0E0P metacell

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0E0P metacell
0E0P metacell image
Pattern type Unit cell
Number of cells ~ 18650000
Bounding box 261841×261841
Cell size 262144×262144
Period 68719476736
Discovered by Adam P. Goucher
Year of discovery 2018

The 0E0P metacell is a unit cell constructed by Adam P. Goucher between 2014 and 2018.[1] Like Goucher's previous p1 megacell, it is capable of simulating any rule using the standard eight cell neighborhood, including non-totalistic rules.

The new feature of the 0E0P metacell, and the one that explains its record-breaking large size, is the fact that a group of these metacells can be placed in an empty Life universe with no background grid of OFF metacells, and the entire universe then simulates the rule for which the 0E0P metacells are programmed, at a larger scale by a factor of 262144 = 218. The acronym "0E0P" was originally short for "[State] Zero Encoded by Zero Population", so the OFF state is simply a metacell-sized region of empty space.

When one of these metacells turns off, it self-destructs completely, and when a metacell birth occurs, it must be constructed from the ground up by one of its neighbors. This allows 0E0P metacell patterns, when viewed from very far away (e.g., at a size where an entire metacell takes up a single pixel in the display), to be indistinguishable from normal patterns that use the same rule -- except that the metacell patterns will run 2^36 times more slowly, and if they're run at a step size lower than 2^36, intermediate states may be visible that will depart from a strict pixel-for-pixel match.


Thomas Cabaret's video explaining various self-replicating machines in cellular automata, including a comprehensive explanation (from 7:35 to 13:05) of the operation of the 0E0P metacell


The metacell's circuitry is sufficiently complex that a single Conway's Life meta-glider requires a compressed pattern file several megabytes in size.[2] It can be run in Golly at small step sizes with no difficulty, but simulating an entire replication cycle (half a metatick) is very difficult. On current computers it might take about half a CPU-year using Golly's standard HashLife algorithm.

An order of magnitude improvement over HashLife is available via Goucher's special-purpose StreamLife algorithm. However, even using StreamLife it might take several months to simulate the eight replication cycles (four full metaticks) needed to return a metaglider to its original phase. The original experimental verification of a single metatick (12:05 to 12:35 in Cabaret's video), using rule where a single ON cell is a still life, took about a month.


  1. "Fully Self-Directed Replication". Adam P. Goucher (November 12, 2018). Retrieved on January 8, 2019.
  2. Dave Greene. Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums