Gray-Scott Model at F 0.0900, 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=0.0900, k=0.0590.

Starting patterns of blue spots produce solitons and worms; the worms grow. Starting patterns of red spots, as seen here, become a network of blue lines enclosing red "bubbles", which gradually coalesce like soap bubbles. Individual bubbles occasionally contain one-ended worms, which disappear if their bubble shrinks too much. Rarely, bubbles will contain solitons; these survive even if their bubble is shrunk, resulting in a small cystlike bubble, seen here starting at 0:45. (Compare this to what happens to the north).

In the pattern shown here, 7 bubbles remain after 1,000,000 tu; after an additional 1,800,000 tu there is a single hexagonal bubble and the "cyst" containing the soliton. (old video ID: XJFY53ppwNs)    (glossary of terms)

               increase F  









      
decrease k
      
after 1,395 tu
after 6,975 tu

15 frames/sec.; each fr. is 465 iter. steps = 232.5 tu; 3601 fr. total (837,232 tu)









      
increase k
      
after 25,575 tu after 104,625 tu after 418,500 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 Model Index


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This page was last updated on 2014 Nov 27. s.11