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Proceed to Safety

Gray-Scott Model at F 0.0300, k 0.0690    

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0300, k=0.0690.

At these parameter values, all viable starting patterns become "pulsars" that oscillate about 35 times (with period of about 182 tu) before reaching the visible limit of ±3×10-6.

The southern limit for solitons at k=0.0690 is about F=0.0274.

Categories: Munafo ν; Wolfram 2      (glossary of terms)

                increase F   









      
decrease k
      
after 141 tu
after 705 tu

15 frames/sec.; each fr. is 47 iter. steps = 23.5 tu; 1800 fr. total (42,300 tu)









      
increase k
      
after 2,585 tu after 10,575 tu after 42,300 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


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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2015 Nov 07. s.27