Wang tiles!

This is a simple implementation of the wang tiling algorithm presented in Tilings and Patterns by Grunbaum and Shephard, and discussed in Aperiodic Texture Mapping by Jos Stam.

The algorithm generates an aperiodic tiling of the following 16 tiles:

The tiles use 6 colors, shown here as red, yellow, cyan, purple, green and grey.

The tiles aren't uniformly distributed in the resulting image. This is their frequency distribution:

And the colors aren't evenly distributed either. Here's their frequency distribution:

Usage

The wang(width, height, [seed]) function returns a Uint8Array of width x height tile indexes. The returned array starts with the first row, then the next row, and so on. Each tile index is an integer from 0-15, corresponding to a tile in the diagram above.

// If you're using node...
var wang = require('wang').wang

// Generate 2 rows of 5 wang tiles
var width = 5;
var height = 3;
var arr = wang(width, height); // width, height

// Print out the tile indexes
for(var y = 0; y < height; y++) {
  for(var x = 0; x < width; x++) {
    console.log("At "+x+","+y + ": ", arr[x + y * width]);
  }
}

Here's the output:

$ node test.js
At 0,0:  11
At 1,0:  3
At 2,0:  1
At 3,0:  9
At 4,0:  3
At 0,1:  0
At 1,1:  14
At 2,1:  13
At 3,1:  0
At 4,1:  12
At 0,2:  9
At 1,2:  5
At 2,2:  2
At 3,2:  8
At 4,2:  1

Or, as a picture:

Tile color list

If you need it, here's a list of the colors on each tile. Each tile is described in left-top-right-bottom order.

c = {r:0, y:1, b:2, g:3, p:4, w:5}
# A list of the colors of each tile, left, top, right, bottom.
colors = [
  [c.r, c.y, c.y, c.r] # 0
  [c.g, c.b, c.b, c.g] # 1
  [c.b, c.p, c.p, c.b] # 2
  [c.w, c.g, c.g, c.w] # 3

  [c.b, c.p, c.b, c.g] # 4
  [c.w, c.g, c.b, c.g] # 5
  [c.g, c.b, c.p, c.b] # 6
  [c.g, c.b, c.g, c.w] # 7

  [c.p, c.r, c.g, c.y] # 8
  [c.b, c.r, c.w, c.y] # 9
  [c.p, c.r, c.b, c.r] # 10
  [c.g, c.y, c.w, c.y] # 11

  [c.y, c.w, c.r, c.b] # 12
  [c.y, c.g, c.r, c.p] # 13
  [c.y, c.w, c.y, c.g] # 14
  [c.r, c.b, c.r, c.p] # 15
]

License

Licensed under the BSD license.

Copyright (c) 2013, Joseph Gentle All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.