We studied the effect of nearest pattern interaction on a global pattern formation in a two-dimensional space, where patterns are to grow initially from a noise in the presence of a periodic supply of energy. Although our approach is general, we found that this study is relevant in particular to the pattern formation on a periodically vibrated granular layer, as it gives a unified perspective of the experimentally observed pattern dynamics such as oscillon and stripe formations, skew-varicose and crossroll instabilities, and also a kink formation and decoration.

• Received 16 May 2000

DOI:https://doi.org/10.1103/PhysRevE.62.7778