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

Introduction | Bibliography

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:oblique Neither diagonal nor orthogonal. See also knightship.

:obo spark A spark of the form `O.O` (so called after its rle encoding).

:octagon II (p5) The first known p5 oscillator, discovered in 1971 independently by Sol Goodman and Arthur Taber. The name is due to the latter.

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

:octagon IV (p4) Found by Robert Wainwright, January 1979.

    .......OO.......
    .......OO.......
    ................
    ......OOOO......
    .....O....O.....
    ....O......O....
    ...O........O...
    OO.O........O.OO
    OO.O........O.OO
    ...O........O...
    ....O......O....
    .....O....O.....
    ......OOOO......
    ................
    .......OO.......
    .......OO.......

:octomino Any 8-cell polyomino. There are 369 such objects. The word is particularly applied to the following octomino (or its two-generation successor), which is fairly common but lacks a proper name:

    ..OO
    ..OO
    OOO.
    .O..

:odd keys (p3) Found by Dean Hickerson, August 1989. See also short keys and bent keys.

    ..........O.
    .O.......O.O
    O.OOO..OO.O.
    .O..O..O....
    ....O..O....

:omino = polyomino

:omniperiodic A cellular automaton is said to be omniperiodic if it has oscillators of all periods. It is not known if Life is omniperiodic, although this seems likely. Dave Buckingham's work on Herschel conduits in 1996 (see My Experience with B-heptominos in Oscillators) left only a short list of unresolved cases, all with periods of 58 or below. The list has been progressively reduced since then. Most recently, period 43 and 53 oscillators were made possible in 2013 by Mike Playle's Snark. As of June 2018, no oscillators are known for periods 19, 23, 38, or 41. If we insist that the oscillator must be non-trivial, then 34 should be added to this list.

Note that if we were to allow infinite oscillators, then all periods are certainly possible, as any period of 14 or more can be obtained using a glider (or LWSS) stream, or an infinitely long 2c/3 wire containing signals with the desired separation.

:one per generation See grow-by-one object.

:one-sided spaceship synthesis A glider synthesis of a spaceship in which all gliders come from the same side of the spaceship's path. Such syntheses are used extensively in the 17c/45 Caterpillar. For example, here is a one-sided way to create an LWSS.

    ...O.....
    ....OO...
    ...OO....
    .........
    .........
    .....O...
    ...O.O...
    ....OO...
    .........
    .........
    .........
    .........
    ......OOO
    ........O
    .......O.
    .........
    .........
    .........
    OOO......
    ..O......
    .O.......

:one-time A term used for turners and splitters, specifying that the reaction in question is not repeatable as it would be in a reflector or fanout device. Instead, the constellation is used up, usually in a clean reaction, but the much more common dirty turners and splitters are also very useful in some situations.

:onion rings For each integer n>1 onion rings of order n is a stable agar of density 1/2 obtained by tiling the plane with a certain 4n x 4n pattern. The tile for order 3 onion rings is shown below. The reader should be able to deduce the form of tiles of other orders.

    ......OOOOOO
    .OOOO.O....O
    .O..O.O.OO.O
    .O..O.O.OO.O
    .OOOO.O....O
    ......OOOOOO
    OOOOOO......
    O....O.OOOO.
    O.OO.O.O..O.
    O.OO.O.O..O.
    O....O.OOOO.
    OOOOOO......

:Online Life-Like CA Soup Search = The Online Life-Like CA Soup Search.

:on-off Any p2 oscillator in which all rotor cells die from overpopulation. The simplest example is a beacon. Compare flip-flop.

:O-pentomino Conway's name for the following pentomino, a traffic light predecessor, although not one of the more common ones.

    OOOOO

:orbit A term proposed by Jason Summers to refer to a natural stabilization of a puffer. For example, the switch engine has two (known) orbits, the block-laying one and the glider-producing one.

:Orion (c/4 diagonally, p4) Found by Hartmut Holzwart, April 1993.

    ...OO.........
    ...O.O........
    ...O..........
    OO.O..........
    O....O........
    O.OO......OOO.
    .....OOO....OO
    ......OOO.O.O.
    .............O
    ......O.O.....
    .....OO.O.....
    ......O.......
    ....OO.O......
    .......O......
    .....OO.......

In May 1999, Jason Summers found the following smaller variant:

    .OO..........
    OO...........
    ..O..........
    ....O....OOO.
    ....OOO....OO
    .....OOO.O.O.
    ............O
    .....O.O.....
    ....OO.O.....
    .....O.......
    ...OO.O......
    ......O......
    ....OO.......

:orphan Conway's preferred term for a Garden of Eden. According to some definitions, an orphan consists of just the minimum living and dead cells needed to ensure that no parent is possible, whereas a GoE is an entire infinite Life plane that contains an orphan.

:Orthogonoid (256c/3476016, p3476016) A self-constructing spaceship analogous to the Demonoids, with a slow orthogonal direction of travel. The first example was completed by Dave Greene on 29 June 2017, with a top speed of 16c/217251 (this is just 256c/3476016 in lowest terms).

