Gray-Scott Model



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*}

These equations can now be implemented into a spatial cellular automata. This system can easily be solved numerically.



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