Gray-Scott Model at F 0.0180, k 0.0530  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0180, k=0.0530.

Spots and rings grow, initially with smooth outer edges, then bending into clovers. When two fronts collide they annihilate and fade; the fading pattern then usually spawns a new growing spots. These new spots are of two types, simple spots (generally small) and "C" shapes that move while growing and generate more spots in their wake.    (glossary of terms)

             increase F









      
decrease k
      
after 90 tu
after 450 tu

15 frames/sec.; each fr. is 30 iter. steps = 15 tu; 1800 fr. total (27,000 tu)









      
increase k
      
after 1,650 tu after 6,750 tu after 27,000 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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