Gray-Scott Model at F 0.0700, k 0.0650  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0700, k=0.0650.

Solitons are the only viable form. At the beginning you can see a few worms that quickly shrink to a soliton. Solitons drift apart from each other very slowly; drift speed diminishes exponentially with distance.

Categories: Munafo ν; Wolfram 2    (glossary of terms)

             increase F









      
decrease k
      
after 648 tu
after 3,240 tu

15 frames/sec.; each fr. is 216 iter. steps = 108 tu; 1800 fr. total (194,400 tu)









      
increase k
      
after 11,880 tu after 48,600 tu after 194,400 tu
             decrease F
(Click on any image to magnify)

In these images:

Wavefronts and other moving objects have decreasing u values (brighter color) on the leading edge of the blue part of the moving object, and increasing u (light pastel color) on the trailing edge. This is true even for very slow-moving objects — thus, you can tell from the coloring what direction things are moving in.

''tu'' is the dimensionless unit of time, and ''lu'' the dimensionless unit of length, implicit in the equations that define the reaction-diffusion model. The grids for these simulations use Δx=1/143 lu and Δt=1/2 tu; the system is 3.2 lu wide. The simulation meets itself at the edges (periodic boundary condition); all images tile seamlessly if used as wallpaper.

Go back to Gray-Scott pattern index


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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11