Gray-Scott Model at F 0.0100, k 0.0410  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0100, k=0.0410.

Most starting patterns produce one or more smooth radial waves, these then usually annihilate cleanly when they contact each other. However, as seen here (at 3 seconds into the movie) a second generation of waves can be created by the first annihilation.

Sustained spirals are also viable. Here, we inject a pair of partial wavefronts (at 20 seconds into the movie). These create two pairs of spiral seeds, which make a long-lasting spiral phenomenon resembling the classic Petri dish B-Z (Belousov-Zhabotinsky) reaction.

By about 1 minute 10 seconds into the movie, the two pairs of spiral seeds have merged into one pair of double-spiral seeds, which form a mirror-image pair due to the initial seed pattern of two parallel wavefronts. The wavefronts seen here are smoother than those to the immediate west.

Categories: Munafo ξ; Wolfram 3    (glossary of terms)

             increase F









      
decrease k
      
after 66 tu
after 330 tu

15 frames/sec.; each fr. is 22 iter. steps = 11 tu; 1801 fr. total (19,811 tu)









      
increase k
      
after 1,210 tu after 4,950 tu after 19,800 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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