Gray-Scott Model at F 0.0060, k 0.0330  

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=0.0330.

Double-spirals with smooth edges. Note that pairs of spirals tend to move towards each other, and annihilate when they meet, so that by 0:30 in the movie there is only one pair left (in the upper-right). That pair also moves together, and disappears just a little while after the end of this movie.

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


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