Minimal interaction conditions for the emergence of biological-like organization

This study examines the minimal interaction conditions under which persistent spatial organization can emerge from stochastic local dynamics. Using a four-state cellular automaton as an abstract symbolic interaction field, we introduce a local rule governed by self-maintenance, neighbor-mediated inhibition, and stochastic noise. The model is not intended to represent specific biochemical processes but to explore whether fundamental organizational properties associated with theoretical biology systems can arise from minimal local interactions alone. We quantify emergent behavior using block entropy, spatial autocorrelation, domain size distributions, and a local closure metric measuring agreement between cells and their neighborhood. Systematic exploration of the parameter space reveals three distinct regimes: ordered, disordered, and an intermediate regime characterized by intermediate entropy and enhanced organizational closure. Phase-space mapping shows that this regime occurs at specific ratios of self-maintenance and neighbor interaction strength rather than through monotonic increases in interaction intensity. Temporal analysis further demonstrates the persistence and reproducibility of spatial domains in this regime. These results suggest that organizational closure and structured spatial patterns can arise as statistical consequences of minimal local interactions, without presupposing biochemical detail. The work provides a conceptual framework for investigating the basic principles underlying organization relevant to theoretical biology and highlights how abstract computational systems can be used to study the conditions that favor the emergence of organized structure in biological systems.