Gray-Scott Model at F 0.1100, k 0.0523  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.1100, k=0.0523.

Blue spots on a red background grow to fill the space; larger spots have a bit of an advantage. After the space is filled, larger blue spots force the smaller spots to shrink, and edges remain straight whenever possible; negative lines exhibit surface tension. A similar phenomenon is seen in negative to the east.

Patterns evolve with homotopy: all spots remain as solitons, clumping at the grain boundaries between the large spots and arranging into a hexagonal close packing.

There are six large regions at the end of the movie. After another 1,300,000 tu the region to the lower-right has been reduced to a soliton, precipitating more rapid reduction of two neighboring regions. After that, evolution continues at a much slower rate.

Categories: Munafo σ; Wolfram 2-a    (glossary of terms)

                









      

      
after 3,003 tu
after 15,015 tu

15 frames/sec.; each fr. is 1001 iter. steps = 500.5 tu; 1801 fr. total (901,400 tu)









      
increase k
      
after 55,055 tu after 225,225 tu after 900,900 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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