Gray-Scott Model at F 0.0820, 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=0.0820, k=0.0610.

Solitons with worms and an occasional branching structure. Worm tips grow to fill the space.

The eastern limit for worms at F=0.0820 is around k=0.0614, beyond which they shrink to solitons.    (glossary of terms)

             increase F









      
decrease k
      
after 1,026 tu
after 5,130 tu

15 frames/sec.; each fr. is 342 iter. steps = 171 tu; 1800 fr. total (307,800 tu)









      
increase k
      
after 18,810 tu after 76,950 tu after 307,800 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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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11