Gray-Scott Model at F 0.0220, k 0.0470  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0220, k=0.0470.

Space quickly fills with blue, but large-amplitude oscillations continue for 10,000 tu or more. A sudden appearance of high u, low v (red state) is typical, as seen here at around 0:18 (4750 tu into the simulation). That event can occur as late as 10,000 tu after the start. After one such event the amplitude seems to diminish enough to preclude a recurrence.    (glossary of terms)

                









      
decrease k
      
after 105 tu
after 525 tu

15 frames/sec.; each fr. is 35 iter. steps = 17.5 tu; 1800 fr. total (31,500 tu)









      
increase k
      
after 1,925 tu after 7,875 tu after 31,500 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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