Gray-Scott Model at F 0.0380, k 0.0630  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0380, k=0.0630.

These parameters support mitosis (as seen in the lower-left area) and symmetrical rings (center) as well as worms and even loops that stay whole while being crowded out (upper-left).

(As explained in the glossary, I would call most of them "rings" because they break up under pressure from other parts of the pattern, but the one in upper-left could arguably be called a "loop" since it seems to survive quite a while without breaking).

After the space is filled, worms tend to align in parallel rows, coexisting with clumps of solitons. Worms shorten to increase alignment but also join end to end. This continues for over 500,000 tu.    (glossary of terms)

             increase F









      
decrease k
      
after 192 tu
after 960 tu

15 frames/sec.; each fr. is 64 iter. steps = 32 tu; 1800 fr. total (57,600 tu)









      
increase k
      
after 3,520 tu after 14,400 tu after 57,600 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


Robert Munafo's home pages on HostMDS   © 1996-2017 Robert P. Munafo.
aboutcontact    mrob    mrob27    @mrob_27    mrob27
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Details here.

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11