Gray-Scott Model

Introduction

The Gray-Scott model is a rather simple reaction, but can create very interesting patterns and visualisatins, reminiscent of those seen in nature. By using the reaction equations

(1) $\begin{gather*}\ce{A + 2 B ->[f] 3 V}\\\ce{V ->[k] P}\end{gather*}$

the rate equations can be constructed and used as such. For this, concentration of species $P$ was set to zero.

(2) $\begin{gather*}\dfrac{\delta a}{\delta t}= -ab^2 + f * (1-a)+D_a \nabla^2 a\\\dfrac{\delta b}{\delta t}= ab^2 - b * (k+f)+D_b \nabla^2 b\end{gather*}$