Gray-Scott Model at F 0.0700, 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=0.0700, k=0.0610.

Negative worms (right, bottom-right) and more elaborate shapes like the "double negative worms" (upper-right) and negative loops (or normal worm surrounded by red space) grow to fill the space. Negatons in isolation are stable and inert (just to left of center). After the space is filled, the worm tips prevail, causing sharp bends to become longer and more convoluted, and simpler loops to get squeezed out. This process continues for 400,000 tu or longer.    (glossary of terms)

             increase F









      

      
after 648 tu
after 3,240 tu

15 frames/sec.; each fr. is 216 iter. steps = 108 tu; 1800 fr. total (194,400 tu)









      
increase k
      
after 11,880 tu after 48,600 tu after 194,400 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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