Gray-Scott Model at F 0.1060, k 0.0550  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.1060, k=0.0550.

Red spots on a blue background form a network of "bubbles" that coalesce, favoring the bubbles with six or more sides. Solitons trapped inside a shrinking bubble are snuffed out (see 0:12 and 0:35). This pattern evolves into a single hexagonal cell after an additional 500,000 tu.

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

             increase F









      
decrease k
      
after 2,574 tu
after 12,870 tu

15 frames/sec.; each fr. is 858 iter. steps = 429 tu; 1801 fr. total (772,629 tu)









      
increase k
      
after 47,190 tu after 193,050 tu after 772,200 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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