Gray-Scott Model at F 0.0940, 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=0.0940, k=0.0570.

Small blue spots in a red field will grow (either as worms or blobs) to fill the space; narrow parts of blobs zipper down the length of the blob to make it entirely linear (possibly with branching); the result is a field of parallel stripes.

Red spots on blue (as seen here) grow in a more complex way. The isolated circular red spots seen near the right side during the first 20 seconds are stable: smaller red spots grow, and larger ones shrink. However, when two spots come into contact, the blue line between them is stronger than open blue space, and makes the spots lengthen parallel to it. Worm tips are stronger still. After 4,000,000 tu this pattern is mostly a labyrinth of lines, with some branching and a few surviving bubble-clumps of red spots.    (glossary of terms)

             increase F









      

      
after 1,626 tu
after 8,130 tu

15 frames/sec.; each fr. is 542 iter. steps = 271 tu; 1801 fr. total (488,071 tu)









      
increase k
      
after 29,810 tu after 121,950 tu after 487,800 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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