Gray-Scott Model at F 0.0700, 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=0.0700, k=0.0630.

Worms grow to fill the space; loops change to worms with relatively little pressure; solitons also turn to worms but can remain stable if confined. Branching structures are also viable (lower right). At 0:45 in the movie we see a worm (just above center) get squeezed back into a soliton. Pattern develops towards parallel lines and 60o angles.

The eastern limit for worms at F=0.0700 is around k=0.0644, beyond which they shrink to solitons.

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

             increase F









      
decrease k
      
after 648 tu
after 3,240 tu

15 frames/sec.; each fr. is 216 iter. steps = 108 tu; 1800 fr. total (194,400 tu)









      
increase k
      
after 11,880 tu after 48,600 tu after 194,400 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


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