Computing with a distributed reaction-diffusion model

Reaction-diffusion models are commonly used to describe dynamical processes in complex physical, chemical and biological systems. Applications of these models range from pattern formation or epidemic spreads to natural selection through ecological systems and percolation systems. Reaction refers to phenomena where two or more entities become in contact and modify their state as a consequence of this fact. Diffusion implies the existence of a space where the involved entities are situated and can move. The Reaction-Diffusion Machine is a computational model we previously introduced inspired by reaction diffusion phenomena. In this work, we prove that a Deterministic Turing Machine can be simulated by a Reaction-Diffusion Machine.