Proceed to Safety

Gray-Scott Model at F 0.1100, k 0.0530    

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.1100, k=0.0530.

Red spots on blue grow into "bubbles" whose boundaries have surface tension. Smaller bubbles (which tend to have a smaller number of edges) shrink while larger bubbles (with a greater number of edges) grow, until a hexagonal pattern is reached. A similar phenomenon is seen in negative to the west.

Surface tension is notably less here than to the immediate east, and the bubbles coalesce more slowly.

Categories: Munafo ρ; Wolfram 2-a      (glossary of terms)


decrease k
after 3,003 tu
after 15,015 tu

15 frames/sec.; each fr. is 1001 iter. steps = 500.5 tu; 1801 fr. total (901,400 tu)

increase k
after 55,055 tu after 225,225 tu after 900,900 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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