Proceed to Safety

Gray-Scott Model at F 0.0820, k 0.0590    

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0820, k=0.0590.

From an initial pattern of red with blue spots, the spots grow to fill the space, then any acute outer boundaries become worm tips that grow to fill the space. Worm tips sometimes merge into walls (look to the right of center at 0:05 to 0:15 in the movie).

Negative worm tips shrink (a few examples of this can be seen starting at about 1:10).

Although some joining of features is possible, pattern evolution is generally homotopic. If a negative initial pattern is used (blue with spots of red), it usually produces negatons (true negative solitons) and negative worms, which shrink to negatons. Negatons themselves are viable only in clumps; any sole negatons die off about 7,500 tu after formation.

Categories: Pearson θ; Wolfram 2-a      (glossary of terms)

                increase F   


after 1,026 tu
after 5,130 tu

15 frames/sec.; each fr. is 342 iter. steps = 171 tu; 1800 fr. total (307,800 tu)

increase k
after 18,810 tu after 76,950 tu after 307,800 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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