the simulation on this new data and see how it turns out.

So you see how numbers start to collect together to create natural, organic looking regions of walls and floors. This is particularly handy technique for generating cave shapes for tilemaps.

Demo Application​

Link to Demo

Link to Repo

The demo simply consists of a 36x36 tilemap of blue and white tiles. Blue tiles represent the walls, and white tiles represent the floor tiles. There are two buttons, one that resets the simulation, and the other button triggers the CA algorithm and uses the tilemap to demonstrate the results.

Also added to the demo is access to some of the variables that manipulate the simulation. We can now modify the behavior of the OOB indexes. For instance, instead of the default 'walls', you can now change the sim to use random setting, mirror the edge tile, or set it constant to 'wall' or 'floor'.

You also have to ability to see what happens when you unbalance the trigger points. Above we defined 3 and 5 as the trigger points for flipping a tile's state. You have the ability to modify that and see the results it has on the simulation.

The demo starts with a noise field which is a plugin for Excalibur. Using a numbered array representing the 36x36 tilemap, which has ones and zeroes we can feed this array into the CA function. You can repeatedly press the 'CA Generation Step' button and the same array can be re-fed into the algorithm to see the step by step iteration, and then can be reset to a new noise field again to start over.

Why Excalibur

Small Plug...

ExcaliburJS is a friendly, TypeScript 2D game engine that can produce games for the web. It is free and open source (FOSS), well documented, and has a growing, healthy community of gamedevs working with it and supporting each other. There is a great discord channel for it HERE, for questions and inquiries. Check it out!!!

Conclusions

So, what did we cover? We discussed the history of Cellular Automata and some generalized use cases for CA within the context of game development. We covered the implementation of the steps to take to perform the simulation on a grid of data, and then we conducted a walk through example of using the algorithm. Finally, we introduced a demo application hosted on itch, and shared the repository in case one is interested in the implementation of it.

This algorithm is one of the easier to implement, as the steps are not that complicated either in cognitive depth or in mathematical processing. It is one of my favorite simple tools that reach for especially for tilemap generation when I create levels. I urge you to give it a try and see what you can generate for yourself!

One challenge of indie game development is about striking a balance. Specifically, the balance between hand crafted level design, player replayability, and the lack of enough hours in a day to commit to being brilliant at both. This is where people turn to procedural generation as a tool to help strike that balance. One of the most magical and interesting tools in the proc gen toolbox is Wave Function Collapse (WFC). In this article, we'll dive into the how/why of WFC, and how you can add this tool to your repertoire for game development.

WFC is a very popular procedural generation technique that can generate unique outputs of tilemaps or levels based off prompted input images or tiles. WFC is an implementation of the model synthesis algorithm. WFC was created by Maxim Gumin in 2016. The WFC algorithm is VERY similar to the model synthesis algorithm developed in 2007 by Paul Merrell. For more information on WFC specifically, you can review Maxim's Github repo here.

It is based off the theory from quantum mechanics. Its application in Game Development though is a bit simpler. Based on a set of input tiles or input image, the algorithm can collapse pieces of the output down based on the relationship of that tile or image area.

Example input image:

(Yes I do have an unhealthy fascination with the original Final Fantasy)

Example output images:

Entropy

Digging into the quantum mechanics context of WFC will introduce us to the term Entropy. Entropy is used as a term that describes the state of disorder. The way we will use it today is the number of different tile options a certain tile can be given the state of its neighbor tiles. We will demonstrate this further down.

The concept essentially states that the algorithm selects the region of the output image with the lowest possible options, collapses it down to its lowest state, then using that, propogating the rules to each of the neighbor tiles, thus limiting what they can be. The algorithm continues to iterate and collapsing down tiles until all tiles are selected. The rules are the meat and potatoes of the algorithm. When you setup the algorithm's run, you not only provide the tileset, but also the rules for what tiles can be

For this discussion, as the demo application focuses on using WFC with the ExcaliburJS game engine, we are focusing on the simple tile-based WFC approach.

Walkthrough of the algorithm

The Rules​

The rules are arguably the most critical aspect of the algorithm. For the simple tile-based mapping, this includes details and mappings between each tile and what other tiles can be used as neighbors. If you were doing the input image form of WFC, the input image's design would dictate the rules pixel by pixel.

Let us consider this subsection of the tilemap to demonstrate this:

Let's identify each tile as tree, treetop, water, road, and grass. For the sake of simplicity, we will focus on just four of them: tree,water, grass, and treetop.

We will define some rules for the tiles as such.

ts
let treeTileRules = {
  up: [treeTopTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
let grassTileRules = {
  up: [treeTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
let treeTopTileRules = {
  up: [grassTile, waterTile, treeTopTile],
  down: [treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
let waterTileRules = {
  up: [treeTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
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ts
let treeTileRules = {
  up: [treeTopTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
let grassTileRules = {
  up: [treeTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
let treeTopTileRules = {
  up: [grassTile, waterTile, treeTopTile],
  down: [treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
let waterTileRules = {
  up: [treeTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
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What these objects spell out is that for tiles above the tree tile, it can be a grass, water, or treetop tile. Tiles below the treetile can be another tree tile, or water, or grass... and so on. One special assignement to note, that below a treeTop tile, can ONLY be a treeTile.

We can proceed to follow this pattern for each of the tiles, outlining for each tile what the 4 neighbor tiles CAN be if selected.

The Process​

The process purely starts out with an empty grid... or you actually can predetermine some portions of the grid for the algorithm to build around... but for this explanation, empty:

Given that none of the tiles have been selected yet, we can describe the entropy of each tile as essentially Infinite, or more accurate, N number of available tiles to choose from. i.e. , if there are 5 types of available tiles, then the highest entropy is 5, and each tile in this grid is assigned that entropy value.

If we entered the algorithm with predetermined tiles, or what we could call collapsed, then the entropy of the surrounding neighbors of those tiles would have a lower entropy as dictated by the rules we discussed above.

Let's begin by selecting a random tile on this grid... {x: 3,y: 4}. Due to the fact that all its neighbors are empty, it's pool of available tiles is 4, tree, grass,water, or tree top. Let us pick tree, as this can simply be randomly picked from the set.

This leads us into the idea of looping through all the tiles and setting their entropy value based on what their neighbors are... we have 4 available tiles for this experiment, so 4 will be the highest entropy value.

Take note that the neighbors of our fully collapsed tile are not at entropy 4, but at 3, as for each of these neighbors, our 'rules' for the tree tile reduces their possible options. So now we start the process again, but instead of randomly selecting any tile, we will form a list of the lowest entropy tiles, and that becomes our available pool. So, in this example:

[{x:3,y:3}, {x:2,y:4}, {x:4, y:4}, {x:3,y:5}] all have entropy values of 3, so they are what we select.

4,4 is selected from that pool, and based on the rules, it can be grass, water, or tree. Randomly selected: tree again. Looping through the tiles and resetting the entropy, we get a new pool of tiles.

4,3 is the next selected from the new pool of lowest entropy tiles, and it becomes a grass tile. Looping through the tiles and resetting entropy, we notice something different.

We see our first shift in the pool of lowest entropy. The reason behind tile 3,3 being entropy level 2 is due to the rules of grass and tree tiles.

ts
let treeTileRules = {
  up: [treeTopTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
let grassTileRules = {
  up: [treeTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
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ts
let treeTileRules = {
  up: [treeTopTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
let grassTileRules = {
  up: [treeTile, grassTile, waterTile],
  down: [grassTile, waterTile, treeTile],
  left: [grassTile, waterTile, treeTile],
  right: [grassTile, waterTile, treeTile],
};
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The left field for grass tiles allows for grass, water, and tree... while the up field for tree only allows grass, water, and treetop. So between those two fields, there are only 2 tile types that match both requirements, thus there are only 2 available tiles to select and now and entropy of 2.

The next iteration of the algorithm has only one tile in its pool of lowest entropy, 3,3 so it gets collapsed to either water or grass based on its neighbors, so it becomes grass as a random selection.

This algorithm carries on until there are no more tiles to collapse

One note on this example is that we have really limited the amount of different tiles that are being accessed, and you see this manifest itself in the entoropies of 3,4 consistently. The rules also are fairly permissive, which is why we don't see a huge variation of entropies. More tiles available, and more restrictive rules, will drive much more variation in the entropy scores that will be witnessed.

