Spiral waves
Art  Chaos  Parabolic  Waves
This is a simulation of a reaction–diffusion system loosely related to $\lambda$$\omega$ models of spiral waves, which takes the form:
\[\begin{aligned}\pd{u}{t}&=D_u\nabla^2 u+au(u+cv)(u^2+v^2),\\ \pd{v}{t}&=D_v\nabla^2v+av+(cuv)(u^2+v^2),\end{aligned}\]
Load the interactive simulation. This plots the solution as the quantity $u^2+v^2$, which evolves from a wavelike 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.