Wow!_A 2-chemical reaction-diffusion_

Tim Hutton - 2014-06-11 07:58:45+0000 - Updated: 2014-06-11 23:47:51+0000

Wow!

"A 2-chemical reaction-diffusion system inspired by the Mandelbrot set.

For chemicals a and b, the relation is
Δa = C_a * (a * a - b * b) + ∇·∇b
Δb = C_b * (2 * a * b) - ∇·∇a
where C_a and C_b are constants and ∇·∇ is the Laplace operator.

Created using Ready https://code.google.com/p/reaction-diffusion "

Edit: Now available as a Ready file: https://reaction-diffusion.googlecode.com/svn/trunk/Ready/Patterns/Experiments/MandelbrotWorms_CornusAmmonis.vti (10kB)

Originally shared by Cornus Ammonis

A 2-chemical reaction-diffusion system inspired by the Mandelbrot set. For chemicals a and b, the relation is Δa = C_a * (a * a - b * b) + ∇·∇b Δb = C_b * (2 * a * b) - ∇·∇a where C_a and C_b are constants and ∇·∇ is the Laplace operator. Created using Ready https://code.google.com/p/reaction-diffusion/

Shared with: Public, Robin Houston, Cornus Ammonis

+1'd by: Elżbieta Zadora-Zuzelska, Torolf Sauermann, Robin Houston, simon gladman, 林則余, Hiroki Sayama, Doug Hackworth, Štěpán Roučka

Reshared by: Dave Gordon, Hiroki Sayama

Robin Houston - 2014-06-13 23:14:07+0000

Interesting. I tried to implement it http://bl.ocks.org/robinhouston/6cfcbff910216ee3abf8 and there seems to be something funny going on. The action takes place on a chequered background, which I suppose suggests that the discrete system is not really approximating a continuous one.

But maybe that’s not what’s going on in Cornus’s Ready implementation. I can’t easily tell.

Robin Houston - 2014-06-13 23:56:23+0000

Here’s a close-up view: http://bl.ocks.org/robinhouston/647eae82dd8d6d9ae71b

Cornus Ammonis - 2014-06-14 00:38:00+0000

+Robin Houston It's easier to see what's going on if you look at the phase diagram of the system in Ready. The system is pretty sensitive to initial conditions, using the default initialization pattern in Ready will send it into a different domain than you see in my video. I also clamp the values of the reagents, that turns out to be crucial to getting the 'worm' pattern. In the process of cleaning up my VTI file I also noticed that the noise source I was using was colored more than I thought it was, because of clamping, and that was influencing the pattern significantly. I have since come up with a variant of this RD system that reliably goes into the 'worm' pattern without needing a noise source, I'll post that soon. The checkered background effect occurs in my Ready implementation as well.

If you hadn't already noticed, I have now posted the Ready VTI file in the video's description. 

Robin Houston - 2014-06-14 00:50:37+0000 - Updated: 2014-06-14 01:03:18+0000

+Cornus Ammonis Interesting. Thanks for the clarification. Yes, I’ve played with your VTI file briefly.

I look forward to your variant. My version uses the same clamping as yours, but no random noise. (Other differences that don’t seem to make any difference to the result include using RK4 rather than Euler and a five- rather than nine-point stencil for the Laplacian.) But I don’t think the patterns I’m seeing are the same as your “worms”. Mine settles into a time-periodic solution eventually.

This post was originally on Google+