Localized excitations in a vertically vibrated granular layer

THE formation of two-dimensional patterns in biological, chemical and physical systems is often described by the nonlinear interaction of plane waves(1). An alternative approach views patterns as ensembles of interacting localized objects, analogous to the assembly of crystals from atoms, For macroscopic pattern-forming systems, one objection to the latter approach is that no 'atoms' exist; however spatially localized excitations can play an analogous role, One-dimensional localized states are observed in many systems-for example, solitary waves in water(2-4) and optical fibres(5)-and can organize into simple patterns(6,7). But few examples of two-dimensional localized states are known, and these tend to be unstable and/or do not show simple pattern-forming interactions(8-11). Here we report the observation of stable, two-dimensional localized excitations in a vibrating layer of sand, These excitations, which we term 'oscillons', have a propensity to assemble into 'molecular' and 'crystalline' structures, Our experimental results, together with the observation of similar localized excitations in model differential equations(12-14), indicate a crucial, cooperative role for hysteresis and dissipation in the formation of oscillons, and suggest that similar behaviour may occur in continuous media.