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) that no explicit example has been made.
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.
