Chemical Basis of Morphogenesis

Art | Parabolic | Patterns

This is the first page of Alan Turing’s The Chemical Basis of Morphogenesis paper undergoing pattern formation. The kinetics are exactly from the Schnakenberg example:

$$\begin{array}{rl}\frac{\partial u}{\partial t}& ={\mathrm{\nabla }}^{2}u+a-u+u^{2}v,\\ \frac{\partial v}{\partial t}& =D{\mathrm{\nabla }}^{2}v+b-u^{2}v,\end{array}$$

but we have taken an initial condition from an image of the first page of Turing’s text.

• Load the interactive simulation.

• Press to see this evolve! You can pause the simulation and press to reset the text.

• Modifying different parameters (particularly $b$) can lead to qualitatively different solutions. Try $b=0.6$ for example. Try decreasing $b$ very slowly with the slider to see the pattern change.

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