Presets
Playback
Automaton
Rule
Dynamics and view
Camera
Layers
Quality
Model check
The science
What the 3D view encodes
Every glazed block is one live cell, positioned by the model state each step. Tower: x = cell index, height = time (newest row at the top of the wall once the page is full it scrolls). Life stack: x,z = board, height = generation age (older generations sink and dim). Ant and Wireworld: raised blocks sit on the board. Life 3D: the cube is the lattice; dying states fade toward violet.
Elementary rules
s'_i = f(s_{i-1}, s_i, s_{i+1}), rule number = binary table of the 8 outputs. Rule 90 (XOR) from a single cell gives Pascal's triangle mod 2: row n has 2^popcount(n) cells. Rule 110 is Turing-complete; Rule 30 is chaotic.
Life-like and Generations rules
2D: a dead cell is born if its Moore count n is in B, a live one survives if n is in S (Conway = B3/S23). 3D "Generations" rules use 26 Moore (or 6 von Neumann) neighbours: state 1 survives if n in S, dead cells are born if n in B, otherwise a live cell enters decay states 2..k-1 and then dies. Rule strings follow the community notation S/B/states/neighbourhood; the named presets are taken from that literature.
Langton's ant and Wireworld
The ant turns by the letter of its colour (R right, L left), recolours the cell and steps forward; after about 10,000 chaotic steps it builds a highway repeating every 104 steps with displacement (+-2,+-2). Wireworld: head becomes tail, tail becomes conductor, a conductor with 1 or 2 head neighbours becomes a head.
Honest simplifications
Boards are finite (torus or dead edges). The wall hides cells scrolled out of view. Statistics are computed on the visible lattice. The checks run in separate small simulations and compare against closed-form counts (Rule 90), a naive reference implementation (3D engine), symmetry invariance and the known glider displacement.