Collisions​

What you will find with this algorithm that there maybe created a conflict where there is no available tiles to select based on the neighbors. This is called either a conflict or a collision, and can be handled in a couple different ways.

One thought is to reset the map and try again. From a process perspective, sometimes this is just the easiest/cheapest method to resolve the conflict.

Another approach is to use a form of the command design pattern, and saving a stack of state snapshots that are captured during each step of the algorithms iteration, and upon reaching a collision, 'backtrack' a bit and retry and generate again from a previous point. The command design pattern essentially unlocks the undo button for an algorithm, and allows for this.

Demo Application

Link To Repo

Link To Demo

The demo application that's online is a simple, quick simulation that runs a few algorithm iterations... and can regenerate the simulation on Spacebar or Mouse/Touch tap.

First, it uses WFC to generate the terrain, only using the three tiles of grass, tree, treetops.

Second, it finds spots to draw two buildings. The rules around this is to not collide the two buildings, and also not have the buildings overrun the edges of the map. I use WFC to generate random building patterns using a number of tiles.

Finally, and this has nothing to do with WFC, I use a pathfinding algorithm I wrote to find a path between the two doors of the houses,and draw a road between them... I did that for my own amusement.

Pressing the spacebar in the demo, or a mouse tap, attempts to regenerate another drawing. Now, not every generation is perfect, but this seems to have a >90% success rate, and for the purposes of this article, I can accept that. I intentionally did not put in a layer of complexity for managing collisions, as I wanted to demonstrate what CAN happen using this method, and how one needs to account for that in their output validation.

Why Excalibur

Small Plug...

ExcaliburJS is a friendly, TypeScript 2D game engine that can produce games for the web. It is free and open source (FOSS), well documented, and has a growing, healthy community of gamedevs working with it and supporting each other. There is a great discord channel for it HERE, for questions and inquiries. Check it out!!!

Conclusions

Wrapping up, my goal was to help demystify the algorithm of Wave Function Collapse. There are some twists to the pattern, but overall it is not the most complicated of generation processes.

We also discussed the concept of Entropy, and how it applies to the algorithm overall, in essence it helps prioritize the next tile to be collapsed. Collapsing a tile is simply the process of picking from of available tiles that a specific tile CAN be by means of the rules provided.

In my experience, and I've done a few WFC projects, the rules provide the constraints of the algorithm. Ultimately, it is where I always spend the most time tweaking and adjusting the project. Too tight of rules, and you'll need to be VERY good at managing collisions. However, too few rules, and you're output maybe a very noisy mess.

I suggest you give WFC a try, it can be VERY fun and rewarding to see the unique solutions it can come up with.

This is a continuation of our discussion on pathfinding. In the first part of our discussion, we investigated Dijkstra's algorithm. This time, we are digging into A* pathfinding.

Link to Part 1

Link to Pathfinding Demo

Pathfinding, what is it​

Quick research on pathfinding gives a plethora of resources discussing it. Pathfinding is calculating the shortest path through some 'network'. That network can be tiles on a game level, it could be roads across the country, it could be aisles and desks in an office, etc. etc.

Pathfinding is also an algorithm tool to calculate the shortest path through a graph network. A graph network is a series of nodes and edges to form a chart. For more information on this: click here.

For the sake of clarity, there are two algorithms we specifically dig into with this demonstration: Dijkstra's Algorithm and A*. We studied Dijkstra's Algorithm in Part 1.

A* Algorithm​

A star is an algorithm for finding the shortest path through a graph that presents weighting (distances) between different nodes. The algorithm requires a starting node, and an ending node, and the algorithm uses a few metrics for each node to systematically find the shortest path. The properties of each node are fCost, gCost, and hCost. We will cover those in a bit.

Quick History​

The A* algorithm was originated in its first state as a part of the Shakey project. That project was about designing a robot that could calculate its own path and own actions. In 1968, the first publishing of the A* project happened and it describes its initial heuristic function for calculating node costs.

A heuristic function is a logical means, not necessarily perfect means, of solving a problem in a pragmatic way.

Over the years the A* algorithm has been refined slightly to become more optimized.

Algorithm Walkthrough​

Load the Graph​

We first load our graph, understanding which nodes are clear to traverse, and which nodes are blocked. We also need to understand the starting node and ending node as well.

Cost the nodes​

We first will assess the cost properties for each node. Cost is a term we are using that represents a distance between nodes. This will be a method that assigns the fCost, gCost, and hCost to each node.

Let's discuss these costs first. The costs are a weighting of each node with respect to its positioning between the starting and ending nodes.

The fCost of a tile is equal to the gCost plus the hCost. This is represented as such:

f=g+h

The gCost of the node is the distance cost between the current node and the starting node.

The hCost of the node is the 'theoretical' distance from the current node to the ending node. This is why we discussed heuristics earlier. This value is an estimate of the distance, a best guess. This makes guessing for a rectangular tilemap easy, since all tiles are distance 1 from each other in a grid, the method of guessing is just using the tile positions of the two nodes and using Pythagorean theorem to assess the distance. If the grid is irregular, some spatial data may need to be injected into the graphs creation to facilitate this heuristic, for example: x/y coordinate locations maybe.

Thus, the fCost is the sum of these two values. While simplistic, this is the value that is leveraged in the algorithm to determine the 'best' path.

Setup Buffers​

After we've looped through all the nodes and costed them appropriately, we will utilize a buffer called openNodes. We will push the starting node into this, as it is the only node we 'know' about as of yet. We will use this openNodes buffer for much of the iterations we conduct in this algorithm.

We will leverage another buffer we will call either 'checked' or 'closed' buffer, and this is where the results of our algorithm will exist, as we process tiles from openNodes into this buffer.

Iteration​

Then we get into the repeating part of the algorithm.

1. Look for the lowest F cost square in the open list. Make it the current square.

2. Move the current square to the closed buffer (list). Remove from openNodes, move to 'checked' nodes.

3. Check if the new current node is the endnode, this is the finishing condition. using the parent node properties of each node, walk backwards to the starting node, that's the shortest path

4. If not ending node, review all neighbor squares of current square, if a neighbor is not traversable, ignore it

5. Check each neighbor is in checked/closed list of nodes, if not, perform parent assignment, and add to open node list

This series continues to iterate while neighbors are being added to the open node list.

Example​

Let's start with this example graph network.

We will manage our walkthrough with two different lists, open nodes and checked nodes. Black tiles above represent nodes that are not traversable. Let's define our start and stop nodes as indicated by the green S node and the blue E node.

The first step of A* algorithm is costing all the nodes, and let's see if we can show this easily.

For more clarity on the 'costing' step, let's talk through the core loop that is applied to each tile.

My process is to loop through each tile, and assuming it has either coordinates or and index, I can determine its distance from the start node and end node.

Let's do the first tile together. The first tile is coordinates (x:0, y:0), and the start node is coordinates (x: 1, y:1), while the end node is (x: 4,y:5). The gCost for this tile we can use Pythagorean theorem to calculate the distance as the hypotenuse.

js
gCost = Math.sqrt(Math.pow((1-0), 2) + Math.pow((1-0)), 2));
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js
gCost = Math.sqrt(Math.pow((1-0), 2) + Math.pow((1-0)), 2));
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This gives us a gCost of ~1.41.

We can repeat this equation for the hCost, but it is with respect to the end node coordinates.

js
hCost = Math.sqrt(Math.pow((4-0), 2) + Math.pow((5-0)), 2));
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js
hCost = Math.sqrt(Math.pow((4-0), 2) + Math.pow((5-0)), 2));
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This yields a hCost of ~6.40.

Knowing both now, we can determine the fCost of that node or tile, by adding the two together, making the fCost 7.82... with rounding.

We can repeat this process for each tile in the graph.

Why am I using floating point values here? There's a reason, if I simply use integers, then the distances wouldn't have enough resolution in digits, creating a little more unoptimized iterations, as the number of cells with equal f Costs would increase, here the fCosts are more absolute, and we will reduce the iterations. Simply put, if all the fCosts between 5.02 - 5.98 all are represented as 5 as an integer, it muddies up how the algorithm moves through and prioritizes the 'next' cell to visit. With floating points, this is explicit. Being a grid, all the distances are simple hypotenuse calculations using Pythagorean theorem.

Before we jump into the overall repetitive loop, we will add the startnode into our list of opennodes.

