Gray-Scott Model at F 0.0420, k 0.0630
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=0.0630.
Loops in isolation grow into clovers; when contacting each other they stay separate. All sharp bends break, resulting in a field of worms of all lengths and a few solitons. Field slowly organizes to make worms straighter and orient along 60o, 90o and 120o angles.
Worms gradually lengthen over the next 500,000 tu or longer, with some worms shrinking into solitons. System keeps evolving for 900,000 tu or longer.
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 2019 Jan 05. s.11