Abstract
This model was originally conceived as a physical framework for understanding the universe, yet it is equally suitable as an automaton model for computational exploration. We present the Energy-Gradient Graph Automaton (EGG), a discrete dynamical system designed for numerical implementation.
The automaton consists of a topologically fixed graph of nodes carrying integer energy quanta. Energy flows from higher to lower adjacent nodes under a simple local gradient rule, conserving total energy automatically. We define a multiplicative entropy as the product of all node energies. This non-statistical entropy updates with every single transfer, assigning a unique coordinate to each step and serving as the system's intrinsic clock. The Second Law holds exactly, while its logarithmic equivalence to Boltzmann entropy ensures consistency with macroscopic thermodynamics.
The node degrees of freedom—resonance, spin, axial rotation, and spacing–tensor modulation—are computationally tractable. By encoding geometric deformation directly in these degrees, mass as local compression curvature and gravity as surrounding stretching become purely graph-theoretic. A geometry–frequency mapping bridges deformation and node dynamics, enabling gravitational simulation analogous to numerical relativity.
With its simple rule, exact conservation and Second Law, and geometrically encoded interactions, the EGG Automaton provides a self-contained, bottom-up framework well-suited for numerical simulation of entropy-driven discrete spacetime dynamics.