Now the algorithm can start to be repetitive. We set the startnode to the current node, and move it from open to checked lists.

We first check if our current node is the end node, which it is not, so we proceed.

The next step is to select the lowest fCost, and since the starting node is the only node in openlist, it gets selected, otherwise we would have selected randomly from the lowest value fCosts in the open node list. Now we look at all the neighbors. I will designate the pale yellow as our 'open node' list. We will use different colors for 'checked'.

None are in the checked list, so we add them all to the opennodes list, and assign the current node as each nodes parent. To note, if a node is not traversable (black) then it gets ignored at this point, and not added to the list.

This then repeats as long as nodes are in the open node list, if we run out of open nodes without hitting the end node, then there's no path. When we hit the end node, we start building our return list by looping back through the parent nodes of each node. Starting at the end node, it will have a parent, that parent will have a parent... and so on until you hit the start node.

Let's walk through the example. Let's pick a tile with lowest f cost. As we select new 'current' nodes, we move that node to our checked list so it no longer is in the open node pool.

The lowest cost is 5.02, and grab its neighbors. Along the way we are assigning parent nodes, and adding the new neighbors to the openNodes list.

...but we keep selecting lowest cost node ( f cost of 5.06 is now the lowest to this point), we add neighers to opennodes, assign them parent nodes...

.. the next iteration, the fCost of 5.24 is now lowest, so it gets 'checked', and we grab its neighbors, assign parents..

.. the next iteration, there are two nodes of 5.4 cost, so let's see how this CAN play out, and the algorithm starts to make sense at this point.

Let's pick the high road...

The new neighbors are assigned parents, and are added to the overall list of open nodes to assess. Which is the new lowest fCost now? 5.4 is still the lowest fCost.

Yes, the algorithm went back to the other path and found a better next 'current' node in the list of open nodes. The process is almost complete. The next lowest fCost is 5.47, and there is more than one node with that value, so for the sake of being a completionist...

Still the lowest fCost is 5.47, so we select the next node, grab neighbors, assign parents... one thing I did differently on this table is showing the fCost of the ending node, which up till now wasn't necessary, but showing it here lets one understand how the overall algorithm loops, because the end node HAS to be selected as the next lowest cost node, because the check for end node is at the beginning of the iteration, not in the neighbor eveluation. So in this next loop, I don't make it yellow, but the end node is now been placed AS A NEIGHBOR into the list of open nodes for evaluation.

We now have our path, because the next iteration, the first thing we'll do is pick the lowest node fCost (5.0) and make it the current tile, and then test if it is the end node, which is true now.

We can return its path walking back all the parent node properties and see how we got there along the way.

The test​

Link to Demo

Link to Github Project

The demo is a simple example of using a Excalibur Tilemap and the pathfinding plugin. When the player clicks a tile that does NOT have a tree on it, the pathfinding algorithm selected is used to calculate the path. Displayed in the demo is the amount of tiles to traverse, and the overall duration of the process required to make the calculation.

Also included, are the ability to add diagonal traversals in the graph. Which simply modifies the graph created with extra edges added, please note, diagonal traversal is slightly more expensive than straight up/down, left/right traversal.

Why Excalibur​

Small Plug...

ExcaliburJS is a friendly, TypeScript 2D game engine that can produce games for the web. It is free and open source (FOSS), well documented, and has a growing, healthy community of gamedevs working with it and supporting each other. There is a great discord channel for it HERE, for questions and inquiries. Check it out!!!

You can also find it on GitHub.

Conclusion​

For this article, we briefly reviewed the history of the A* algorithm, we walked throught the steps of the algorithm, and then applied it to an example graph network.

This algorithm I have found is faster than Dijkstra's Algorithm, but it can be tricky if you're not using a nice grid layout. The trick comes into the 'guessing' heuristic of the distance between the current node and the endnode (hCost). If you using a grid, you can use the coordinates of each node and calculate the hypotenuse as the hCost. If it is an unorganized, non standard shaped graph network, this becomes trickier. For the moment, for the library I created, I am limiting A* to grid based tilemaps to make this much simpler. If the grid is not simple, I use Dijkstra's algorithm.

One of the most common problems that need solved in game development is navigating from one tile to a separate tile somewhere else. Or sometimes, I need just to understand if that path is clear between one tile and another. Sometimes you can have a graph node tree, and need to understand the cheapest decision. These are the kinds of challenges where one could use a pathfinding algorithm to solve.

Link to Pathfinding Demo

Pathfinding, what is it​

Quick research on pathfinding gives a plethora of resources discussing it. Pathfinding is calculating the shortest path through some 'network'. That network can be tiles on a game level, it could be roads across the country, it could be aisles and desks in an office, etc etc.

Pathfinding is also an algorithm tool to calculate the shortest path through a graph network. A graph network is a series of nodes and edges to form a chart. For more information on this: click here

For the sake of clarity, there are two algorithms we specifically dig into with this demonstration: Dijkstra's Algorithm and A*.

We study A* more in Part 2

Quick History​

Dijkstra's Algorithm​

Dijkstra's Algorithm is a formula for finding the shortest path through a graph that presents weighting (distances) between different nodes. The algorithm essentially dictates a starting node, then it systematically calculates the distance to all other nodes in the graph, thus, giving one the ability to find the shortest path.

Edsger Dijkstra, was sipping coffee at a cafe in Amtserdam in 1956, and was working through a mental exercise regarding how to get from Roggerdam to Groningen. Over the course of 20 minutes, he figured out the algorithm. In 1959, it was formally published.

Algorithm Walkthrough​

Dijkstra's Algorithm​

Let's start with this example graph network. We will manage our walkthrough using a results table and two lists, one for unvisited nodes, and one for visited nodes.

Let's declare A our starting node and update our results object with this current information. Since we are starting at node A, we then review A's connected neighbors, in this example its nodes B and C.

Knowing that B is distance 10 from A, and that C is distance 5 from A, we can update our results chart with the current information.

With that update, we can move node A from unvisited to visited list, and we have this new state.

Now the algorithm can start to be recursive. We identify the node with the smallest distance to A of our unvisited nodes. In this instance, that is node C.

Now that we are evaluating C, we start with identifying its unvisited neighbors, which in this case is only node D. The algorithm would update all the unvisited neighbors with their distance, adding it to the cumulative amount traveled from A to this point. So with that, D has a distance of 15 from C, and we'll add that to the 5 from A to C.

We continue to repeat this algorithm until we have visited all nodes.

From here we will quickly loop through the rest of the table.

This is when we visit node C:

Node B is closer to Source than node D, so we visit it next.

Unvisited neighbors of B are E and F. E is closes to A, so we visit it next.

D is E's unvisited neighbor, but its distance via E is longer than what's already in the result index, so we do not add this data up.

D is the only unvisited neighbor, and we hit a dead end on this branch, so D gets visited, but with no updates to the results table

So since we are looping through all unvisited Nodes, F is the final unvisited node, and its a neighbor of B. We can now visit F through B, and we do not have any results table updates with this visit, as F has no unvisited neighbors.

What do we do with this data?​

My library module for using this algorithm includes a method that runs the analysis, then uses the results table to get the shortest path.

It takes in the starting node, and ending (destination) node and returns the list of nodes needed to traverse the path.

ts
  shortestPath(startnode: Node, endnode: Node): Node[] {
    let dAnalysis = this.dijkstra(startnode);
    //iterate through dAnalysis to plot shortest path to endnode
    let path: Node[] = [];
    let current: Node | null | undefined = endnode;
    while (current != null) {
      path.push(current);
      current = dAnalysis.find(node => node.node == current)?.previous;
      if (current == null) {
        break;
      }
    }
    path.reverse();
    return path;
  }
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ts
  shortestPath(startnode: Node, endnode: Node): Node[] {
    let dAnalysis = this.dijkstra(startnode);
    //iterate through dAnalysis to plot shortest path to endnode
    let path: Node[] = [];
    let current: Node | null | undefined = endnode;
    while (current != null) {
      path.push(current);
      current = dAnalysis.find(node => node.node == current)?.previous;
      if (current == null) {
        break;
      }
    }
    path.reverse();
    return path;
  }
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So for Example, if I said starting node is A, and endingnode is D, then the returned array would look like.

ts
//[Node C, Node D]
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ts
//[Node C, Node D]
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If you need the starting node in the path, you can unshift it in.

ts
path.unshift(startnode);
//[Node A, Node C, Node D]
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ts
path.unshift(startnode);
//[Node A, Node C, Node D]
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The test​

Link to Demo

Link to Github Project

The demo is a simple example of using a Excalibur Tilemap and the pathfinding plugin. When the player clicks a tile that does NOT have a tree on it, the pathfinding algorithm selected is used to calculate the path. Displayed in the demo is the amount of tiles to traverse, and the overall duration of the process required to make the calculation.

