Spherical Design Competition

Last year at the Wolfram Technology Conference in Illinois the participants were invited to join a friendly coding competition. The challenge this time was to write a program that would make an Egg-Bot would print (in less than 15 minutes) the most interesting design possible, thus giving attendees a chance to exercise their graphics skills. I always liked the patterns that differencing polygons would create. With a single line of code I was able to explore this space of intricate motifs, (a sample of which is shown below on the left). After mapping a few of these into spherical coordinates you get the following 2nd place entry on the right.

Manipulate[ Graphics[Polygon[Table[r^n {-Sin[n*a], Cos[n*a]}, {n, 0, L}]], PlotRange -> P], {P, 1, 0}, {{r, .98}, 1, .95}, {{a, 2.6}, 0, 2 Pi}, {{L, 300}, 1, 1000, 1}]