Which "Life"-Like Systems Have Gliders?

John Conway's "Game of Life" has fascinated and inspired many enthusiasts, due to the emergence of complex behavior from a very simple system. One of the many interesting phenomena in life is the existence of "gliders": small patterns that move across the grid. Some authors have asserted that the gliders and other complex behaviors occurring in Life are unusual, for instance Wolfram: "Except for a few simple variants on the Game of Life, no other definite class-4 two-dimensional cellular automata were found in a random sample of several thousand outer totalistic rules." Are gliders really so rare?

I have investigated whether gliders exist in many semitotalistic rules similar to Life, where the behavior of a cell depends only on its own state and the number of live neighbors. The results show that the existence of gliders is commonplace, contradicting Wolfram and calling into question his classification of cellular automata.

Jason Summers' c/5 diagonal spaceship in Life

Online interactive database of rules with gliders

Paper describing my glider search program and MSRI talk on streaming video

Rules with self-replicating patterns
New! Replicators in rules with B0, July 2002

Old maps of rules with known gliders: rules with B3, rules with B2

Program to list known gliders and its database
(db size , last update )

"Most wanted" list of rules for which I would still like to find gliders

Search software

Some discoveries in the rule B35/S236

A selection of other cellular automaton web sites


D. Eppstein