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!
To the left is the matrix of cell configurations that lead to the central cell being turned on (highlighted) or turned off (dim) in the next step.
The determination of a cell's on/off state in the next step is made by consulting the rule that corresponds to the states of each of the six neighbors (x+, x-, y+, y-, z+, z-) and the present state of the cell itself.
For example, the rule to the right says that if a cell is on and the state above it (y+) is on, the cell will turn off in the next step.
If the rule is highlighted , the cell will be "on" in the next step.