This is a simulation of a reaction–diffusion system loosely related to $\lambda$-$\omega$ models of spiral waves, which takes the form:

\[\begin{aligned}\pd{u}{t}&=D_u\nabla^2 u+au-(u+cv)(u^2+v^2),\\ \pd{v}{t}&=D_v\nabla^2v+av+(cu-v)(u^2+v^2),\end{aligned}\]

  • Load the interactive simulation. This plots the solution as the quantity $u^2+v^2$, which evolves from a wave-like initial condition into broken waves which coalesce into spiral waves as the seemingly most stable structures.

  • Clicking can perturb these waves, and clicking with dragging can induce new spiral centres (or destroy old ones).

  • You can also generate your own waves by setting the initial conditions to zero under   → Initial conditions, and then clicking to generate radial pulses, or dragging to perturb them.