Proceed to Safety

Gray-Scott Model at F 0.0860, 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=0.0860, k=0.0590.

From initial field of negative solitons, evolves into long loops, with serpentine maze patterns which ultimately prevail. Pattern evolution is generally a homotopy for periods in excess of 5,000,000 tu — if the pattern begins with (normal positive) solitons, the result is all worms with a few branches and no closed loops.    (glossary of terms)

             increase F


after 1,197 tu
after 5,985 tu

15 frames/sec.; each fr. is 399 iter. steps = 199.5 tu; 1800 fr. total (359,100 tu)

increase k
after 21,945 tu after 89,775 tu after 359,100 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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