After becoming interested in digital physics, I came across Randall O'Reilly's model called "EmeWave":
...an autonomous computational model of fundamental physics, based generally on the cellular automaton framework, but using analog state values instead of the usual binary or discrete ones.
I thought it would be interesting to implement a similar model and watch real-time simulations of it. Specifically, I set up discrete 2D and 3D lattices of cells with analog state values. The system dynamics were based on a simple spring equation, where each cell's state is pulled toward the average of its neighbors' states. The spring constants define the dynamics of the entire simulation.
The images and video below show the results of several simulations with various starting conditions (e.g., uniformly random initial states, high energy at the center of the universe, etc.).