Nearest pattern interaction and global pattern formation

We studied the effect of nearest pattern interaction on a global pattern fo rmation in a two-dimensional space, where patterns are to grow initially fr om a noise in the presence of a periodic supply of energy. Although our app roach 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 a s oscillon and stripe formations, skew-varicose and crossroll instabilities , and also a kink formation and decoration.