Polyps is a reaction-diffusion system that repeatedly grows polyp-like structures, which fan out, and shrink away at a later time. The equations are quite simple, and represent a type of reaction between chemicals, one inside and one outside the body of the polyp.
Average Things: what does the average polygon look like? or the average repeating signal? It may not be what you think.
Here is a visual summary.
Smooth gems: Polyhedrons with infinite numbers of faces make nice looking gem stones