Gray-Scott Model at F 0.0980, k 0.0550  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0980, k=0.0550.

Any starting pattern will quickly fill the field with blue; blue spots remain separate for a while creating a pattern of linked neagtive loops; these then gradually coalesce as smaller loops shrink and boundaries occasionally break down. This is an almost exact negative of the phenomenon seen immediately to the east, although faster. At the end we see a single curved line; this becomes almost completely straight after about 1,000,000 tu.    (glossary of terms)

               increase F  









      

      
after 1,893 tu
after 9,465 tu

15 frames/sec.; each fr. is 631 iter. steps = 315.5 tu; 1801 fr. total (568,215 tu)









      
increase k
      
after 34,705 tu after 141,975 tu after 567,900 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 Model Index


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