Gray-Scott model

Governing equations

Rolls and spots

A nice demo for the sensitivity of the parameters F and kappa is given by Prof. Trefethen (click here).

The first parameter set generates a beautiful pattern with "rolls". The parameters for this solution are

• F = 0.04
• kappa = 0.06

By slightly perturbing F a completely different solution is found, this time a "spot" pattern is observed. The parameters for this simulation are

• F = 0.025
• kappa = 0.06

To reproduce these images, run the command

./run_simulation.py --demo

Running the code

The Gray-Scott model is implemented in python/gray_scott.py. A simulation wrapper around the GrayScott class is implemented in python/run_simulation.py. A simulation can be started with

./run_simulation.py

which integrates the system until time T=3500 using the default parameter F=0.04 and k=0.06 (kappa). Output is generated every 100 integration steps. A list of all options can be obtained with

./run_simulation.py --help

Running a simulation for parameter F=0.02 and k=0.06 is achieved by

./run_simulation.py -F 0.02 -k 0.06 --outdir sim_F0.02_k0.06

where in addition the output is written to a directory sim_F0.02_k0.06 in the current folder. If the --outdir option is omitted then output is written into the current directory.

Generating movies from output frames

If the option --movie is specified, the simulation wrapper will generate a movie from dumped frames. This option requires that ffmpeg is installed on the system (ffmpeg download). The default frame dump frequency is every 100 integration steps. For a high-resolution (temporal resolution) specify more frequent dumps with the --dump_freq option. For example, 10-times more frames are generated with --dump_freq 10.