Proceed to Safety

Gray-Scott Model at F 0.0060, k 0.0410    

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0060, k=0.0410.

Proto-spiral seeds, and wavefronts that are smooth at first (as seen in the first 20 seconds) but quickly become irregular and fragmented. Spirals never get to be very big, new seeds are created from the breaks in the wavefronts, and opposite pairs of spiral seeds annihilate.

This pattern kept going for 1,140,000 tu, with the spiral centers continually moving and changing in quantity, then abruptly ended. Other patterns last as little as 10,000 tu, and a few produce a single linear wavefront like that seen here.      (glossary of terms)

                increase F   

decrease k
after 57 tu
after 285 tu

15 frames/sec.; each fr. is 19 iter. steps = 9.5 tu; 1801 fr. total (17,109 tu)

increase k
after 1,045 tu after 4,275 tu after 17,100 tu
(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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