Hyperbolic Neural Cellular Automata: A Geometric Framework for Emergent Complexity
E. G. Reis · Zenodo (CERN European Organization for Nuclear Research) · 2026
We introduce Hyperbolic Neural Cellular Automata (H-NCA), addressing the GeometricCapacity Bottleneck and Temporal Binding Problem. By situating cellular automata onhyperbolic tessellations (pentagrid {5, 4}) and integrating phase-oscillator dynamics via H-AKOrN, we achieve exponential capacity growth (∝ er ) and intrinsic temporal coherence.H-NCA is formalized as a Riemannian dynamical system with Euler discretization of naturalgradient flows on Lorentz manifolds.