Gray-Scott Model at F 0.0500, k 0.0650  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0500, k=0.0650.

After some initial cell division (two-way, as seen in center, or 3-way as seen to the right of center) all forms become worms that grow to fill the space, remaining separate and intact except when acutely bent (as in lower-right near end of movie). Solitons are also viable and will remain circular if constrained to a small space from the start, and small loops can grow for a time. Pattern evolves towards straight, parallel lines and 120o angles.

Categories: Pearson μ; Wolfram 2-a    (glossary of terms)

             increase F









      
decrease k
      
after 300 tu
after 1,500 tu

15 frames/sec.; each fr. is 100 iter. steps = 50 tu; 1800 fr. total (90,000 tu)









      
increase k
      
after 5,500 tu after 22,500 tu after 90,000 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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