Gray-Scott Model at F 0.0300, k 0.0530  

These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0300, k=0.0530.

All initial patterns fill the field with blue within 250 tu; irregularities slowly smooth out but the entire field continues to oscillate indefinitely.

In my simulations a new void spontaneously appears every 95,000 tu; after three cycles the field became blank red. This may reflect the actual dynamics of this parameter value or may be an artifact of roundoff error.

Categories: Pearson B; Wolfram 1    (glossary of terms)

                









      
decrease k
      
after 141 tu
after 705 tu

15 frames/sec.; each fr. is 47 iter. steps = 23.5 tu; 1800 fr. total (42,300 tu)









      
increase k
      
after 2,585 tu after 10,575 tu after 42,300 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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