Gray-Scott Model at F 0.0060, k 0.0350  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0060, k=0.0350.

Fairly smooth wavefronts (note occasional irregularities) and long-lasting spiral seeds. Pairs of spirals move towards each other and annihilate when they meet.

At 0:42, after the last spiral pair has vanished, a wavefront is artificially removed, leaving just a single wavefront travelling to the right. From about 0:50 to 1:20 the values of u and v are plotted in white and black, respectively, with the full height representing the range from 0.00 to 1.00. This wave front continues to move to the right indefinitely (tested for 1,000,000 tu). The irregularities in the wavefront retain the appearance seen here, with the individual "bumps" endlessly changing in number, relative size, and position.

At smaller k values (and the same F) the wavefront becomes considerably smoother, becoming almost a straight line just before reaching the edge of the homogeneous blue state region. At higher k values the wavefront becomes more irregular, but remains stable up to about k=0.0419.

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

             increase F









      
decrease k
      
after 57 tu
after 285 tu

15 frames/sec.; each fr. is 19 iter. steps = 9.5 tu; 1801 fr. total (17,109 tu)









      
increase k
      
after 1,045 tu after 4,275 tu after 17,100 tu
                
(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   © 1996-2016 Robert P. Munafo.aboutcontact    mrob    mrob27    @mrob_27
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 2016 May 15. s.11