Gray-Scott Model at F 0.0980, k 0.0570  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0980, k=0.0570.

The blue state is stable, but any red state grows to overpower it. Here, red spots grow into "bubbles". Smaller bubbles shrink and vertices gradually coalesce, maintaining angles as close to 120o as possible. (Compare to the phenomenon seen immediately to the west). This pattern takes over 2,300,000 tu to turn into a single hexagonal bubble.

Categories: Munafo ρ; Wolfram 2-a    (glossary of terms)

             increase F









      
decrease k
      
after 1,893 tu
after 9,465 tu

15 frames/sec.; each fr. is 631 iter. steps = 315.5 tu; 1801 fr. total (568,215 tu)









      
increase k
      
after 34,705 tu after 141,975 tu after 567,900 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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