Live Free or Die Universe

An exploration of the Moore neighborhood s0/b2 cellular automaton.

Live Free or Die, like Conway’s Game of Life, is a two-dimensional two-state Moore neighborhood cellular automaton. In other words, it is an infinite grid of cells which can either be live or dead. Given an initial configuration of cells, each cell applies simple rules based on its eight neighboring cells to determine whether its state will change. A live cell will die if it has any neighbors, and a dead cell will come to life if it has exactly two neighbors. Every cell in the grid changes at the same instant. As the pattern evolves through consecutive generations, it exhibits emergent and often beautiful behavior.

A p12 anchor track flotilla: the radar puffer.

NewsDated list of discoveries and explorations Glossary222 terms and objects, 37 oscillators, 46 spaceships, 55 puffers and rakes Object tablesStatistics for each object or its smallest iteration Period explorationsThe smallest oscillator, puffer and spaceship for each known period Iteration guidesPossible iterations of puffer and spaceship families ChallengesObjects nobody had found yet FilesRun-length encoded collections and explorations About this restorationWhat was recovered, from where, and what is lost

A short explanation

I found Live Free or Die while messing around with simple variations of Seeds (/b2). It is so named because the only cells that survive between generations are free of neighbors. What first intrigued me about it were the extremely common free ship, the double and 2-2 dot puffers, and the key ship.

Live Free or Die is a small, fast, intuitive universe, in which most objects are more reminiscent of machinery than of the organic fluidity that is characteristic of Conway’s Life (s23/b3). It is full of readily visible patterns, and flotillas and other large projects are easy to assemble. The explosive nature of the rule makes it receptive to the naturalistic study of mobile objects. It has oscillators of each period and spaceships of each speed that is possible in the Seeds universe, along with objects that are impossible or undiscovered in Seeds: stable fuses, oscillators with stators, and oscillators and spaceships of indefinitely large period.

Since then, objects of many periods and speeds have been discovered, such as the p10 decade ship, the c/3 wasp ship and the moon laser gun, along with various types of breeders, from the first MMS breeder in 2015 to the first MMM breeder in 2025 (see News). The construction of a Rule 110 unit cell in 2020 proved that Live Free or Die is Turing-complete.

— Luke Bradford. Text from the 2009 home page, except the last paragraph.

monster

This site is a historical restoration, not a complete and actively maintained catalog of patterns and discoveries in Live Free or Die.

Contributors

Most objects were found by Luke Bradford. Major contributions came from Josh Ball (dozens of oscillators, ships, puffers and rakes, 2008–2009), David Eppstein (the first slower-than-light ship), Jason Summers (oscillators from his Seeds collection) and Brian Prentice (anchor track flotilla explorations), and, after 2012, Paul Tooke, Matthias Merzenich, Arie Paap (wildmyron), Michael Simkin, Nora Brown, and many others on the ConwayLife forums, including Game of Life Fun, praosylen, AforAmpere, confocaloid and FWKnightship. The Glider Database credits earlier finds of the key ship to Peter Naszvadi (2001) and the robot ship to Alex Fink (2000).