Skin patterns are the first example of the existence of Turing patterns in living organisms. Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the principles of pattern formation at the molecular and cellular levels. Surprisingly, although the networks of cell- …
@jab01701mid In an email conversation, I told someone that tiling theory might be of limited use in a context like this, where you're trying to simulate morphogenesis or other natural processes. As a mathematical subject, tiling theory really pays dividends when there are significant regularity properties or other kinds of repetition, and that's often to constraining for real-world situations.
In the intersection with Turing patterns, raw symmetry may suffice for visual interest, and tilings might be overkill. See especially Jonathan McCabe's symmetric, multi-scale Turing patterns: http://www.jonathanmccabe.com/Cyclic_Symmetric_Multi-Scale_Turing_Patterns.pdf (also: https://rreusser.github.io/multiscale-turing-pattern-gallery/). Gorgeous stuff.
Craig S. Kaplan
John Breen