Proceed to Safety

Gray-Scott Model at F 0.0540, k 0.0630    

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0540, k=0.0630.

Loops and worms grow to fill the space; solitons are also viable if constrained (seen just above center for a brief time at the beginning). Loops and worms join each other, and the latter prevail over time; the pattern evolves towards long, straight parallel worms with occasional branching.

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

                increase F   

decrease k
after 351 tu
after 1,755 tu

15 frames/sec.; each fr. is 117 iter. steps = 58.5 tu; 1800 fr. total (105,300 tu)

increase k
after 6,435 tu after 26,325 tu after 105,300 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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