Nicholas P. Timms
Submitted: April 2026 : Published: 26th April 2026
Abstract
Neural Cellular Automata (NCAs) advance biologically inspired computation but are historically constrained by homogeneous grid topologies. Recent Brain-inspired NCAs overcome this by integrating dynamic attention layers and long-range connections. This paper presents a novel synthesis merging these architectures with analogue gravity biophysics—specifically models of gastrointestinal electrophysiology. We introduce the Analogue Gravity Neural Cellular Automata framework, which reinterprets normalized attention matrices as discrete Riemannian metric tensors, transforming the computational grid into an emergent spacetime manifold. Through this physical lens, long-range connections mathematically function as Einstein-Rosen bridges that drastically accelerate morphogenetic self-organization by bypassing local diffusion limits. The network achieves long-term morphological stability by dynamically severing attention weights at phenotypic boundaries, generating analogue event horizons that trap signals and suppress noise. In motor control applications, global observations act as an artificial gut-brain axis, curving the computational manifold for optimal geodesic signal routing, whereas chaotic wiring induces pathological conduction blocks. Ultimately, mapping deep learning topologies to analogue gravity provides profound mechanistic explanations for the robustness, learning speed, and noise tolerance of complex, self-organizing systems.
