Gray-Scott Model at F 0.0100, k 0.0390  

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=0.0390.

Most starting patterns produce one or more smooth radial waves, these then usually annihilate cleanly when they contact each other, as seen here.

However, sustained spirals are also viable. Here, we inject a partial wavefront (at 20 seconds into the movie) which creates a long-lasting phenomenon resembling the classic Petri dish B-Z (Belousov-Zhabotinsky) reaction. The waves here are noticably less smooth than those to the immediate west.

Categories: Munafo ξ; 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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