Game of Life in 3D


Originally published at:


Now we need to discover the analog of the R-pentomino for the 3D version.



I think I remember that being called an “acorn” a long time ago, but I don’t think there was a clear definition.


One of Piers Anthony’s less awful books, Ox (book 3 of Omnivore/Orn/Ox) has a 3-D analogue of Life as a key player.


Obviously, it’s pretty two dimensional, and that implementation is very “written in java”. Now there’s all this fun “HTML5” stuff like canvases and the like, so I figure that it’s about time I figure out how they work.

A bit of an odd statement, since the page at the link uses HTML5 Canvas. (There used to be a Java version, but that one is not.)

Maybe they are just talking about aesthetics? Gray boxes with yellow, instead of white, a tasteful muted gray, and HTML5y-light blue?


I read about 3d variants of the Game of Life in a book I have (can’t remember if it’s a collection of articles by Martin Gardner or Jean-Paul Delahaye - I have both and they’re similar). I remember it exposed two sets of rules that were “dynamic” enough to give interesting results. One of them even allowed to simulate the classic 2d version, on two layers of cells.


Researchers have been looking into 3D versions of Life ever since it was popularized in the early 1970’s. Carter Bays, then at the University of South Carolina, published some of the first rigorous work on the subject in 1987. Here’s one of his early papers:


The balance is off, always ends up over populated.

John Conway spent quite a while (manually) working out the ideal balance - would be lovely to see a similar effort :slight_smile:



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