Gray-Scott Model at F 0.0100, k 0.0350  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0100, k=0.0350.

Most starting patterns produce small blue spots and blobs on a red background, which grow with smooth outer edges and slowly decaying trailing edges, mostly annihilating each other as they fill the space. However, as seen here, a few second and third generation waves will arise, and some of these develop into spiral seeds which lead the transformation to a field of spirals similar to those in the B-Z (Belousov-Zhabotinsky) reaction. This pattern continued to produce spirals for at least 27,000,000 tu.

Categories: Munafo ξ; Wolfram 3    (glossary of terms)

                









      
decrease k
      
after 66 tu
after 330 tu

15 frames/sec.; each fr. is 22 iter. steps = 11 tu; 1801 fr. total (19,811 tu)









      
increase k
      
after 1,210 tu after 4,950 tu after 19,800 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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