Jon Willcutt
CWRU Undergraduate Student Mathematics and Computer Science

Triangles
What could have possibly made these complicated, triangular patterns? There is a misconception that patterns can only be as interesting as the rules that govern them- either it takes genuine randomness or an obtuse set of mathematical equations to form complexity. The above cellular automata are a simple and visually striking counter example. Each of the six designs are the product of a unique, two-colored pattern, built up by stacking the previous row with the pattern applied to it. All patterns are fundamentally the same- look at each cell and its two nearest neighbors and see whether that ordering of input colors should be colored or not for the next iteration. Each pattern starts with one colored cell in the middle and is allowed to evolve under slightly different rules. The outputs are shockingly, beautifully, and perhaps mystically, different. In just six out of a nearly unlimited number of patterns, simple rules create tremendous diversity of outputs. Interesting phenomenon can happen with enough interacting parts. Flocks of birds or schools of fish aren’t trying to form pulsating blobs as they fly or swim, but they form regardless. Simple mechanics can make something complicated and awe-inspiring. Maybe even art.