Gray-Scott Model at F 0.0180, k 0.0450  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0180, k=0.0450.

Any initial pattern quickly fills the space with blue (low u) state. Oscillations persist indefinitely, with wavelengths on a somewhat larger size scale than the spots seen in neighboring areas with higher k or F values. There are also occasional appearances of a patch of red that quickly fill in again with blue.    (glossary of terms)

             increase F









      
decrease k
      
after 90 tu
after 450 tu

15 frames/sec.; each fr. is 30 iter. steps = 15 tu; 1800 fr. total (27,000 tu)









      
increase k
      
after 1,650 tu after 6,750 tu after 27,000 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   © 1996-2016 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