Gray-Scott Model at F 0.0140, k 0.0450  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0140, k=0.0450.

Initial patterns of spots grow with smooth continuous wave fronts that completely annihilate each other. After this happened, I manually injected proto-spiral patterns (at 0:04 in the movie) to show that wavefronts with free ends result in a long-term sustained pattern. Gradually the wavefronts become more irregular, and by 12,500 tu (halfway through the movie) these irregularities are able to spawn new protospiral seeds. Double-spiral seeds also occur rarely; one is seen below-right of center near the end of the movie.

For 350,000 tu or more, the pattern continues as seen here, resembling the classic Petri dish B-Z (Belousov-Zhabotinsky) reaction photos.

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

               increase F  









      
decrease k
      
after 78 tu
after 390 tu

15 frames/sec.; each fr. is 26 iter. steps = 13 tu; 1800 fr. total (23,400 tu)









      
increase k
      
after 1,430 tu after 5,850 tu after 23,400 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 Model Index


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This page was last updated on 2014 Nov 27. s.11