Inspired by the new substitution rules that Shigeki Akiyama and Yoshiaki Araki propose (along with a new proof of aperiodicity!), here are some drawings from the last few days. These aren’t quite the same as
The trilobite and cross tiles clearly generalize to higher dimensions. Though a simpler method soon appeared”Threelobites” were a first early graphic / mathematical exploration. Here’s a nice pic of a tiling by the trilobite and
Through a local self-assembly rule these tiles are forced to form arbitrarily large patches of Robinson tilings, with some extra markings that are used to manage the process. In the animation, at each green dot,
I was curious about the actual algorithm for geometrizing an orbifold — it’s only lightly sketched at in Thurston’s Three Dimensional Topology and Geometry. Hence the app. The details are now inside some javascript: Check
Doodlebug joins us on a tour of topological surfaces, with drawings and paper and scissor exercises. Another project to complete! Videos of the physical exercises will appear sometime — they do not seem to be