Gray-Scott Model at F 0.0940, 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=0.0940, k=0.0590.

Initial patterns of blue spots on red produce solitons; any worms quickly shrink to solitons. Red spots on blue, as seen here, quickly grow into a matrix of bubbles, that coalesce into larger bubbles as the smallest ones tend to shrink. As seen here, isolated solitons can exist as islands inside the bubbles. If a soliton's bubble shrinks, the soliton is snuffed out (seen at 0:32; note this is unlike what happens to the south). This pattern takes 815,000 tu to evolve into a single large hexagonal bubble; after about another 500,000 tu the edges are almost stationary, straight and with 120o angles.

(old videos: HU8NMvU21r4 was encoded poorly; fmhy0Qhy2oQ takes 500,000 tu to evolve into two large hexagonal bubbles, each containing one soliton.)

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

             increase F









      
decrease k
      
after 1,626 tu
after 8,130 tu

15 frames/sec.; each fr. is 542 iter. steps = 271 tu; 1801 fr. total (488,071 tu)









      
increase k
      
after 29,810 tu after 121,950 tu after 487,800 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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