Topology as biological code: information-driven evolution of neighborhood structures in self-organizing cellular...

Understanding how biological information is generated, transmitted, and organized remains a central challenge in theoretical biology and complex systems science. While classical cellular automata assume fixed neighborhood structures, biological systems exhibit highly adaptive and evolving interaction topologies. Here, we propose an information-driven evolutionary cellular automaton framework in which neighborhood structures co-evolve with local dynamics, enabling spatial connectivity to function as an emergent form of structural biological coding, where "code" refers to a functional organization of interactions rather than arbitrary, symbolic correspondences. In the proposed model, each cell is endowed with a genotype encoding its interaction radius and connection probability, which collectively define its topological phenotype. Local topologies adapt through evolutionary mutations guided by time-lagged mutual information, serving as a computational proxy for information transfer efficiency. Through extensive simulations with statistical replication, we demonstrate that evolving topologies self-organize toward configurations that significantly enhance global information transmission, stability, and morphological coherence compared with fixed-topology controls. Spatial analyses further reveal the emergence of structured topological patterns, indicating the spontaneous formation of functional connectivity architectures. These findings support the hypothesis that biological information may also be embedded in adaptive spatial organizations, where interaction topology functions as a structural information substrate rather than a literal symbolic code. Our framework provides a general computational paradigm for exploring the origins of biological coding, self-organization, and evolutionary design principles in complex living systems.