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Striped and Spotted Pattern Generation on Reaction-diffusion Cellular Automata – Theory and LSI Implementation
Youhei Suzuki, Takahiro Takayama, Ikuko N. Motoike and Tetsuya Asai

A novel reaction-diffusion cellular-automaton model that generates Turing-like spatial patterns is proposed. The model employs linear diffusion fields of activators and inhibitors and a discrete transition rule after diffusion. Theoretical analysis of the one dimensional model proved that i) spatial distribution given by a periodic square function is stable at the equilibrium and ii) the spatial frequency is inversely proportional to the square root of a diffusion coefficient of the inhibitors. We also designed LSI circuits that implement the RD model on a silicon chip that has a compact construction and low-power consumption. Circuit simulations revealed that the proposed LSIs could restore stripe and spot images in a short time regardless of the number of pixels in the image.

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