QuickLife is a fast, conventional (non-hashing) algorithm for exploring Life and other 2D outer-totalistic rules. Such rules are defined using "B0...8/S0...8" notation, where the digits after B specify the counts of live neighbors necessary for a cell to be born in the next generation, and the digits after S specify the counts of live neighbors necessary for a cell to survive to the next generation. Here are some example rules:
B3/S23 [Life]
John Conway's rule is by far the best known and most explored CA.
B36/S23 [HighLife]
Very similar to Conway's Life but with an interesting replicator.
B3678/S34678 [Day & Night]
Dead cells in a sea of live cells behave the same as live cells
in a sea of dead cells.
B35678/S5678 [Diamoeba]
Creates diamond-shaped blobs with unpredictable behavior.
B2 [Seeds]
Every living cell dies every generation, but most patterns still explode.
B234 [Serviettes or Persian Rug]
A single 2x2 block turns into a set of Persian rugs.
B345/S5 [LongLife]
Oscillators with extremely long periods can occur quite naturally.
QuickLife also supports Stephen Wolfram's 1D CA rules. These rules are specified as "Wn" where n is an even number from 0 to 254. For example:
W22
A single live cell creates a beautiful fractal pattern.
W30
Highly chaotic and an excellent random number generator.
W110
Matthew Cook proved that this rule is capable of universal computation.