Gray-Scott Model at F 0.0060, k 0.0390  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0060, k=0.0390.

Fairly smooth wavefronts, long-lasting spiral seeds. Close pairs of spiral seeds tend to annihilate, however, irregularities in the wavefronts sometimes cause new seeds to form (this can be seen several times throughout the movie). In large enough domains, the new seeds tend to outnumber those that annihilate, allowing a pattern to remain viable indefinitely.

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

             increase F









      
decrease k
      
after 57 tu
after 285 tu

15 frames/sec.; each fr. is 19 iter. steps = 9.5 tu; 1801 fr. total (17,109 tu)









      
increase k
      
after 1,045 tu after 4,275 tu after 17,100 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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