Gray-Scott Model at F 0.0540, k 0.0610  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0540, k=0.0610.

Rings grow with smooth edges and complex centers, and merge into a field of interlinked loops enclosing negative solitons and short to medium negative worms. Pattern evoloves over 100,000 tu or longer, favoring a hexagonal lattice alignment.    (glossary of terms)

             increase F









      
decrease k
      
after 351 tu
after 1,755 tu

15 frames/sec.; each fr. is 117 iter. steps = 58.5 tu; 1800 fr. total (105,300 tu)









      
increase k
      
after 6,435 tu after 26,325 tu after 105,300 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