Gray-Scott Model at F 0.1060, k 0.0570  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.1060, k=0.0570.

Solitons that drift apart at an exponentially diminishing rate (for example, note a couple pairs in the lower-left). In the lower-right a single "loop" shrinks to a soliton very quickly.

Categories: Munafo ν; Wolfram 2    (glossary of terms)

                









      
decrease k
      
after 2,574 tu
after 12,870 tu

15 frames/sec.; each fr. is 858 iter. steps = 429 tu; 1801 fr. total (772,629 tu)









      

      
after 47,190 tu after 193,050 tu after 772,200 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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