Replicator
A replicator is any pattern that produces copies of itself. There is currently no precise definition.
Natural replicators
Replicators occur naturally in some cellular automata.[1] A well-known example in a Life-like cellular automaton is the simple replicator in HighLife (B36/S23). It repeatedly copies itself along a diagonal line every 12 generations according to a one-dimensional parity rule (Wolfram Rule 90).
 RLE: here |
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In Life, both the pre-pulsar and its skewed variant produce additional copies of themselves after 15 generations. However, the two copies interact, preventing any further copying. Because neither pattern copies itself in unlimited fashion, they are typically not considered true replicators.
RLE: here
Parity-rule replicators are common in B1 rules. For example, the pattern consisting of a single alive cell is a replicator in many B1 rules such as Gnarl (B1/S1). In the parity-rule Life-like cellular automata Replicator rule (B1357/S1357) and Fredkin rule (B1357/S02468), every pattern is a replicator.
Replicators can be used to create spaceships by using objects to delete one replicated part, which can be seen in HighLife's bomber and the pre-pulsar spaceship in normal Life.
Construction-based replicators
John von Neumann proved the existence of a pattern of about 200,000 cells that self-replicates in a 29-state von Neumann neighbourhood cellular automaton.[2] In particular, the cellular automaton supports both universal computation (by simulating a Turing machine) and universal construction and so a universal computer, connected to a universal constructor, would self-replicate when given a blueprint of itself.
In 1982, Berlekamp, Conway, and Guy proved that Life supports universal computation and universal construction, and thus that there exist self-replicating machines in Life.[3]
Prior to 2013, no explicit examples of construction-based replicators in Life were known. However, on November 23, 2013, Dave Greene constructed an explicit example by feeding a universal slow-salvo constructor (without any underlying universal computer) a tape of gliders that functions as a recipe for the constructor's own construction.[4]
A universal computer and constructor is known to exist also for B35/S236.[5] Therefore, replicators exist in that rule.
See Also
References
- ↑ David Eppstein. "Cellular Automata: Replicators". Retrieved on February 17, 2016.
- ↑ Gardner, Martin (1983), Wheels, Life, and Other Mathematical Amusements, W.H. Freeman, pp. 226-227
- ↑ Berlekamp, Elwyn R.; Conway, John H.; Guy, Richard K. (2004), Winning Ways for Your Mathematical Plays, 4 (2nd ed.), pp. 927-961
- ↑ Dave Greene (November 23, 2013). "Re: Geminoid Challenge". Retrieved on November 24, 2013.
- ↑ David Eppstein. "B35/S236". Retrieved on February 9, 2016.
External Links
- Replicator at the Life Lexicon