OCA:Live Free or Die

Live Free or Die
x=0, y = 0, rule = B2/S0 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]] LifeViewer-generated pseudorandom soup
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Rulestring	0/2 B2/S0
Rule integer	516
Character	Explosive
Black/white reversal	B01234567/S01234578

Live Free or Die (or LFoD) is a Life-like cellular automaton where a cell survives if it has no neighbors, and a cell is born if it has two neighbors. Like Seeds, LFoD 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

Oscillators

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 × 2ⁿ - 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.

Spaceships

x = 2, y = 4, rule = B2/S0 bo$o$o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] [[ THUMBSIZE 3 ZOOM 42 GPS 2 AUTOSTART TRACKLOOP 2 -1 0 ]]

The moon in Live Free or Die (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

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

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 periods 3, 5, 6, 7, 8, and 9. Puffer flotillas can be built with any period of the form 8 × 2ⁿ or 6 × 2ⁿ, 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.

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

W110 unit cell

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

External links

• Live Free or Die (discussion thread) at the ConwayLife.com forums
• Glider 7171 at David Eppstein's Glider Database
• Live Free or Die at Adam P. Goucher's Catagolue