Also included, are the ability to add diagonal traversals in the graph. Which simply modifies the graph created with extra edges added, please note, diagonal traversal is slightly more expensive than straight up/down, left/right traversal.

Conclusion​

In this article, we reviewed a brief history of Dijkstra's Algorithm, then we created and example graph network and stepped through it using the algorithm, and then was able to use it to determine the shortest path of nodes.

This algorithm I have found is more expensive than A*, but is a nice tool to use when you don't understand the shape and size of the graph network. As a programming exercise, I had a lot of fun interating on this problem till I got it working, and it felt like an intermediate coding problem to tackle.

I have been in need of an AI system that can execute a simulation that I desire to run. In my research, I have come across Goal-Oriented Action Planning. This technique can give me the flexibility I need to run my simulation, let's dive into the implementation a bit.

Link to GOAP Demo

GOAP, what is it​

Goal-Oriented Action Planning, or GOAP, is a flexible AI technique that enables the developer build up a set of actions and objectives, and allows the NPC (agent) itself determine what the best objective is, and how to accomplish said objective.

GOAP includes the use of Agents, Goals, Actions, and State, to plan out its next series of decisions and activities. This is a useful system for Non-Playable Characters(NPCs) or enemy AI logic.

Quick History​

GOAP was developed by Jeff Orkin in the early 2000's while working on the AI system for F.E.A.R.

The desire was to generate automated planning sequences for Enemies and NPCs to create a more immersive game experience.

GOAP can be considered an alternative to classic behavioral trees, which was more standard at that time.

Theory of operations​

There are 5 aspects of GOAP that interact to create the magic: State, Agents, Goals, Actions, and the Planner.

First, let's talk about State.

State​

State is the data set conditions that describes the world in which an agent exists. For my implementation, an established set of key/value pair data was used to fuel the simulation. A simple example of a world state:

ts
	world = {
		trees: 3;
		bears: 1;
		playerPosition: {x: 100, y:200};
	};
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ts
	world = {
		trees: 3;
		bears: 1;
		playerPosition: {x: 100, y:200};
	};
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This is the data that gets used, not only as a starting point, but gets cloned and mutated over the course of the algorithm processing the plan.

Goals​

Next, let us review the goals or objectives that are intended to be accomplished. The goal defines the target state that the algorithm evaluates against to determine if the objectives are met.

The goal assessment will take a copy of the mutated state and compare it against the target state defined for the goal, and if it matches, let's the algorithm know that is done with that branch of evaluation.

The goal also contains a method of assessing its own priority conditions, which takes in the world state and returns a defined factor of prioritization. For example, a floating-point value from 0.0 to 1.0, where 1.0 is the highest priority.

Agents​

Agencts are the entities (enemies or other NPCs) that get the planning system attached to it. If the entity is not currently executing a plan, it can call the planning process to assess what it should do next.

One aspect of the agents that is important to remember, is including the ability to cancel the plan, and reassess, even if the sequence isn't complete.

Think about if the environment in which the current plan was created, no longer is viable, you need to be able to change your mind. i.e. a power up is no longer available, or a targeted enemy is dead, etc...

Actions​

Actions are very discrete units of activity:

• Move to spot
• Pick up Item
• Fire weapon
• Duck

These actions should have a cost component, time or energy is common, and the actions will be linked together to form a sequence of actions that constitutes 'plan'.

What is unique about components of an action beyond cost, is the precondition and effect components. These are super important.

The precondition component is what the planner evaluates if the action is viable under the current condition. The current condition is the cloned, mutated state that is considered for that sequence of the plan.

If the conditions are true for the precondition, then the action is considered an available choice for the next step.

The effect component of an action is the defined changes to state that occur when that action is executed. This is used by the planner to clone and mutate the state as it churns through the different possible options.

Planner​

The planner is the algorithm which generates the plan, and it has several tasks. To use the Planner, you pass the current world state, all available actions for the agent, all available goals for the agent.

The planner's first task is to assess all available goals for the agent to determine which is the highest priority.

Then, with that goal selected and the current world state, find a list of actions that can be executed.

With your state, your goal, and your available actions, you can start building a graph network, a branching tree of available plans.

When the graph is constructed, the planner can assess the best course of action based on any number of custom factors, and returns the sequence of actions as the plan.

The algorithm​

There are two aspects of the algorithm that should be discussed. The graph network and the assessment.

The graph network​

The graph network is built with a recursion that forms a tree structure, and branching is based on the new available list of actions that meet the mutated state condition, for that branch.

As you walk through each branch, the actions taken at each node will mutate the state. That mutated stated then gets checked against the goal provided, to see if you are done.

If the goal passes, an endnode is created. If not, then that newly mutated state is used to generate the new list of available actions and the recursion continues.

The recursion ends when a branch's mutated state cannot create further list of actions, or the goal is met.

Picking a plan​

Once the graph is assembled, you can filter out any branches that do not end in a completed goal, then the Planner can assess which path makes most sense.

This is where you can have different style planners. The planner i created simply creates a 'cheapest cost' plan based on the the aggregate cost of each plan created.

I use a dijkstra's algorithm to calculate, based on each actions 'cost', the cheapest path to execute.

But there is flexibility here as well, including using different costing structures, maybe you want to balance energy and time both? Then you could construct a planner that favors one over the other based on conditions.

The test​

Link to Demo

I spent a couple weeks building a simulation of my GOAP library that I created. It is a simple "actor feeds fire with wood, while avoiding bears" simulation.

The Actor has two goals, "keep fire aive", and "avoid bear"

If the actor is currently without a plan to execute, it passes its worldstate into the planner. The world state looks vaguely like this:

ts
export const world = {
  tree: 500,
  tree2: 500,
  tree3: 500,
  campfire: 0,
  player: 0,
  playerState: playerState.idle,
  bearDistance: 300,
};
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ts
export const world = {
  tree: 500,
  tree2: 500,
  tree3: 500,
  campfire: 0,
  player: 0,
  playerState: playerState.idle,
  bearDistance: 300,
};
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The actions available are:

ts
player.goapActions = [
  feedFireAction,
  collectWoodAction,
  moveToTreeAction,
  moveToFireAction,
  moveToTree2Action,
  collectWood2Action,
  moveToTree3Action,
  collectWood3Action,
  runAwayAction,
  relaxAction,
];
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ts
player.goapActions = [
  feedFireAction,
  collectWoodAction,
  moveToTreeAction,
  moveToFireAction,
  moveToTree2Action,
  collectWood2Action,
  moveToTree3Action,
  collectWood3Action,
  runAwayAction,
  relaxAction,
];
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When the planner is fed these components, it assesses the priority of each action based on their weighting, is the fire getting low? or is the bear close by?

With the goal selected, it uses the state data to determine which actions to take, for the fire building, the first round of actions usually are moving to trees. That is unless the player is holding some wood, then it will decide to just go to the fire directly.

If the player moves to a tree, it then collects its wood, then it moves to fire, and feeds the fire, and it waits till the fire gets lower before going to collect more wood.

I mentioned earlier that agents have to be able to cancel their plans. If the bear comes close to the player, it triggers a cancelPlan() method and the player is forced to generate a new plan.

Since the bear is close, it picks "avoid bear" plan, and then the process starts again with that new goal.

Conclusion​

We have covered GOAP, some history of it, what the components of a GOAP system are, and how to implement them.

What I have learned in this process is that GOAP is very powerful and flexible. That does not imply that GOAP is easy, I would consider implementing a GOAP system at the intermediate level.

When trying to connect different actions and insuring they chain together to form a complete plan, there are many chances in implementation to create issues. But when dialed in, GOAP can provide a foundation for a very flexible AI system that can lead to enriching gameplay.

The Excalibur team has built a number of games over the years. During our last few game jams, we started paper prototyping soon after our brainstorming process. It’s been working great and we highly recommend giving it a try!

