Gray-Scott Model at F 0.1020, 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=0.1020, k=0.0550.

On a red background, blue spots form solitons or worms that grow to fill the space.

On a blue background (as seen here), red spots below a critical size shrink and vanish, while spots above that minimum size grow into a network of lines with the occasional worm. Cells coalesce like soap bubbles and the pattern evolves towards a network of hexagons, except for the occasional defect caused by a cell containing a worm. As seen here (1:05-1:32) cells containing worms can get squeezed out. Sometimes a few negatons can survive longer by clumping (compare top-right at 1:15-1:28 to bottom-center at 1:40-2:10). This pattern evolves for about another 5,000,000 tu.

(old video: fm9TqketQqw was encoded poorly.)

Categories: Munafo ρ; Wolfram 2-a    (glossary of terms)

             increase F









      

      
after 2,208 tu
after 11,040 tu

15 frames/sec.; each fr. is 736 iter. steps = 368 tu; 3601 fr. total (1,325,168 tu)









      
increase k
      
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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