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.

  • 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.