Proceed to Safety

Gray-Scott Model at F 0.0660, k 0.0610    

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0660, k=0.0610.

Loops and worms grow into negative space which also contains negative solitons. Negative solitons appear spontaneously in ideal conditions (e.g. near left side at 0:39 in the movie). Pattern evolves towards straight edges, 120o angles and negative solitons in hexagonal grid arrangement.      (glossary of terms)

                increase F   


after 555 tu
after 2,775 tu

15 frames/sec.; each fr. is 185 iter. steps = 92.5 tu; 1800 fr. total (166,500 tu)

increase k
after 10,175 tu after 41,625 tu after 166,500 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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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2015 Nov 07. s.27