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