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.

=================

This [mathworld.wolfram.com/Polyomino.html] may be of help.

– DavidC

Jan 8 ’13 at 3:40

@dude Thanks, yeah, I read the MathWorld article, but it doesn’t have any suggestions for implementations. Given, you know, N.K.S., I’m suspicious that there should be a way to do what I’m asking in four or less lines of Mathematica.

– Roger Harris

Jan 8 ’13 at 3:46

3

Possible duplicate: mathematica.stackexchange.com/q/6822/5

– R. M.♦

Jan 8 ’13 at 4:00

=================

1 Answer

1

=================

Take a look at the following articles:

Tiling Rectangles with Polyominoes by JAIME RANGEL-MONDRAGÃ“N

Polyominoes and Related Families by JAIME RANGEL-MONDRAGÃ“N

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

Also related:

Demonstrations

MathWorld