Gray-Scott Model at F 0.0900, k 0.0570  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0900, k=0.0570.

Blue spots on a red background quickly grow into a network of connected negative loops or "soap-bubbles"; loops then coalesce as smaller blue regions shrink and larger regions grow. This system is still evolving with two closed loops after 1,000,000 tu.

Categories: Munafo σ; Wolfram 2-a    (glossary of terms)

             increase F









      

      
after 1,395 tu
after 6,975 tu

15 frames/sec.; each fr. is 465 iter. steps = 232.5 tu; 1801 fr. total (418,732 tu)









      
increase k
      
after 25,575 tu after 104,625 tu after 418,500 tu
                
(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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