Art of PDEs
Chemical Basis of Morphogenesis
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:
\[\begin{aligned}\pd{u}{t}&=\nabla^2 u+a-u+u^2v,\\ \pd{v}{t}&=D\nabla^2v+ b-u^2v,\end{aligned}\]but we have taken an initial condition from an image of the first page of Turing’s text.
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Load the interactive simulation.
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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.