Gray-Scott Model at F 0.0420, k 0.0610  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0420, k=0.0610.

Rings grow into clovers, develop more convolutions and join each other, forming a field of negative worms of all lengths, some with branching. Negative worms then link up, forming after 50,000 tu a hedgerow maze appearance, but with occasional small negative loops enclosing negatons.

The isolated loop (Benzene-ring like structure in upper left) survives unchanged for 150,000 tu, then grows a tail but remains as an island for another 200,000 tu. Meanwhile other negative solitons come and go, and similar "island loop with tail" structures arise elsewhere.

During this time the field is slowly arranging into parallel lines, with 120o angles. Pattern is still evolving after 600,000 tu.    (glossary of terms)

             increase F









      
decrease k
      
after 222 tu
after 1,110 tu

15 frames/sec.; each fr. is 74 iter. steps = 37 tu; 1800 fr. total (66,600 tu)









      
increase k
      
after 4,070 tu after 16,650 tu after 66,600 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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