Gray-Scott Model at F 0.1020, k 0.0590  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.1020, k=0.0590.

Solitons that drift apart at a speed that decreases exponentially with distance (for example, note a pair towards the lower-right that can be seen drifting during the first 10 seconds of the video; drag the slider to see these and a few others noticably moving)

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

                









      
decrease k
      
after 2,208 tu
after 11,040 tu

15 frames/sec.; each fr. is 736 iter. steps = 368 tu; 1801 fr. total (662,768 tu)









      

      
after 40,480 tu after 165,600 tu after 662,400 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


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