Cellular automata are systems consisting of a lattice (grid) of cells and a rule governing the cells’ evolution. As the system steps forward (evolves), the rule governing each cells’ on-off state is applied to determine the new configuration of cells.
This tool explores what are called three dimensional (3D) “totalistic” cellular automata.
The state of a cell going forward depends on its present state and that of its six neighbor cells: north, south, east, west, above, and below. The set of “rules of evolution" specify which configurations turn a cell on and which turn it off.
The initial state of the lattice greatly impacts its future evolution. Experiment with starting with a hollow cube or a solid sphere to see how a rule of evolution reacts.
This app can simulate over a trillion trillion trillion different rulesets across tens of thousands of cubic cells. There has never been a systematic study of these systems in 3D. If you find something interesting, be sure to tell us. Take a snapshot, or tweet your discoveries!