Proceed to Safety

Gray-Scott Model at F 0.0780, 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=0.0780, k=0.0610.

Loops and worms with occasional branches grow to fill the space, then loops are squeezed down into worms. Pattern evolves towards straight, parallel lines.

The eastern limit for worms at F=0.0780 is around k=0.0625, beyond which they shrink to solitons.

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

                increase F   

decrease k
after 879 tu
after 4,395 tu

15 frames/sec.; each fr. is 293 iter. steps = 146.5 tu; 1800 fr. total (263,700 tu)

increase k
after 16,115 tu after 65,925 tu after 263,700 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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