Gray-Scott Model at F 0.0260, 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=0.0260, k=0.0670.

With these parameter values, all viable solitons are "pulsars" that oscillate a fixed number of times before reaching the visible limit of ±3×10-6. The period of oscillation is about 185 tu, and the number of oscillations for these values of F and k is about 50.

The eastern limit for solitons at F=0.0260 is about k=0.0678.

The southern limit for solitons at k=0.0670 is about F=0.0251.

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

             increase F









      
decrease k
      
after 120 tu
after 600 tu

15 frames/sec.; each fr. is 40 iter. steps = 20 tu; 1800 fr. total (36,000 tu)









      

      
after 2,200 tu after 9,000 tu after 36,000 tu
                
(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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