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Proceed to Safety

Gray-Scott Model at F 0.0420, k 0.0670    

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0420, k=0.0670.

All patterns become inert solitons (an oval soliton can be seen regularizing itself near the left edge). 2 or 3 initial pulsations are seen before they diminish below the visible limit of ±3×10-6. Close pairs drift apart very slowly; drift speed diminishes exponentially with distance.

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

                increase F   









      
decrease k
      
after 222 tu
after 1,110 tu

15 frames/sec.; each fr. is 74 iter. steps = 37 tu; 1800 fr. total (66,600 tu)









      
increase k
      
after 4,070 tu after 16,650 tu after 66,600 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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