More flexibility​

Changing rules or mechanics that only exist on paper is a lot faster than having to adjust any code you may have written for those changes. It’s possible to alter your game without much worry, because you’re operating primarily in the realm of imagination, rather than within the constraints of your software development environment.

Paper prototyping can also help avoid the “sunk-cost fallacy”, which encourages you to stick with whatever you’ve spent a lot of time on just because you’ve spent a lot of time on it. Instead, you can change as much or as little as you wish without having to worry about deleting a bunch of code that you’ve already written.

Identify problems early​

You also have the opportunity to fix game design problems before you've devoted time to implementing them in the actual software. While we were paper prototyping Sweep Stacks, we uncovered a game design complication with how the board filled up over time. Without having to write any code, we were able to determine a solution for the issue and implement it directly when we started programming the game.

Easier once you start writing code​

If you’ve spent time prototyping, you'll have a more concrete idea of what you want your game to be. When you actually start writing code, you can begin with a more specific idea of what you want to accomplish. We’ve found it’s much easier to visualize and architect our code when we have a clear idea of how the rules and systems of a game will work together.

Virtual paper​

While it's called “paper prototyping”, this process doesn't literally have to be done with paper, or any physical components at all. Virtual paper prototyping can be just as effective, and allows you to collaborate more easily with remote teammates. There are plenty of wireframing and “virtual tabletop” web apps out there that you can use to put together a digital prototype for your game (we usually use Excalidraw).

Give paper prototyping a try​

The next time you’re working on a game, try doing some prototyping before you write any code. Adjust your rules, modify your designs, and dream of what you want to build.

Updated to the latest Excalibur, Capacitor.js & Parcel!

In this post we put a web canvas game built in Excalibur into an Android (or iOS) app with Capacitor.js!

In the past I would have used something like Cordova, but this new thing from the folks at Ionic has TypeScript support out of the box for their native APIs and support for using any Cordova plugins you might miss.

TLDR show me the code

Capacitor Setup​

The capacitor project setup is pretty straightforward from their docs, it can drop in place in an existing project or create a brand new project from scratch.

I opted for the brand new project:

> npm init @capacitor/app
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> npm init @capacitor/app
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Then follow their wizard and instructions to configure.

After that step add the platforms you're interested in, in this case Android

> npx cap add android
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> npx cap add android
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I recommend reading the capacitor documentation on workflow with a hybrid native app. The gist is this

1. Run npx cap sync to copy your web project into capacitor
2. Run npx cap run android to start the project on android (or start in the Android SDK)

Android Setup​

Before you try to run the project

1. Download Android Studio Android Studio
2. Open it up and check for updates if needed (first time initialization takes some time)
3. Accept your SDK package licenses, the easiest way I've found to do this is with the SDK command line tools with Powershell on W.
   1. Find the SDK Manager
   2. In SDK Tools, check Android SDK Command-line Tools
4. Next we need to accept licenses.
   • In powershell, navigate to the Android SDK Location for command line tools C:\Users\<username>\AppData\Local\Android\Sdk\cmdline-tools\latest\bin
   • Set your java home temporarily $env:JAVA_HOME = 'C:\Program Files\Android\Android Studio\jre'
   • Run .\sdkmanager.bat --licenses and select y for each

Starting the App​

Now that we have Android all setup we can start the app with the capacitor command line.

The gist is that it copies the final compiled html/css/js assets from your favorite frontend frameworks and build tools into the native container

> npx cap sync
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> npx cap sync
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After that we can open it in Android Studio with the capacitor commandline

> npx cap open android
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> npx cap open android
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Building the project and running the first time can take some time, so be patient after hitting the big green play button.

ProTip^TM The Emulator is MEGA slow to start so once you get it on, leave it on. You can redeploy the app to a running emulator with the "re-run" hightlighted below.

If your Android emulator crashes on the first try like mine did with something like The emulator process for AVD Pixel_3a_API_30_x86 was killed, this youtube video was super helpful. For me the problem was disk space, the AVD needs 7GBs of disk space to start so I had to clean out some junk on the laptop 😅

Building Your Canvas Game​

The dev cycle is pretty slick, run npm cap copy android to move your built JS living in the www to the right android folder. The default app looks like this after running it in the android emulator.

Setting Up Your JS Build​

First let's setup our TypeScript by installing and creating an empty tsconfig.json

> npm install typescript --save-dev --save-exact
> npx tsc --init`
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> npm install typescript --save-dev --save-exact
> npx tsc --init`
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Recently I've been a big fan of parcel(v1) for quick and easy project setup, and it works great with excalibur also webpack is cool too if you need more direct control of your js bundling.

> npm install parcel --save-dev --save-exact
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> npm install parcel --save-dev --save-exact
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I copied the generated manifest.json, index.html, and css/ folder out of the original generated www/ and put it into game/.

We need to setup our development and final build script in the package.json. The npm "start" script tells parcel to run a dev server and use game/index.html as our entry point to the app and follow the links and build them (notice the magic inline <script type="module" src="./main.ts"></script>) ✨

html
<!DOCTYPE html>
<html lang="en" dir="ltr">
<head>
  <meta charset="UTF-8">
  <title>Game Test</title>
  <meta name="viewport" content="viewport-fit=cover, width=device-width, initial-scale=1.0, minimum-scale=1.0, maximum-scale=1.0, user-scalable=no">
  <meta name="format-detection" content="telephone=no">
  <meta name="msapplication-tap-highlight" content="no">
  <link rel="manifest" href="./manifest.json">
  <link rel="stylesheet" href="./css/style.css">
</head>
<body>
  <script type="module" src="./main.ts"></script>
</body>
</html>
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html
<!DOCTYPE html>
<html lang="en" dir="ltr">
<head>
  <meta charset="UTF-8">
  <title>Game Test</title>
  <meta name="viewport" content="viewport-fit=cover, width=device-width, initial-scale=1.0, minimum-scale=1.0, maximum-scale=1.0, user-scalable=no">
  <meta name="format-detection" content="telephone=no">
  <meta name="msapplication-tap-highlight" content="no">
  <link rel="manifest" href="./manifest.json">
  <link rel="stylesheet" href="./css/style.css">
</head>
<body>
  <script type="module" src="./main.ts"></script>
</body>
</html>
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In this setup I'm sending all my built output with --dist-dir into the www directory, which is what capacitor will copy to android. I went ahead and deleted the provided default app in the www directory.

json
/* package.json */
{
  "name": "my-cool-game",
  "scripts": {
    "start": "parcel game/index.html --dist-dir www",
    "typecheck": "tsc -p . --noEmit",
    "build": "parcel build game/index.html --dist-dir www"
  }
  ...
}
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json
/* package.json */
{
  "name": "my-cool-game",
  "scripts": {
    "start": "parcel game/index.html --dist-dir www",
    "typecheck": "tsc -p . --noEmit",
    "build": "parcel build game/index.html --dist-dir www"
  }
  ...
}
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Vanilla Canvas code​

To start with I have a really awesome game that shows the fps and a red square. This shows how get started from scratch with the HTML Canvas.

typescript
// main.ts
const canvas = document.createElement('canvas') as HTMLCanvasElement;
const ctx = canvas.getContext('2d') as CanvasRenderingContext2D;
canvas.height = window.innerHeight;
canvas.width = window.innerWidth;
document.body.appendChild(canvas);
let lastTime = performance.now();
const mainloop: FrameRequestCallback = (now) => {
    const delta = (now - lastTime)/1000;
    lastTime = now;
    ctx.fillStyle = 'blue';
    ctx.fillRect(0, 0, canvas.width, canvas.height);
    
    ctx.font = '50px sans-serif';
    ctx.fillStyle = 'lime';
    ctx.fillText((1/delta).toFixed(1), 20, 100);
    ctx.fillStyle = 'red';
    ctx.fillRect(canvas.width/2, canvas.height/2, 40, 40);
    requestAnimationFrame(mainloop);
}
mainloop(performance.now());
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typescript
// main.ts
const canvas = document.createElement('canvas') as HTMLCanvasElement;
const ctx = canvas.getContext('2d') as CanvasRenderingContext2D;
canvas.height = window.innerHeight;
canvas.width = window.innerWidth;
document.body.appendChild(canvas);
let lastTime = performance.now();
const mainloop: FrameRequestCallback = (now) => {
    const delta = (now - lastTime)/1000;
    lastTime = now;
    ctx.fillStyle = 'blue';
    ctx.fillRect(0, 0, canvas.width, canvas.height);
    
    ctx.font = '50px sans-serif';
    ctx.fillStyle = 'lime';
    ctx.fillText((1/delta).toFixed(1), 20, 100);
    ctx.fillStyle = 'red';
    ctx.fillRect(canvas.width/2, canvas.height/2, 40, 40);
    requestAnimationFrame(mainloop);
}
mainloop(performance.now());
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Using Excalibur🗡​

Using the Excalibur engine with capacitor and parcel will be a breeze! Really any web based game engine could be substituted here if you want. Here is the source on github!

