Replicators: B36/S23 (HighLife)

This near-relative of Conway's Life was the first interesting rule in which a replicator was discovered, by Nathan Thompson in 1994. The replicator (shown in its symmetric phase) operates in a one-dimensional diagonal 2-unit grid, replicating itself every 12 generations.

HighLife 2c/12 replicator

Rows of replicators can be capped off by blocks or eaters, resulting in arbitrarily high-period oscillators.

HighLife p48 oscillator     HighLife p96 oscillator

Since HighLife is so similar to life, it has many of the same spaceships, including the small c/4 diagonal glider. An alternate method of capping a row of replicators produces glider guns of arbitrarily high periods.

HighLife p72 glider gun

Another method of capping a row of replicators, by a single blinker, produces a spaceship known as the bomber. The bomber moves diagonally 4 positions every 24 generations, after which a blinker appears in the same position on the other side of the bomber.

HighLife bomber

Two side-by-side bombers can form puffers such as these two rakes, which leave sideways- and backwards-going trails of gliders.

HighLife sideways rake     HighLife backwards rake

Dirtier puffers, spewing irregular patterns of blinkers and biloafs, can be formed by capping a row of replicators in yet another way.

HighLife p96 puffer

It's even possible for a puffer based on a bomber and replicator to spew out a trail of rows of replicators. Each row copies itself perpendicularly to the motion of the puffer. The pattern evolves to form a large Sierpinski triangle filled with replicators. The growth rate of the pattern (number of live cells after n generations) is O(nlog23), where the exponent is the fractal dimension of the Sierpinski triangle.

HighLife Sierpinski breeder

It's possible to use replicator-based oscillators to make a gun that periodically shoots bombers

HighLife p192 bomber gun

or a "breeder" that shoots sideways glider rakes, producing a quadratic growth rate.

HighLife rake breeder

Finally, Dean Hickerson has found a "push reaction" in which two sets of replicators push a blinker forward eight units diagonally. Since the bomber reaction allows replicators to pull a blinker the same amount, it should be possible to set up arbitrarily-slow replicator-based spaceships in which two sets of replicators push a blinker at the front end, and each pull a blinker at the other end. However, the likely size of these things is so huge (exponential in the period, leading to a pattern size of around 236 replicator units for Dean's reaction with the shortest possible repeat time) that no explicit example has been made. ETA January 2013: After the discovery of better reactions, Adam Goucher, Helmut Postl, and others have explicitly constructed "basilisks", spaceships of this type, with speeds c/24, c/32, c/63, and c/69. In principle infinitely many other speeds should also be possible. Goucher even constructed a basilisk gun, for the c/24 basilisk.

For more detailed descriptions of many more interesting patterns in this rule, see David Bell's article on HighLife.

Replicators -- Cellular Automata -- D. Eppstein -- UCI Inf. & Comp. Sci.