Proceed to Safety

Gray-Scott Model at F 0.0380, k 0.0590    

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=0.0590.

All initial shapes become loops that grow with smooth outer edges and standing waves of concentric rings and negative solitons on the interior.

Even when starting with complete symmetry as shown here, slight irregularities (invisible at first) ensure the pattern will eventually become asymmetrical. Some of this can be seen here if you look closely; after another 125,000 tu the central loop has lost its symmetry too.

Clumps of negative solitons and parallel sets of negative worms co-exist, but the latter prevail in the long run. The pattern continues evolving for well over 500,000 tu.      (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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