> npm install excalibur --save-exact
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> npm install excalibur --save-exact
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Update the main.ts with some Excalibur

typescript
import { Actor, DisplayMode, Engine, Input, Loader, ImageSource } from "excalibur";
const game = new Engine({
    displayMode: DisplayMode.FillScreen,
    pointerScope: Input.PointerScope.Canvas
});
const sword = new ImageSource('assets/sword.png');
const loader = new Loader([sword]);
game.start(loader).then(() => {
    game.input.pointers.primary.on('move', event => {
        const delta =  event.worldPos.sub(actor.pos);
        actor.vel = delta;
        // Original asset is at a 45 degree angle need to adjust
        actor.rotation = delta.toAngle() + Math.PI/4;
    });
    const actor = new Actor({
        x: game.halfDrawWidth,
        y: game.halfDrawHeight,
        width: 40,
        height: 40
    });
    actor.graphics.use(sword.toSprite());
    game.add(actor);
});
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typescript
import { Actor, DisplayMode, Engine, Input, Loader, ImageSource } from "excalibur";
const game = new Engine({
    displayMode: DisplayMode.FillScreen,
    pointerScope: Input.PointerScope.Canvas
});
const sword = new ImageSource('assets/sword.png');
const loader = new Loader([sword]);
game.start(loader).then(() => {
    game.input.pointers.primary.on('move', event => {
        const delta =  event.worldPos.sub(actor.pos);
        actor.vel = delta;
        // Original asset is at a 45 degree angle need to adjust
        actor.rotation = delta.toAngle() + Math.PI/4;
    });
    const actor = new Actor({
        x: game.halfDrawWidth,
        y: game.halfDrawHeight,
        width: 40,
        height: 40
    });
    actor.graphics.use(sword.toSprite());
    game.add(actor);
});
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Note, depending on your emulator settings you may need to tweak it's graphics settings and restart Android Studio for it to build and run (This works out of the box fine on real hardware tested in BrowserStack, for some reason the emulator graphics can be confused)

Tada! 🎉

Hope this helps you web game devs out there!

-Erik

After the winter break, the team has released [email protected] with a lot of improvements to the core engine and plugins! Check the roadmap for our current plans.

Check out the new version on npm!

> npm install [email protected]
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> npm install [email protected]
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"Winter holiday, when developers work on their side projects" - Anonymous Coworker

Dev tools​

> npm install @excaliburjs/dev-tools
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> npm install @excaliburjs/dev-tools
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We've built a new tool to help debug Excalibur games! This tool lets you see information about the Excalibur engine, scenes, actors, clocks, and more!

Debugging why things aren't working has historically been pretty difficult. This plugin will greatly assist in the game development cycle. Nearly everything is available and configurable.

It's pretty low effort to install into your game:

typescript
import { DevTool } from '@excaliburjs/dev-tools';
const game = new ex.Engine({...});
const devtool = new DevTool(game);
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typescript
import { DevTool } from '@excaliburjs/dev-tools';
const game = new ex.Engine({...});
const devtool = new DevTool(game);
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Tiled updates​

> npm install @excaliburjs/plugin-tiled
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> npm install @excaliburjs/plugin-tiled
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The Tiled plugin now implicitly adds a z-index to each layer (which can be overridden) which means things will look as you expect in Excalibur as they do in the Tiled editor.

Set the starting layer z (defaults to -1) and get gaming!

typescript
const map = new TiledMapResource('path/to/map.tmx', { firstLayerZIndex: -2 });
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typescript
const map = new TiledMapResource('path/to/map.tmx', { firstLayerZIndex: -2 });
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Renderer performance improvements​

The performance gains were achieved through some core renderer refactors and identifying places where expensive calculations could be cached!

This is huge, we stay above 30fps in the 4000 actor benchmark, and we have dramatic improvement in average fps in both cases!

This benchmark was performed in Chrome on a Surface Book 2 with the power plugged in.

• Processor: Intel(R) Core(TM) i7-8650U CPU @ 1.90GHz, 2112 Mhz, 4 Core(s), 8 Logical Processor(s)
• Physical Memory: (RAM) 16.0 GB
• Graphics: NVIDIA GeForce GTX 1060

A number of improvements were made to the Excalibur graphics systems to get to this performance. The big factors to this improvement were:

1. Avoiding recalculation of graphics transforms and other expensive operations when they can be cached
2. Refactoring the renderer to be simpler and to use index buffers to share geometry vertices.
3. Rendering batches at the actual maximum for the batch renderer
4. Avoid recreating Matrix types, they are somewhat expensive to create then garbage collect

Post processing​

The postprocessor improvements allow custom WebGL shaders, which can produce some cool effects! (Minimally modified from this ShaderToy)

To produce the above effect, Excalibur has a new built in ScreenShader type for doing quick shaders meant for the whole screen.

typescript
class CrtPostProcessor implements ex.PostProcessor {
  private _shader: ex.ScreenShader;
  initialize(gl: WebGLRenderingContext): void {
    const crtEffectSource = document.getElementById("modified-crt-shader-source").innerText;
    this._shader = new ex.ScreenShader(crtEffectSource);
  }
  getLayout(): ex.VertexLayout {
    return this._shader.getLayout();
  }
  getShader(): ex.Shader {
    return this._shader.getShader();
  }
}
game.graphicsContext.addPostProcessor(new CrtPostProcessor());
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typescript
class CrtPostProcessor implements ex.PostProcessor {
  private _shader: ex.ScreenShader;
  initialize(gl: WebGLRenderingContext): void {
    const crtEffectSource = document.getElementById("modified-crt-shader-source").innerText;
    this._shader = new ex.ScreenShader(crtEffectSource);
  }
  getLayout(): ex.VertexLayout {
    return this._shader.getLayout();
  }
  getShader(): ex.Shader {
    return this._shader.getShader();
  }
}
game.graphicsContext.addPostProcessor(new CrtPostProcessor());
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Renderer improvements​

Renderer design​

When v0.25.0 was released, it was a "monolithic" renderer design, meaning everything Excalibur could possibly draw was built into a single renderer and shader program. This became onerous fairly quickly. And as the old adage goes: "you don't know how to build something until you've built it twice".

With v0.25.2, each type of drawing is split internally into separate renderer plugins. While this does come with some overhead when switching shader programs, it's worth it for the the simplicity, maintainability, and extensibility benefits.

Image filtering​

Excalibur now allows you the ability to control the WebGL image filtering mode both implicitly and explicitly. Really this means Excalibur will try to pick a smart default, but allows overrides

Explicitly when loading ex.ImageSource:

typescript
const myImage = new ex.ImageSource('path/to/image', false, ex.ImageFiltering.Pixel);
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typescript
const myImage = new ex.ImageSource('path/to/image', false, ex.ImageFiltering.Pixel);
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• ex.ImageFiltering.Blended - Blended is useful when you have high resolution artwork and would like it blended and smoothed

  

• ex.ImageFiltering.Pixel - Pixel is useful for pixel art when you do not want smoothing aka antialiasing applied to your graphics.

  

Implicitly if the ex.EngineOption antialiasing property is set:

• antialiasing: true, then the blend mode defaults to ex.ImageFiltering.Blended
• antialiasing: false, then the blend mode defaults to ex.ImageFiltering.Pixel

Custom renderer plugins​

Excalibur knows how to draw many types of graphics to the screen by default comes with those pre-installed into the ExcaliburGraphicsContext. However, you may have a unique requirement to provide custom WebGL commands into Excalibur, this can be done with a custom renderer plugin.

