445 rule
From Softology's collection · B4/S4/C5
Born and survives with exactly 4; the dying fade for three generations. Fragile: most seeds die out in a small box, so it opens on one that pulses for good. N tries another seed.
The rule
445 is one of the named rules in Softology's collection of 3D cellular automata, written there as 4/4/5/M: a live
cell survives with exactly 4 live neighbours, a dead cell is born with exactly 4, there are 5 states, and the neighbourhood is
Moore (all 26 cells around). The 5 states are alive, three dying and dead. A cell that fails to survive spends three generations
dying; meanwhile it does not count as a neighbour and nothing can be born where it is.
What it does
It is fragile. Its start is a random block half the box wide and half full, and in the 15×15×15 box the app opens with, 60 of 100 seeds died out within 300 generations, most of them within 40. So the preset pins a seed whose world keeps going.
A bigger box is kinder. Of 100 seeds in a 30×30×30 box, 12 died out, 23 were still changing after 300 generations, 64 settled into a cycle 30 or 60 generations long, and one froze. The cycle lengths are a clue: in a 24×24×24 box the cycles that turned up were 24 generations long, and in a 40×40×40 box 40. The cycle is the time something takes to travel once round the wrapped box.
How the rule works
- Each cell has 26 neighbours: every cell that shares a face, an edge or a corner with it (the Moore neighbourhood).
- An empty cell comes alive when exactly 4 of its neighbours are alive.
- A live cell stays alive when exactly 4 of its neighbours are alive; otherwise it starts dying: for 3 generations it fades, is not counted as a neighbour and blocks births, then the cell is empty again.
- With 5 states in all (alive, 3 dying, dead), this is a Generations rule.
Picking it in the app restarts the world from a random block in the middle of the box, 50% full and half as wide as the box. Its seed is fixed, so it is the same world every time, one still alive 40 generations later in the default 15×15×15 box; N tries another seed.
Notation
| Birth/survival | B4/S4/C5 |
|---|---|
| Softology, MCell (S/B/C/N) | 4/4/5/M |
| Neighbourhood | Moore (26 cells) |
B lists the neighbour counts at which an empty cell is born, S those at which a live cell survives, and C the number of states. How to read a rule
More of Softology's rules
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B3/S4-6 - Builder 1
B4,6,8-9/S2,6,9/C10 - Builder 2
B1/S5-7 - Clouds 1
B13-14,17-19/S13-26 - Clouds 2
B13-14/S12-26 - Coral
B6-7,9,12/S5-8/C4 - Crystal Growth 1
B1,3/S0-6 - Crystal Growth 2
B1,3/S1-2/C5 - Pyroclastic
B6-8/S4-7/C10 - Spiky Growth
B13,17,20-26/S0-3,7-9,11-13,18,21-22,24,26/C4 - 3D Brain
B4/S
All 30 rules · From 2D to 3D: why Conway's rule needs changing in 3D