Gray-Scott Model at F 0.0220, 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=0.0220, k=0.0550.

Spots grow with smooth outer edges; when colliding form a mixture of stripes and spots. Oscillation continues indefinitely, with regions dying out at random, and spots growing and splitting in a somewhat disorganized manner, and a continued occasional occurance of stripes.    (glossary of terms)

             increase F









      
decrease k
      
after 105 tu
after 525 tu

15 frames/sec.; each fr. is 35 iter. steps = 17.5 tu; 1800 fr. total (31,500 tu)









      
increase k
      
after 1,925 tu after 7,875 tu after 31,500 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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