Gray-Scott Model at F 0.0180, k 0.0450
These images and movie demonstrate the behavior of the Gray-Scott reaction-diffusion system with σ=Du/Dv=2 and parameters F=0.0180, k=0.0450.
Any initial pattern quickly fills the space with blue (low u) state. Oscillations persist indefinitely, with wavelengths on a somewhat larger size scale than the spots seen in neighboring areas with higher k or F values. There are also occasional appearances of a patch of red that quickly fill in again with blue. (glossary of terms)
15 frames/sec.; each fr. is 30 iter. steps = 15 tu; 1800 fr. total (27,000 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 2015 Nov 07. s.27