Gray-Scott Model at F 0.0420, k 0.0590
These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0420, k=0.0590.
Rings grow, remaining circular with new, non-growing concentric loops forming inside; these then merge to form a field of negative solitons and short worms after 2500 to 3500 tu. The negative solitons slowly replace most of the worms, which survive only along grain boundaries as a transitional state between single and double soliton. Stability sometimes takes over 500,000 tu.
15 frames/sec.; each fr. is 74 iter. steps = 37 tu; 1800 fr. total (66,600 tu)
In these images:
- Color indicates level of u, ranging from purple (lowest u values) through blue, aqua, green, yellow and pink/red (highest u values)
- Areas where u is increasing are lightened to a light pastel tone; where u is decreasing the color is vivid.
- In areas where u is changing by less than ±3×10-6 per tu, an intermediate pastel color is seen. This includes areas that are in steady state or equilibrium.
''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
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11