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.
Rows of replicators can be capped off by blocks or eaters, resulting in
arbitrarily high-period oscillators.
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.
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.
Two side-by-side bombers can form puffers such as these two rakes,
which leave sideways- and backwards-going trails of gliders.
Dirtier puffers, spewing irregular patterns of blinkers and biloafs,
can be formed by capping a row of replicators in yet another way.
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.
It's possible to use replicator-based oscillators to make a gun
that periodically shoots bombers
or a "breeder" that shoots sideways glider rakes, producing a quadratic
growth rate.
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.
