Coding Example: Reaction-Diffusion

Problem Description

Reaction and diffusion of chemical species can produce a variety of patterns, reminiscent of those often seen in nature. The Gray-Scott equations model such a reaction. For more information on this chemical system see the article Complex Patterns in a Simple System (John E. Pearson, Science, Volume 261, 1993).

Let’s consider two chemical species U and V with respective concentrations u and vand diffusion rates Du and Dv.

V is converted into P with a rate of conversion k. f represents the rate of the process that feeds U and drains U, V and P. This can be written as:

Chemical reaction	Equations
$U + 2V \rightarrow 3V$	$\dot{u}=Du{\mathrm{\nabla }}^{2}u-u{v}^2+f($

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