A custom renderer can be registered with Excalibur and draw in any draw routine! Read more in the docs about custom rendere plugins

typescript
const game = new ex.Engine({...});
export class MyCustomRenderer extends ex.RendererPlugin {
    public readonly type = 'myrenderer';
    ...
}
game.start().then(() => {
    // register
    game.graphicsContext.register(new MyCustomRenderer());
});
// call from a graphics callback or event
const actor = new ex.Actor({...});
actor.graphics.onPostDraw = (graphicsContext) => {
    graphicsContext.draw<MyCustomRenderer>('myrenderer', ...);
}
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typescript
const game = new ex.Engine({...});
export class MyCustomRenderer extends ex.RendererPlugin {
    public readonly type = 'myrenderer';
    ...
}
game.start().then(() => {
    // register
    game.graphicsContext.register(new MyCustomRenderer());
});
// call from a graphics callback or event
const actor = new ex.Actor({...});
actor.graphics.onPostDraw = (graphicsContext) => {
    graphicsContext.draw<MyCustomRenderer>('myrenderer', ...);
}
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Community​

We've had a lot of community engagement this iteration, especially through the issues and github discussions. Lots of good issues, and lots of cool things in the show and tell

Big thanks to everyone who helped with this release:

• @ivasilov
• @luttje
• @tsanyqudsi
• @lampewebdev
• @joshuadoan
• @berkayyildiz
• @simon-jaeger
• @YJDoc2
• @JumpLink

The future​

We are progressing at full speed toward the v1 vision, there is still a lot to do but the end is in sight. Here are a few things that I'm personally really excited for:

• Event system redo
• Particle system refactor
• Final deprecation of old drawing api
• New TileMap enhancements for hexagonal and isometric maps

This was a point release, but despite that a lot of exciting things were added! Looking forward to v0.26.0!

-Erik

After a year of work, a lot of great additions and improvements have made it into Excalibur, and we are making good progress towards our v1.0 release! Check the development roadmap for our current plans. It's hard to believe how different things are now since the first commit of Excalibur (back when it was called GameTS)!

Excalibur started as a tech demo in a presentation to show how powerful TypeScript can be. The engine has come so far since then, it's really amazing!

We are really excited to share this release with you! This release contains over 30 bug fixes and 50 new features! It's been a labor of love over the last year by many people, and we have some big features to share.

Check out the official release!

npm install [email protected]

Performance​

There is a combination of features (mentioned below) that resulted in big performance gains. Across the board, there's been a dramatic increase in what Excalibur can do in v0.25.0 vs v0.24.5.

In the gif below, we demonstrate the graphics performance specifically.

There is much better performance across the board with a higher baseline FPS in v0.25.0 for the same number of actors. You'll notice that FPS improves over time as more actors are offscreen in v0.25.0 compared to v0.24.5.

This benchmark was performed in the Chrome browser on a Surface Book 2 with the power plugged in.

• Processor: Intel(R) Core(TM) i7-8650U CPU @ 1.90GHz, 2112 Mhz, 4 Core(s), 8 Logical Processor(s)
• Physical Memory: (RAM) 16.0 GB
• Graphics: NVIDIA GeForce GTX 1060

New plugin versioning strategy​

We are adopting a similar versioning strategy to Angular, during pre-1.0. All plugins compatible with the core library will share the same prefix through the minor version. For example, if core Excalibur is [email protected], then the plugins that support that version are formatted like @excaliburjs/[email protected].

DisplayMode updates​

Excalibur DisplayModes have been refactored and renamed to clarify their utility.

• FillContainer - Fill the game viewport to take up as much of the immediate parent as possible
• FillScreen - Fill the game viewport to take up as much of the screen as possible
• FitContainer - Fit the game maintaining aspect ratio into the immediate parent
• FitScreen - Fit the game maintaining aspect ration into the screen
• Fixed - Specify a static size for the game width/height

Refactor to Entity Component System (ECS) based architecture​

The core plumbing of Excalibur has been refactored to use an ECS style architecture. However, developers using Excalibur do not need to know or care about the this underlying change to ECS if they don't want to.

What does ECS mean for Excalibur? At a high level, ECS architecture breaks down into three things:

• Components contain data needed for various systems.
• Systems implement the "behavior" by looping over entities that match a list of components.
  • For example, the graphics system processes all entities with a TransformComponent and a GraphicsComponent
• Entities are the "holders" of components

Actor, Scene, and Engine remain as the familiar interface to build games; they're only implemented differently under-the-hood. The reason for the change was to break down ever-growing and complex logic that had accumulated in the Actor and Scene implementations into Components and Systems for maintainability. This change increases the flexibility of Excalibur, and allows you to add new novel behavior directly into the core loop with custom components ones if you desire.

Excalibur does not have the purest implementation of an ECS by design; our built-in components are more than just data. The built-in components do provide behavior, convenience features, and helper functions to maintain our core mission of keeping Excalibur easy to use. The Excalibur core team goal with ECS is flexibility and maintainability, not performance. If you wish, you can read more about our goals for ECS.

Here's A quick example of using the new ECS features:

typescript
class SearchComponent extends ex.Component<'search'> {
    public readonly type = 'search'
    constructor(public target: ex.Vector) {
        super();
    }
}
class SearchSystem extends ex.System<ex.TransformComponent | SearchComponent> {
    // Types need to be listed as a const literal
    public readonly types = ['ex.transform', 'search'] as const;
    // Lower numbers mean higher priority
    // 99 is low priority
    public priority = 99;
    // Run this system in the "update" phase
    public systemType = ex.SystemType.Update
    private _searchSpeed = 10 // pixels/sec
    public update(entities: ex.Entity[], delta: number) {
        for (let entity of entities) {
            const target = entity.get(SearchComponent)!.target;
            // ex.TransformComponent is a built in type
            const transform = entity.get(ex.TransformComponent) as ex.TransformComponent;
            const direction = target.sub(transform.pos);
            const motion = direction.normalize().scale(this._searchSpeed);
            // Moves these entities towards the target at 10 pixels per second
            transform.pos = transform.pos.add(motion.scale(delta / 1000))
        }
    }
}
// Actors come with batteries included built in features
const actor = new ex.Actor({
    pos: ex.vec(100, 100),
    width: 30,
    height: 30,
    color: ex.Color.Red
});
actor.addComponent(new SearchComponent(ex.vec(400, 400)));
// Create a scene with your new system
const scene = new ex.Scene();
scene.world.add(new SearchSystem());
scene.add(actor);
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typescript
class SearchComponent extends ex.Component<'search'> {
    public readonly type = 'search'
    constructor(public target: ex.Vector) {
        super();
    }
}
class SearchSystem extends ex.System<ex.TransformComponent | SearchComponent> {
    // Types need to be listed as a const literal
    public readonly types = ['ex.transform', 'search'] as const;
    // Lower numbers mean higher priority
    // 99 is low priority
    public priority = 99;
    // Run this system in the "update" phase
    public systemType = ex.SystemType.Update
    private _searchSpeed = 10 // pixels/sec
    public update(entities: ex.Entity[], delta: number) {
        for (let entity of entities) {
            const target = entity.get(SearchComponent)!.target;
            // ex.TransformComponent is a built in type
            const transform = entity.get(ex.TransformComponent) as ex.TransformComponent;
            const direction = target.sub(transform.pos);
            const motion = direction.normalize().scale(this._searchSpeed);
            // Moves these entities towards the target at 10 pixels per second
            transform.pos = transform.pos.add(motion.scale(delta / 1000))
        }
    }
}
// Actors come with batteries included built in features
const actor = new ex.Actor({
    pos: ex.vec(100, 100),
    width: 30,
    height: 30,
    color: ex.Color.Red
});
actor.addComponent(new SearchComponent(ex.vec(400, 400)));
// Create a scene with your new system
const scene = new ex.Scene();
scene.world.add(new SearchSystem());
scene.add(actor);
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Collision system improvements​

The collision system has been significantly overhauled to improve the quality of the simulation and the stability of collisions. The core simulation loop "solver" has been redone to use an iterative impulse constraint solver, which provides a robust method of computing resolution that has improved performance and stability.

Collision intersection logic has now also been refactored to report multiple contact points at once. Multiple contacts improves the stability of stacks of colliders over single contact collisions (which can result in oscillations of boxes back and forth).

