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.

  • $\begingroup$ This [mathworld.wolfram.com/Polyomino.html] may be of help. $\endgroup$ – DavidC Jan 8 '13 at 3:40
  • $\begingroup$ @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. $\endgroup$ – Roger Harris Jan 8 '13 at 3:46
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    $\begingroup$ Possible duplicate: mathematica.stackexchange.com/q/6822/5 $\endgroup$ – rm -rf Jan 8 '13 at 4:00

Take a look at the following articles:

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

enter image description here

Also related:

| improve this answer | |
  • $\begingroup$ The two Mathematica Journal articles are no longer available through the links. I was able to get the notebook files by contacting the editor at editor@mathematica-journal.com. $\endgroup$ – Michael Wijaya Jul 21 at 1:20

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