Life Lexicon (U)
Author: Stephen A. Silver
Description: Part of Stephen Silver's Life Lexicon.

Introduction | Bibliography

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:underpopulation Death of a cell caused by it having fewer than two neighbours. See also overpopulation.

:unit Life cell A rectangular pattern, of size greater than 1x1, that can simulate Life in the following sense. The pattern by itself represents a dead Life cell, and some other pattern represents a live Life cell. When the plane is tiled by these two patterns (which then represent the state of a whole Life universe) they evolve, after a fixed amount of time, into another tiling of the plane by the same two patterns which correctly represents the Life generation following the one they initially represented. It is usual to use capital letters for the simulated things, so, for example, for the first known unit Life cell (constructed by David Bell in January 1996), one Generation is 5760 generations, and one Cell is 500x500 cells.

In December 2005, Jason Summers constructed an analogous unit cell for Wolfram's Rule 100, a one-dimensional cellular automaton that is know be universal.

:universal computer A computer that can compute anything that is computable. (The concept of computability can be defined in terms of Turing machines, or by Church's lambda calculus, or by a number of other methods, all of which can be shown to lead to equivalent definitions.) The relevance of this to Life is that both Bill Gosper and John Conway proved early on that it is possible to construct a universal computer in the Life universe. (To prove the universality of a cellular automaton with simple rules was in fact Conway's aim in Life right from the start.) Conway's proof is outlined in Winning Ways, and also in The Recursive Universe.

Until recently, no universal Life computer had ever been built in practice, because it would be enormous, even with the improvements that have been devised since those early proofs. In April 2000, Paul Rendell completed a Turing machine construction (described in http://www.cs.ualberta.ca/~bulitko/F02/papers/tm_words.pdf). This, however, has a finite tape, as opposed to the infinite tape of a true Turing machine, and is therefore not a universal computer. But in November 2002, Paul Chapman announced the construction of a universal computer, details of which can be found at http://www.igblan.free-online.co.uk/igblan/ca/. This is a universal register machine based around Dean Hickerson's sliding block memory.

See also universal constructor.

:universal constructor A pattern that is capable of constructing almost any pattern that has a glider synthesis. This definition is a bit vague. A precise definition seems impossible because it has not been proved that all possible glider fleets are constructible. In any case, a universal constructor ought to be able to construct itself in order to qualify as such. An outline of Conway's proof that such a pattern exists can be found in Winning Ways, and also in The Recursive Universe. The key mechanism for the production of gliders with any given path and timing is known as side-tracking, and is based on the kickback reaction. A universal constructor designed in this way can also function as a universal destructor - it can delete almost any pattern that can be deleted by gliders.

In May 2004, Paul Chapman and Dave Greene produced a prototype programmable universal constructor. This is able to construct objects by means of slow glider constructions. It likely that it could be programmed to be construct itself, but the necessary program would be very large; moreover an additional mechanism would be needed in order to copy the program.

A universal constructor is most useful when attached to a universal computer, which can be programmed to control the constructor to produce the desired pattern of gliders. In what follows I will assume that a universal constructor always includes this computer.

The existence of a universal constructor/destructor has a number of theoretical consequences.

For example, the constructor could be programmed to make copies of itself. This is a replicator.

The constructor could even be programmed to make just one copy of itself translated by a certain amount and then delete itself. This would be a (very large, very high period) spaceship. Any translation is possible (except that it must not be too small), so that the spaceship could travel in any direction. It could also travel slower than any given speed, since we could program it to perform some time-wasting task (such as repeatedly constructing and deleting a block) before copying itself. Of course, we could also choose for it to leave some debris behind, thus making a puffer.

It is also possible to show that the existence of a universal constructor implies the existence of a stable reflector. This proof is not so easy, however, and is no longer of much significance now that explicit examples of such reflectors are known.

:universal destructor See universal constructor.

:universal register machine = URM

:universal regulator A regulator in which the incoming gliders are aligned to period 1, that is, they have arbitrary timing (subject to some minimum time required for the regulator to recover from the previous glider).

Paul Chapman constructed the first universal regulator in March 2003. It is adjustable, so that the output can be aligned to any desired period.

:unix (p6) Two blocks eating a long barge. This is a useful sparker, found by Dave Buckingham in February 1976. The name derives from the fact that it was for some time the mascot of the Unix lab of the mathematics faculty at the University of Waterloo.

    .OO.....
    .OO.....
    ........
    .O......
    O.O.....
    O..O..OO
    ....O.OO
    ..OO....

:up boat with tail = trans-boat with tail

:U-pentomino Conway's name for the following pentomino, which rapidly dies.

    O.O
    OOO

:URM A universal register machine, particularly Paul Chapman's Life implementation of such a machine. See universal computer for more information.

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