Mollusc Shell Pigmentation: Cellular Automaton Simulations and Evidence for Undecidability

We present a cellular automaton (CA) to simulate the reaction-diffusion processes which determine the pigmentation of natural mollusc shells. We obtained self-organization into stationary (Turing) structures, travelling waves and the four classes formed in Wolframʹs automata. In particular, very complex “undecidable” structures (Wolframʹs class IV) obtained at the transition between periodicity (class II) and chaos (class III). Agreement between the calculations and natural shells suggests evidence for class IV behaviour in the natural process.