OCA:Live Free or Die

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Live Free or Die
Live Free or Die rule
Rulestring 0/2
Rule integer 516
Character Explosive
Black/white reversal B01234567/S01234578

Live Free or Die (or LFoD) is a totalistic Life-like cellular automaton in which cells survive if they have no neighbors and are born if they have two neighbors. Like Seeds, it naturally explodes at light speed, but spaceships, puffers, and oscillators of infinitely extensible size and period have been discovered, along with guns, rakes, and spaceships which move diagonally.

Notable patterns


The rule also allows for the presence of only one still life consisting of a single cell, the dot. Other small oscillators include the checker (duoplet) at p2, the lever, anchor, and radar at p4, the ant at p6, and the monster at p19. The anchor track is an infinitely extensible oscillator that can have any period 4 * (2^n) - 4, which is useful in various flotillas of arbitrarily large periods. Oscillators have also been discovered at p3, p5, and p8. Many oscillators are extensible.


x = 2, y = 4, rule = B2/S0 bo$o$o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ AUTOSTART GPS 2 TRACKLOOP 2 -1 0 ]]
The moon in Live Free or Die (click above to open LifeViewer)
RLE: here Plaintext: here

Most spaceships and puffers in Live Free or Die travel at light speed. There is one p1 spaceship with four cells, the moon (known as a photon in Seeds.) Other small, common c spaceships include the free ship (p6), the key ship, plus ship, robot ship, and sun ship (p4), and the octopus ship (p8). Light speed spaceships have also been discovered at p2, p3 and p5, and spaceship flotillas can be built with any period of the form 8 * 2^n or 6 * 2^n.

Spaceships that travel at c/2, 2c/5, c/3, c/4, and c/5 orthogonally and at c/4 diagonally have also been discovered.

Puffers, rakes, and guns

There are a large number of light speed puffers, including many small, common puffers that produce dots or checkers at p4. Other c puffers have been discovered at p3, p5, p6, p7, p8, and p9. Puffer flotillas can be built with any period of the form 8 * 2^n or 6 * 2^n, and complex flotillas can be built to produce oscillators like the monster and radar or to create rakes.

There are known c clean backward moon rakes at a variety of periods and at c/2 and c/5. Sideways or backward free ship rakes can be built using flotillas.

There is one known gun, a p4 double-barreled moon gun known as the moon laser discovered by Matthias Merzenich in August 2012.[1]

A non-chaotic breeder based on a p4 puffer was discovered by Arie Paap on March 5, 2015.[2]

W110 unit cell

On October 20, 2020, FWKnightship constructed a Rule 110 unit cell in Live Free or Die, proving the rule Turing-complete.[3]


  1. Matthias Merzenich (August 1, 2012). Re: Live Free or Die (discussion thread) at the ConwayLife.com forums
  2. Arie Paap (March 5, 2015). Re: Live Free or Die (discussion thread) at the ConwayLife.com forums
  3. FWKnightship (October 20, 2020). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums

External links