Internalized Morphogenesis: A Self-Organizing Model for Growth, Replication, and Regeneration via Local Token Exchange in Modular Systems

This study presents an internalized morphogenesis model for autonomous systems, such as swarm robotics and micro-nanomachines, that eliminates the need for external spatial computation. Traditional self-organizing models often require calculations across the entire coordinate space, including empty areas, which is impractical for resource-constrained physical modules. Our proposed model achieves complex morphogenesis through strictly local interactions between adjacent modules within the "body." By extending the "Ishida token model," modules exchange integer values using an RD-inspired discrete analogue without solving differential equations. The internal potential, derived from token accumulation and aging, guides autonomous growth, shrinkage, and replication. Simulations on a hexagonal grid demonstrated the emergence of limb-like extensions, self-division, and robust regeneration capabilities following structural amputation. A key feature is the use of the body boundary as a natural sink for information entropy (tokens) to maintain a dynamic equilibrium. These results indicate that sophisticated morphological behaviors can emerge from minimal, internal-only rules. This framework offers a computationally efficient and biologically plausible approach to developing self-repairing, adaptive, and autonomous hardware.