Pentacell

Conway's rule, taken literally into five dimensions. A cell has 242 neighbours here, not 8 — the full 5D Moore neighbourhood (3⁵−1), wrapped on a torus in every axis. Two of the five axes (x, y) are the grid you see in each tile; two more (z, w) are shown by tiling those grids into a meta-grid; the fifth (v) is a hyperplane you scrub with the slider below — the simulation runs on the full 5D volume the whole time, the slider only chooses which slice is drawn.

gen 0 · alive 0 / 0 (0%)

grid size per axis

hyperplane v 0 / 4

step interval 220 ms

random fill 22%

tap/click a cell in the visible slice to toggle it by hand.

rule — birth / survival by neighbour density

B3/S23 doesn't carry over: 3 live neighbours out of 8 is a density of 37.5%, but 3 out of 242 is nothing. So this rule is stated as a density band (fraction of the 242 neighbours alive) instead of a fixed count — the only way to give "the same rule" a meaning that survives a change of dimension. The defaults below are centred on classic Life's own density (birth at ~3/8, survival at 2/8–3/8); they are not proven special in 5D the way B3/S23 is in 2D, and are yours to retune.

birth min %

birth max %

survive min %

survive max %

why presets, and why they're a prediction

242 neighbours is a lot to average over. At a 22% global density the fraction any one cell sees is spread only about ±2.7 percentage points from cell to cell (√(p(1−p)/242)); 2D Life's 8 neighbours spread by tens of points at the same density. So almost every cell sees close to the whole grid's density, not its own neighbourhood's — the birth/survival bands act less like a local rule and more like a threshold on one number. The five presets below are what that threshold-on-a-number picture predicts for each band placement, worked out by hand, not by watching them run — this build has no browser. Load one, hit Randomize, then Play, and see if the population readout does what its description says.