Gray-Scott Model at F 0.0460, 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=0.0460, k=0.0650.

Solitons in isolation multiply into 4 solitons (or sometimes 3, not seen here) which then become worms unless crowded out. Loops can also grow intact if undisturbed (bottom-left and bottom-center). The result is generally a field of worms and solitons.

Sharp bends break and solitons can turn into worms if they have the space but otherwise, the demographics persist, with the final count of worms and solitons depending highly on the nature of the starting pattern. The 4-way bend at left slowly turns into two 3-way bends like the one on the right. Stability takes another 375,000 tu or more.

Although mitosis does not last long at these parameter values, it is the most common form of growth just a bit to the east. The eastern limit for mitosis at F=0.0460 is near k=0.0660.

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

             increase F









      
decrease k
      
after 258 tu
after 1,290 tu

15 frames/sec.; each fr. is 86 iter. steps = 43 tu; 1800 fr. total (77,400 tu)









      
increase k
      
after 4,730 tu after 19,350 tu after 77,400 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 pattern index


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