Colliding bodies can now optionally go to sleep. This relieves some of the pressure on the collision solver and improves the stability of the simulation by not moving these objects if they don't need to move. Colliders can be started asleep before a player in a game might interact with them

New CompositeColliders now make it possible to combine Excalibur Collider primitives (PolygonCollider, CircleCollider, and EdgeCollider) to make any arbitrary collision geometry. These new composite colliders power the new TileMap cell collisions and also power the new ex.Shape.Capsule(width, height) collider.

The Capsule collider is a useful geometry tool for making games with ramps or slightly jagged floors you want a character to glide over without getting stuck. This collider also helps with any "ghost collisions" that you might run into under certain conditions in your game.

CollisionGroups allow more granular control over what collides above and beyond collision type. Collsion groups allow you to create named groups of colliders like "player", "npc", or "enemy". With these groups, you can specify that players and enemies collide, player and npcs don't collide, and that npcs and enemies don't collide without needing to implement that logic in a collision event handler.

typescript
// Create a group for each distinct category of "collidable" in your game
const playerGroup = ex.CollisionGroupManager.create('player');
const npcGroup = ex.CollisionGroupManager.create('npcGroup');
const floorGroup = ex.CollisionGroupManager.create('floorGroup');
const enemyGroup = ex.CollisionGroupManager.create('enemyGroup');
// Define your rules
const playersCanCollideWith = ex.CollisionGroup.collidesWith([
  playersGroup, // collide with other players
  floorGroup, // collide with the floor
  enemyGroup // collide with enemies
]);
const player = new ex.Actor({
  collisionGroup: playersCanCollideWith
});
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typescript
// Create a group for each distinct category of "collidable" in your game
const playerGroup = ex.CollisionGroupManager.create('player');
const npcGroup = ex.CollisionGroupManager.create('npcGroup');
const floorGroup = ex.CollisionGroupManager.create('floorGroup');
const enemyGroup = ex.CollisionGroupManager.create('enemyGroup');
// Define your rules
const playersCanCollideWith = ex.CollisionGroup.collidesWith([
  playersGroup, // collide with other players
  floorGroup, // collide with the floor
  enemyGroup // collide with enemies
]);
const player = new ex.Actor({
  collisionGroup: playersCanCollideWith
});
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New graphics system​

The new Excalibur graphics system has been rebuilt from the ground up with speed in mind. It is now built on a WebGL foundation with a built-in batch renderer. This means that Excalibur will batch up draw commands and submit the minimum amount of draw calls to the machine when the screen is updated. This dramatically improves the draw performance and also the number of things wec can display on screen (as noted in the benchmarks earlier).

For drawing hooks the ExcaliburGraphicsContext is replacing the browser CanvasRenderingContext2D. If you still need to do some custom drawing using the CanvasRenderingContext2D the new Canvas graphic can help you out.

typescript
const canvas = new ex.Canvas({
  cache: true, // If true draw once until flagged dirty again, otherwise draw every time
  draw: (ctx: CanvasRenderingContext2D) => {
    ctx.fillStyle = 'red';
    ctx.fillRect(0, 0, 200, 200);
  }
});
actor.graphics.use(canvas);
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typescript
const canvas = new ex.Canvas({
  cache: true, // If true draw once until flagged dirty again, otherwise draw every time
  draw: (ctx: CanvasRenderingContext2D) => {
    ctx.fillStyle = 'red';
    ctx.fillRect(0, 0, 200, 200);
  }
});
actor.graphics.use(canvas);
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TileMap and Tiled updates​

Tiled is easily one of the best tools out there for building and designing levels for your game. It has certainly been a valuable tool in our toolbox. We have doubled down on our efforts to provide a first class Tiled integration with Excalibur via the excaliburjs/plugin-tiled. This work also involved a few improvements to the TileMap to improve it's graphics API and collision performance.

Check out the Tiled Excalibur Plugin!

• Full support for the Tiled object model
• Full support for all Tiled file types
• Excalibur built ins
• Not yet supported
  • Tiled Group Layers
  • Custom Tile colliders
  • Isometric/Hexagonal maps
  • Parallax

Documentation​

A lot of time was spent reviewing and improving our documentation. Part of this work was ensuring that the snippets don't go stale over time by building them in GitHub Actions.

Please check out the new and shiny doc site with new code examples at excaliburjs.com!

Testing​

The Excalibur core repo now has WallabyJS enabled to improve the VS Code test development and debugging experience. Wallaby is a paid tool; because of that Excalibur will always also support the Karma based testing framework for official tests.

A useful update to excalibur-jasmine allows async matchers, which greatly simplifies checking image diffs in Jasmine unit tests.

typescript
it('should match images', async () => {
  let engine = new ex.Engine({width: 100, height: 100});
  await expectAsync(engine.canvas).toEqualImage('images/expectedcanvas.png', .99);
});
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typescript
it('should match images', async () => {
  let engine = new ex.Engine({width: 100, height: 100});
  await expectAsync(engine.canvas).toEqualImage('images/expectedcanvas.png', .99);
});
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A brand new integration test utility has been created called @excaliburjs/testing, which provides a quick way to drive Excalibur games with Puppeteer and do image-based snapshot testing.

typescript
// excalibur testing
test('An integration test', async (page) => {
    // Check for the excalibur loaded page
    await expectLoaded();
    // Compare game to expected an expected image
    await expectPage('Can check a page', './images/actual-page.png').toBe('./images/expected-page.png');
    // Use puppeteer page object to interact
    await page.evaluate(() => {
        var actor = ((window as any).actor);
        actor.pos.x = 400;
        actor.pos.y = 400;
    });
    // Compare game to a new expected image
    await expectPage('Can move an actor and check', './images/actual-page-2.png').toBe('./images/expected-page-2.png');
});
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typescript
// excalibur testing
test('An integration test', async (page) => {
    // Check for the excalibur loaded page
    await expectLoaded();
    // Compare game to expected an expected image
    await expectPage('Can check a page', './images/actual-page.png').toBe('./images/expected-page.png');
    // Use puppeteer page object to interact
    await page.evaluate(() => {
        var actor = ((window as any).actor);
        actor.pos.x = 400;
        actor.pos.y = 400;
    });
    // Compare game to a new expected image
    await expectPage('Can move an actor and check', './images/actual-page-2.png').toBe('./images/expected-page-2.png');
});
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Templates​

There are a lot of different ways to build web apps; we've created repo templates for some of the popular ones:

• Webpack v5
• Parcel v2
• Parcel v1
• Rollup

Samples​

• Brick Breaker
• Platformer
• Shoot'em Up

Community​

We've had tons of community contributions since the last release. Heartfelt thanks to everyone in the discussions, issues and pull requests!

Contributors:

• @jedeen
• @kamranayub
• @alanag13
• @DaVince
• @DrSensor
• @djcsdy
• @catrielmuller
• @AndrewCraswell
• @miqh
• @rledford
• @SirPedr
• @helloausrine
• @dpayne5
• @herobank110
• @didii
• @Charkui
• @muirch
• @rumansaleem
• @mogoh
• @kala2
• @MrBartusek
• @josh-greenlaw
• @LokiMidgard
• @romaintailhurat
• @EduardoHidalgo
• @jaredegan

Breaking changes​

There are some breaking changes in v0.25.0 from v0.24.5; see the changelog and release notes for more specifics, but they generally fall into the categories below. See the migration guide for guidance.

• New APIs replacements
  • Graphics API
  • Actor drawing functions moved to graphics component
• API renames for clarity
• Bug fixed necessitated change
• Extracted behavior to a plugin
  • Perlin noise is now offered as a plugin and is no longer included in the core library @excaliburjs/plugin-perlin
• Big plugin changes
  • The Tiled plugin is now published under @excaliburjs/plugin-tiled and will start with version v0.25.0

Looking towards "version 1"​

• Pointer events plumbing refactor; the current system is hard to follow and debug/enhance
• Particle system refactor
• Graphics enhancements to support advanced postprocessing/shaders
• ExcaliburGraphicsContext enhancements to grant more flexibility
• Event system redo
• Better Scene management and granular asset loading
• Expand and enhance TileMap
• Progressive WebAssembly enhancements in the physics simulation
• Potential new plugins on the horizon
  • Browser Debugger Utility
  • Aseprite
  • Pyxel Edit
• AI patterns and plugins like A* search
• API finalization

I want to thank everyone who helped make this version of Excalibur possible. A lot of effort went into it and I'm really proud of what we achieved.

- Erik