Gray-Scott Model at F 0.0420, 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=0.0420, k=0.0630.

Loops in isolation grow into clovers; when contacting each other they stay separate. All sharp bends break, resulting in a field of worms of all lengths and a few solitons. Field slowly organizes to make worms straighter and orient along 60o, 90o and 120o angles.

Worms gradually lengthen over the next 500,000 tu or longer, with some worms shrinking into solitons. System keeps evolving for 900,000 tu or longer.

Categories: Pearson κ; Wolfram 2-a    (glossary of terms)

             increase F









      
decrease k
      
after 222 tu
after 1,110 tu

15 frames/sec.; each fr. is 74 iter. steps = 37 tu; 1800 fr. total (66,600 tu)









      
increase k
      
after 4,070 tu after 16,650 tu after 66,600 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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