Gray-Scott Model at F 0.0260, 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=0.0260, k=0.0510.

Field quickly fills with blue but remains active. Distribution of irregularities in initial pattern recurs 960 tu later, then voids appear in any places that did not originally have voids. System alternates between a fairly uniform blue makeup and red/yellow/blue chaos, with a period of 1400 tu, through 2 or 3 cycles. After that, different areas of the field fall out of sync with each other. The occurance of voids continues without a global periodicity.

Categories: Pearson β; Wolfram 3    (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)









      
increase k
      
after 2,200 tu after 9,000 tu after 36,000 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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