3D Game of Life rules
All 30 rules in the app: what each one does, how it is written, and a link that runs it.
How to read a rule
In the Game of Life every cell is alive or dead, and all cells update together from how many of their neighbours are alive. In three dimensions a cell has 26 neighbours (the Moore neighbourhood: faces, edges and corners) or, in some rules, only the 6 that share a face (von Neumann).
B4-5/S4-6: an empty cell is born (B) with 4 or 5 live neighbours; a live cell survives (S) with 4 to 6. Conway's 2D rule isB3/S2-3.B4/S4/C5: a Generations rule with 5 states. A cell that fails to survive spends 3 generations dying, is not counted as a neighbour meanwhile, and nothing is born in its place.4/4/5/M: the same rule as Softology and MCell write it, survival first: survive/birth/states/neighbourhood (M Moore, N von Neumann).
The app can also count neighbours by weight (faces 3, edges 2, corners 1, so sums run to 50). The Explorer rules have a weighted form; Softology's are written for plain counting. From 2D to 3D explains why Conway's rule does not simply carry over to three dimensions.
Classic rules
Range rules from the app's first version. Each is a set of neighbour counts that give birth (B) and survival (S).
| Rule | Notation | What it does |
|---|---|---|
| Standard | B4-5/S4-6 | The rule the first version shipped with: slow, structured growth. |
| Stable | B4/S4-5 | Settles into still lifes quickly. |
| Chaotic | B3-6/S2-5 | Wide ranges keep everything churning. |
| Die-Off | B5-6/S5-6 | Most seeds thin out and vanish. |
| Explosive | B2-6/S1-6 | Fills the box within a few generations. |
| Crystal | B5/S3-5 | Crystalline lattices grow from dense seeds. |
| Pulsating | B4-6/S3-4 | Blobs expand and collapse in cycles. |
| Maze | B3-4/S3-4 | Corridors and walls. |
| Sparse | B6/S5 | Thin filaments that rarely thicken. |
Explorer rules
Rules worth exploring, among them Carter Bays' Life 4555 and Life 5766 from his 1987 search for a Game of Life in three dimensions, and Conway's own 2D rule applied in 3D.
| Rule | Notation | What it does |
|---|---|---|
| 2D Conway | B3/S2-3 | The 2D rule applied in 3D; use a planar pattern to see it. |
| Life 4555 | B5/S4-5 | Supports gliders and stable structures. |
| Spiky | B4-6/S5 | Spines shoot out and die back. |
| Seeds | B3/S | Nothing survives; only births. Explosive fireworks. |
| Maze | B3/S1-5 | Labyrinths that freeze once formed. |
| Explosive | B4-5/S3-4 | Fast, chaotic expansion. |
| Day & Night | B3,6-8/S3-4,6-8 | Symmetric between alive and dead. |
| Life 5766 | B6/S5-7 | Bays' Life 5766: B6/S5-7, slow solid growth. The 2x2x2 block is a still life. (Earlier versions also listed it as Stable Growth.) |
Softology's rules
Named rules from Softology's collection of 3D cellular automata (softologyblog.wordpress.com). Most are Generations rules: a cell that fails to survive fades through dying states before it is gone.
| Rule | Notation | What it does |
|---|---|---|
| 445 | B4/S4/C5 | Born and survives with exactly 4; the dying fade for three generations. Fragile: many seeds die out, some grow a pulsing lattice. N tries another seed. |
| Amoeba | B5-7,12-13,15/S9-26/C5 | A blob that swells until it fills the box, then sets solid. |
| Architecture | B3/S4-6 | Fills the box with a restless scaffold of struts, about a fifth full. |
| Builder 1 | B4,6,8-9/S2,6,9/C10 | Sparse builders sprawl through the box, trailing eight generations of dying cells. |
| Builder 2 | B1/S5-7 | A cell is born beside any single live cell, so even one cell floods the box with churning lace. |
| Clouds 1 | B13-14,17-19/S13-26 | A dense random fill clumps into smooth clouds within a few generations, then holds still. |
| Clouds 2 | B13-14/S12-26 | Clouds 1 with fewer births: thinner, lumpier clouds. |
| Coral | B6-7,9,12/S5-8/C4 | Grows outward like coral and keeps shifting once it reaches the walls. |
| Crystal Growth 1 | B1,3/S0-6 | One cell grows a symmetric crystal that freezes once it fills the box. |
| Crystal Growth 2 | B1,3/S1-2/C5 | A crystal from one cell whose inside never stops flickering. |
| Pyroclastic | B6-8/S4-7/C10 | Plumes erupt and burn out, each dying cell fading through eight states. |
| Spiky Growth | B13,17,20-26/S0-3,7-9,11-13,18,21-22,24,26/C4 | Noise hardens into spiky clumps within a few generations. |
| 3D Brain | B4/S | Nothing survives a generation; births with exactly 4 neighbours spread in waves. |