NINDI: Morphogenic Modeling via Spatial Phase Automata — Emergent Coacervate Structures and Phase-Gated Steering in Mobile Kuramoto Networks

This paper introduces NINDI (Non-symbolic Internal-phase Navigation for Dynamical Individuals), a continuous spatial automaton framework designed to model non-symbolic embodied intelligence and cellular morphogenesis without centralized control or explicit symbolic rules (if/switch). By coupling local Kuramoto phase dissonance directly to heading turning torques under a strict constant cruising speed constraint ($S$), the system induces the spontaneous multicellular self-assembly of active agents into stable coacervates (NINDIs). Within these emergent entities, perimeter particles radially align their velocity vectors outward ($A_{rad}^{perim} \approx 0.95$), stabilizing macro-scale structural equilibrium through balanced kinetic boundary thrust. Furthermore, the system establishes a soft phase-gated boundary that selectively permits resonant assimilation or enforces elastic scattering based on contact phase alignment. This release includes both a serverless HTML5/JavaScript web laboratory and a high-throughput parallel PyTorch CUDA backend for reproducible research in continuous spatial automata and active matter.