Gray-Scott Model at F 0.0580, k 0.0630  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0580, k=0.0630.

Sufficiently symmetrical blue spots grow into regular loops that meander into clovers; less symmetrical spots become corals. Both types fill the space initially with loops and bends; once the space is full, worm tips prevail over bends. The system eventually attains maze or fingerprint appearance after 250,000 tu.

At F=0.0580, loops grow when k is about 0.0649 or less; above this k value (further east) they shrink to solitons.

Categories: Pearson κ; Wolfram 2-a    (glossary of terms)

             increase F









      
decrease k
      
after 408 tu
after 2,040 tu

15 frames/sec.; each fr. is 136 iter. steps = 68 tu; 1800 fr. total (122,400 tu)









      
increase k
      
after 7,480 tu after 30,600 tu after 122,400 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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