Breaking the Tiles
Four years ago, when I came back from Memphis, I started meeting every other tuesday for lunch and after with mathematician Javier Bracho a.k.a. Roli, to talk about symmetry and art, and help him translate part of his talk about tilings into a script for a television capsule.
Some of those times we would just fool around with shapes to see what we could come up with, por example, using tiles that don’t fit to see what patterns we could find. Without knowing much about tilings back then, I happily rediscovered Kepler’s pentagonal tiling one day, and came back excited to the tuesday meeting with a giant hand made drawing of a massive portion of it. Roli told me about the history of this tiling, about Kelper and the archimedean tilings, and then we spend a few expressos looking for a set of rules that would procedurally generate kepler’s pentagonal non-periodic tiling. We wanted to write a set of instructions that the dumbest person, or even a machine, could follow to tile an arbitrary region of the plane this way. By the end of the evening we still didn’t know how to tell a machine how to make that tiling for us. I was astonished because I had no problem making the tiling myself based on observation and intuition, but I couldn’t figure out the rules that determined my decisions.
Then I took the Adventures in Advanced Symbolic Programming class this spring, and for the final project I considered revisiting the tiling problem. What if a program could be wrote that could figure out good enough rules (when possible) by looking at a given shape, kind of like I do when I make a tiling? Of course I am not In a position to write such a program (yet), but with the help of my super smart fellow classmates Kyle and Justin, maybe we could get something done. And we did.
Our system is a work in progress. Much still has to be done to it. For detailed information on its implementation and some background on tilings you can visit our project website here. You can also download the Scheme source code there.
