Category: Nonlinear Dyn.

Summary: Measuring how often boundary-regime Gray-Scott simulations settle into spot versus stripe patterns from different random initial conditions.

Gray-Scott reaction-diffusion systems can produce spots, stripes, and mixed transients near regime boundaries, but short simulations often hide how much the final state depends on initial conditions. This experiment asks whether the fraction of runs ending in each pattern can be used to map the basin structure near the spot-stripe boundary.

The simulation performs very long PDE integrations on large grids and repeats them across random perturbations. By treating the outcome frequencies themselves as observables, it characterizes multistability rather than forcing the system into a single representative morphology.

That is useful because boundary regions are often where simple phase labels break down. The experiment is designed to show whether deep runs reveal persistent basin competition that shorter studies would misclassify as noise or transient ambiguity.

Method: Long-horizon Gray-Scott reaction-diffusion simulations on 512x512 grids, repeated over random initial perturbations near the spot-stripe boundary.

What is measured: Fraction of runs converging to spots versus stripes, long-lived transient behavior, and basin-of-attraction structure near boundary parameters.