Gray-Scott Model at F 0.0460, k 0.0610  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0460, k=0.0610.

Loops grow with smooth outer edges and complicated centers, and merge into a field of negative worms of all lengths, some with branches. Over the course of 300,000 tu or longer, the worms lengthen by joining, but negative solitons (small loops) also survive.    (glossary of terms)

               increase F  









      
decrease k
      
after 258 tu
after 1,290 tu

15 frames/sec.; each fr. is 86 iter. steps = 43 tu; 1800 fr. total (77,400 tu)









      
increase k
      
after 4,730 tu after 19,350 tu after 77,400 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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