I've played with coupled reaction diffusion systems a few times in the past (Gray Scott and Ginzburg-Landau/Fitzhugh Nagumo), but the technique I've used is to simply swap over the values of chemical species from one equation into another.
After reading Klaus Kyttä's Computational Studies of Pattern Formation in Multiple Layer Turing Systems, I thought I'd experiment with a new approach: cubic coupling.
Cubic coupling adds a new term into a reaction diffusion equation. For example, the term for the u species in a binary coupling, where q is a coupling coefficient would be:
q ui uj (uj - ui)
However, because I'm coupling three equations, I'm using:
The results have been really interesting. With Ginzburg-Landau, I've got some Turing-McCabe style multi-scale effects and with Fitzhugh-Nagumo some nice tip splitting and labyrinthine effects. There were a series of surprise explosions in the Purwins experiment.
On the downside, because I'm using three or six chemical species, I haven't been able to easily create shaders in AGAL to use in ReDiLab. These equations run in ActionScript workers which, although pretty nippy, don't compare to running on the GPU. Some of the videos here are an hour's worth of computation compressed down to a minute of footage in After Effects.
This application is available here.
This application is available here.
q ui uj (uk - ui)
The results have been really interesting. With Ginzburg-Landau, I've got some Turing-McCabe style multi-scale effects and with Fitzhugh-Nagumo some nice tip splitting and labyrinthine effects. There were a series of surprise explosions in the Purwins experiment.
On the downside, because I'm using three or six chemical species, I haven't been able to easily create shaders in AGAL to use in ReDiLab. These equations run in ActionScript workers which, although pretty nippy, don't compare to running on the GPU. Some of the videos here are an hour's worth of computation compressed down to a minute of footage in After Effects.
Fitzhugh-Nagumo
This application is available here.
Ginzburg-Landau
This application is available here.
Purwins Group Three Component Reaction Diffusion
This application is available here.
A big nod to Tim Hutton and the team at Ready where I get a lot of inspiration and links to helpful papers.