Gray-Scott Model at F 0.0140, k 0.0410  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0140, k=0.0410.

Spots grow with smooth outer edges and feathered inside edges, mostly annihilating when they meet each other. However, a few sharp-edged decay products spawn new wavefronts. For about the next 2500 tu the pattern resembles the classic petri dish Belousov-Zhabotinsky reaction. Gradually the defects (proto-spiral seeds) increase in number, so that by the 10,000 tu there are many small irregular wavefronts. Protospirals remain stationary until disrupted by the arrival of another wave.

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

             increase F









      
decrease k
      
after 78 tu
after 390 tu

15 frames/sec.; each fr. is 26 iter. steps = 13 tu; 1800 fr. total (23,400 tu)









      
increase k
      
after 1,430 tu after 5,850 tu after 23,400 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