Control of morphology and topology in a lattice model of branching morphogenesis

What the math gives to ML

The paper provides a constructive non-equilibrium growth mechanism in which local occupation and removal rates are modulated by a diffusing morphogen field, while a local operator can preserve or change cluster topology. Its transferable asset is an explicit stochastic birth-death rule with neighborhood dependence and a topology-preserving transition test. A neural analogue is a dynamically sparse network whose edges or units are grown and pruned according to a diffusing utility field, while local connectivity tests prevent disconnection or unintended changes in the computational graph. The predicted signature is a controllable transition from compact to branched connectivity and a measurable scaling exponent near the reported cluster value when topology-preserving remodeling dominates.