Stable localized moving patterns in the 2-D Gray-Scott model
I show stable, localized, single and multi-spot patterns of three classes { stationary, moving, and rotating { that exist within a limited range of parameter values in the two-dimensional Gray-Scott reaction-diusion model with = Du=Dv = 2. These patterns exist in domains of any size, and appear to derive their stability from a constructive reinforcement eect of the standing waves that surround any feature. There are several common elements { including a spot that behaves as a quasiparticle, a U-shaped stripe, and a ring or annulus, or a portion thereof { which combine to form a great variety of stable structures. These patterns interact with each other in a variety of ways. There are similarities to other reaction-diusion systems and to physical experiments; I oer several suggestions for further research.