Gray-Scott Model at F 0.0220, k 0.0510  

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=0.0510.

Spots grow with smooth outer edges, then after colliding proto-spirals appear briefly inside. The system then passes through a phase resembling the area directly to the west, but a pattern of recognizable negative stripes and spots emerges by about the 2500 tu. Oscillation continues indefinitely, and small areas periodically revert to the red state briefly. When this happens a small region of the stripes/spots pattern is rebuilt; through such events the pattern evolves towards many straight parallel stripes at 60o and 120o angles.

Categories: Pearson γ; Wolfram 3    (glossary of terms)

             increase F









      
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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