Some slides at RIMS meeting on December:
Current favorate: Quasiperiodic self-inducing (self-similar) structures. Here are some nice pictures:
First: Minimal Pisot number tiling, Second: sofic Pisot Tiling
You find different ones in Japanese side. This research has close connection with ergodic theory, symbolic dynamics and Diophantine approximation.
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Shigeki Akiyama