Is there an easy way to specify an arbitrary two-dimensional Polyomino tiling in Mathematica 8.0?

Question

Is there an easy way to generate an arbitrary two-dimensional Polyomino tiling: http://en.wikipedia.org/wiki/Polyomino?

Specifically, I would like to generate an array of integer coordinates, for example: {{0,1},{10,11},{15,6},...}, and then output a graphic showing a tiling pattern where a tile is centered at each integer coordinate in my array, and where each tile is labeled with its integer coordinate.

Is there a way for me to do this in three-dimensions?

I have access to Wolfram Mathematica 8.0.

Answer 1

Take a look at the following articles:

• Tiling Rectangles with Polyominoes by JAIME RANGEL-MONDRAGÓN
• Polyominoes and Related Families by JAIME RANGEL-MONDRAGÓN

Here is an example of a custom function usage from 1st article producing a tiling:

Also related:

• Demonstrations
• MathWorld