Gray-Scott Model at F 0.0380, k 0.0610  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0380, k=0.0610.

Rings quickly bend and link into serpentine branching structure. System evolves towards straighter lines and 120o angles while keeping the mix of branches, bends and isolated short worms, and even an occasional lone soliton.

Stability occurs after 500,000 tu or longer.

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

             increase F

decrease k
after 192 tu
after 960 tu

15 frames/sec.; each fr. is 64 iter. steps = 32 tu; 1800 fr. total (57,600 tu)

increase k
after 3,520 tu after 14,400 tu after 57,600 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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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11