The construction recipe is a stream of MWSSes, with the recovery time limited to 90 ticks by the Lx200 dependent conduit that follows the initial syringe converter. The design is hashlife-friendly, meaning that the spaceship can be trivially adjusted so that spatial and temporal offsets are exact powers of two; period 4194304 and period 8388608 versions have been constructed, with speeds of c/16384 and c/32768 respectively.

The MWSSes are converted to Herschels, which produce a standard single-channel glider stream that runs the Orthogonoid's single construction arm. After the child circuitry is complete, a previously constructed Snark in the parent is removed from the construction arm lane, converting it to a "destruction arm" that shoots down the previous constructor/reflector in the series.

:oscillator Any pattern that is a predecessor of itself. The term is usually restricted to non-stable finite patterns; period 1 oscillators are stable and are usually just called still lifes. The blinker is the smallest non-stable oscillator, having period 2. There are oscillators of almost all higher periods (see omniperiodic). In general cellular automaton theory the term "oscillator" usually covers spaceships as well, but this usage is not normal in Life.

Oscillators consisting of separate objects which do not react in any phase are usually ignored. For example, a separated blinker and pulsar makes a period 6 oscillator, but is considered trivial.

An oscillator can be divided into a rotor and a stator, and the stator can be further subdivided into bushing and casing. Some oscillators have no casing cells, and a few 100%-volatility oscillators also have no bushing cells.

An oscillator can be constructed from any gun as long as eaters can be added to consume its output. If it is a true gun then the period of the oscillator will be the same as the gun - unless the eating mechanism multiplies the period, as in the case of gliders caught by a boat-bit.

With the discovery of reflectors, relays provide an easy way to create oscillators of all large periods. For example, eight gliders travelling in a loop created by four Snarks can create any period above 42, with a population never exceeding 356 live cells.

For the very lowest periods, whole families of extensible oscillators are known. Examples of this are barberpole, cross, pentoad, p6 shuttle, snacker, and multiple roteightors. Any of the shuttles are oscillators by definition, for example the queen bee shuttle. Many of these are also extensible. Other oscillators such as figure-8 and tumbler have unique mechanisms that are not part of an extended family.

Some oscillators are useful because of the perturbations they can cause to other objects. This is especially true if they provide a spark on their boundary. Some oscillators are explicitly found by search programs in order to produce these sparks, such as pipsquirters.

Some higher period oscillators have been found while running random soups. This is especially true if the soup is run on a cylindrical or torus universe. Sometimes the found objects can be moved to the normal universe and supported there by added catalysts. Achim's p144 is an example.

:Osqrtlogt (p1 circuitry) A pattern constructed by Adam P. Goucher in 2010, which uses an unbounded triangular region as memory for a binary counter. Empty space is read as a zero, and a boat as a one, as shown in the example pattern in memory cell. The pattern's diametric growth rate is O(sqrt(log(t))), which is the slowest possible for any Life pattern, or indeed any 2D Euclidean cellular automaton. The population returns infinitely often to its initial minimum value (during carry operations from 11111...1 to 100000...0, so it can be considered to be an unusual form of sawtooth.

:OTCA metapixel (p46 circuitry) A 2048 x 2048 period 35328 metacell constructed by Brice Due in 2006. It contains a large "pixel" area that contains a large population of LWSSes when the metacell state is ON, but is empty when it is OFF. This allows the state of the metacell to be visible at high zoom levels, unlike previous unit cells where the state was signaled by the presence or absence of a single glider in a specific location.

:out of the blue See natural Heisenburp. Other similar mechanisms, particularly the method of LWSS creation used in the pixel part of the OTCA metapixel, may also be referred to as "out of the blue" reactions.

:overclocking A term used when a circuit can accept a signal at a specific period which it cannot accept at a higher period. A syringe is a simple example.

Some staged recovery circuits also permit overclocking, and can function successfully at a rate faster than their recovery time. A Silver reflector has a recovery time of 497 ticks, but can be overclocked to reflect a period 250 glider stream, or any nearby period above 248, simply by removing a beehive after the first glider enters the reflector. However, a continuous stream of gliders is then required to maintain the circuit, with timing within a tightly bounded range.

:overcrowding = overpopulation

:over-exposure = underpopulation

:overpopulation Death of a cell caused by it having more than three neighbors. See also underpopulation.

:over-unity reaction An important concept in gun and macro-spaceship construction. To be a good candidate for building one of these types of patterns with a new period or speed, a stationary reaction (for a gun) or a moving reaction (for a macro-spaceship) must be able to produce some number of output signals, strictly greater than the number of input signals required to maintain the reaction. The extra signal becomes a gun's output stream, or may be used in a variety of ways to construct the supporting track for a macro-spaceship. By implication, "over-unity" refers to the ratio of output signals to input signals.

If all signal outputs must be used up to sustain a stationary reaction, a high-period oscillator may still be possible. See emu for example.

:overweight spaceship = OWSS

:OWSS A would-be spaceship similar to LWSS, MWSS and HWSS but longer. On its own an OWSS is unstable, but it can be escorted by true spaceships to form a flotilla.

:Ox A 1976 novel by Piers Anthony which involves Life.

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