Gray-Scott Model at F 0.0660, k 0.0630  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0660, k=0.0630.

Loops, worms, and occasional branching structures grow to fill the space; features remain autonomous but loops are eventually squeezed into worms. Pattern evolves towards straight parallel lines.

At F=0.0660, loops grow when k is about 0.0638 or less; above this k value (further east) they shrink to solitons.

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

             increase F









      
decrease k
      
after 555 tu
after 2,775 tu

15 frames/sec.; each fr. is 185 iter. steps = 92.5 tu; 1800 fr. total (166,500 tu)









      
increase k
      
after 10,175 tu after 41,625 tu after 166,500 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 pattern index


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