Gray-Scott Model at F 0.1020, 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=0.1020, k=0.0570.

Blue spots on a red background form solitons and worms that quickly shrink to solitons.

Red spots on blue (as seen here) form "bubbles" (a network of connected lines); bubbles with fewer than six sides tend to shrink, ceding their space to neighboring bubbles with six or more sides. Solitons trapped inside a shrinking bubble vanish when their bubble gets too small (1:00-1:10).

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

             increase F









      
decrease k
      
after 2,208 tu
after 11,040 tu

15 frames/sec.; each fr. is 736 iter. steps = 368 tu; 2201 fr. total (809,968 tu)









      
increase k
      
after 40,480 tu after 165,600 tu after 662,400 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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