Proceed to Safety

Gray-Scott Model at F 0.0100, k 0.0450    

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=0.0450.

These parameters support continuous spiral patterns, similar to those in the B-Z (Belousov-Zhabotinsky) reaction. Wavefronts develop many irregularities, helping to create new spiral seeds and preventing any one spiral from getting much bigger than the examples seen here. (Compare to the smoother wavefronts, and larger spirals, seen to the immediate west.)

This pattern continued with the same appearance seen here for over 420,000 tu, then quickly changed to a single wave front traveling to the right.

This simulation was performed with the same starting pattern as that to the immediate west; note the initial similarity, and substantial differences after about the first 500 tu.

Categories: Pearson β; Wolfram 3      (glossary of terms)

                increase F   

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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