The theoretical backbone of pattern formation is found in nonlinear partial differential equations. While the specifics vary, the emergence of patterns usually follows a universal pathway.

Morphogenesis (how embryos develop shape) and the synchronization of fireflies.

The theory is validated across diverse physical, chemical, and biological domains: Pattern Formation and Dynamics in Nonequilibrium Systems

: Unlike equilibrium states where entropy is maximized and structures are static, these systems are "sustained" by a continuous flow of energy or matter.

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