Emergent complexity, such as the billowing patterns of a swallow murmuration or spontaneously arising hexagonal cells which can occur in boiling water, represent the lowest (i.e. most efficient) energy state of a dynamical system. Information processing systems such as brains (or civilisations) tend towards forming autonomous, self-propagating patterns and these structural relationships seek out the lowest energy and most efficient form (i.e. morphology, phenotype). System state exploration is of a volatile (i.e. stochastic) information and (free) energy space through non-volitional, non-agency experiment, exploration or testing and evolution; incorporating human agency or social and cultural contexts, we might recognise this exploratory process as innovation or directed (i.e. useful) creativity. Low-energy dynamical system states are also the most efficient information storage systems in that the minimally complex description of an emergent patterned or structured dynamical system is of significantly less descriptive magnitude than is the sum description of all component parts and their properties.
The existence of non-organic patterns (as codes, genetic structure, grammars, logic) demonstrates that, while life and sentience may be deeply saturated with the self-propagating potentials written into physics and biological complexity, the structures and patterns are themselves and to some extent independent entities. Assertions regarding the primacy of mathematics (and by extension – physics) as the symbolic language of choice for the explanation of the emergence of complexity are powerful but do not sufficiently explain the arrival or emergence of symbolic languages and similarly structured logical or linguistic systems which reflect the structural depth of the world. Why should the world exhibit mathematical (or logical) regularity and possess such deep structural and systemic complexity at all ?
The emergence of structured and patterned complexity may just be an inevitable consequence of a Cosmos in which the self-replicating, iterating logical process of self-replication itself represents the simplest, low-energy (and minimal algorithmic information complexity) state of any dynamical process. The often misconstrued degeneration or disassembly of order into entropy is that process or aperture of opportunity by which the logic of self-replication (and the self-replication of a dynamical logic) autonomously or algorithmically seeks to find instantiation and continuity through sustainable low-energy patterns and regularities of dynamical systems or network configuration.