Gray-Scott Model at F 0.0340, k 0.0630  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0340, k=0.0630.

Rings and solitons are both viable in isolation — rings grow normally, solitons grow by mitosis. When the two encounter each other, the rings are broken up into worms, which then are slowly broken down into solitons. Pattern becomes stable (hexagonal grid) within 100,000 to 150,000 tu.

Categories: Pearson η; Wolfram 3    (glossary of terms)

             increase F









      
decrease k
      
after 165 tu
after 825 tu

15 frames/sec.; each fr. is 55 iter. steps = 27.5 tu; 1800 fr. total (49,500 tu)









      
increase k
      
after 3,025 tu after 12,375 tu after 49,500 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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