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 o...

The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics term, accounting for the local rate of variation of the field variable, (ii) a noise component (additive or multiplicative) accounting for the unavoidable env...

Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. Possible mechanisms include oscillating consumer-resource interactions, localized disturbance-recovery processes and scale-dependent feedback. Despite abundant theoretical literature, studies revealing spatial self-organization in real ecosystems are limited. Rec...

Societies emerge as changing alignments of social groups, segments, and classes, without either fixed boundaries or stable internal constitutions... Therefore, instead of assuming transgenerational continuity, institutional stability, and normative consensus, we must treat these as problematic. We need to understand such characteristics historically, to note the conditions for their emergence, ...