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

Introduction | Bibliography

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:Q = Quetzal

:qd Abbreviation for quarter diagonal.

:Q-pentomino Conway's name for the following pentomino, a traffic light predecessor.

    OOOO
    ...O

:quad (p2) Found by Robert Kraus, April 1971. Of all oscillators that fit in a 6x6 box this is the only flipper.

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

:QuadLife A form of colourised Life in which there are four types of ON cell. A newly-born cell takes the type of the majority of its three parent cells, or the remaining type if its parent cells are all of different types. In areas where there are only two types of ON cell QuadLife reduces to Immigration.

:quadpole (p2) The barberpole of length 4.

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

:quad pseudo A still life that can be broken down into four stable pieces but not into two or three. This term may refer to the following 34-bit pattern, found by Gabriel Nivasch in July 2001, or any similar pattern with the same property.

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

As a consequence of the Four-Colour Theorem, there can be no analogous objects requiring decomposition into five or more pieces. By convention, patterns like this and the triple pseudo are considered to be pseudo still lifes, not strict still lifes. As of June 2018, it has been shown that no quad pseudo patterns exist with 32 or fewer bits, but a 33-bit pattern with this property may theoretically still be found.

:quadratic filter A toolkit developed by Dean Hickerson and Gabriel Nivasch in 2006, enabling the construction of patterns with asymptotic population growth matching an infinite number of different sublinear functions - namely, O(t(1/2n)) for any chosen n. See also exponential filter, recursive filter.

:quadratic growth The fastest possible asymptotic rate of population growth for any Life pattern - O(t2) in big-O notation, where t is the number of ticks. The first quadratic-growth pattern found was Bill Gosper's 1971 breeder. Many other types of breeders and spacefillers have been constructed since.

In April 2011, Stephen Silver gave an example of a one-cell-thick pattern over a million cells long that exhibited quadratic growth. In October 2015, Chris Cain constructed a one-cell-thick pattern with a reduced bounding box of 2596x1, improving on a series of previous longer results. The smallest known quadratic growth pattern by initial population is the 23-cell switch-engine ping-pong by Michael Simkin.

There are an infinite number of possible growth rates between linear and quadratic growth. See superlinear growth.

:quadratic replicator A pattern that fills all or part of the Life plane by making copies of itself in a nonlinear way. Small quadratic replicators are known in other Life-like rules, but as of July 2018 no example has been found or constructed in Conway's Life.

:quadratic sawtooth Any sawtooth pattern with a quadratic envelope, or specifically a pattern assembled by Martin Grant in May 2015, consisting of two caber tossers with period multipliers for timing which activate and deactivate two toggleable rake guns (see toggleable gun). The gliders emitted by those rakes annihilate on the diagonal while the rakes are eaten by 2c/5 ships. All the rakes and gliders are destroyed before the next cycle. See also Osqrtlogt.

:quadri-Snark A period-multiplying colour-preserving signal conduit found by Tanner Jacobi in October 2017, producing one output glider for every four input gliders. It is made by replacing one of the eaters in a tremi-Snark with a catalyst found using Bellman. The catalyst causes the formation of a tub which then requires an additional glider to delete. However, this adds 5 ticks to the repeat time, so that it becomes 48. If period quadrupling is needed with a colour-changing reaction, a CP semi-Snark and a CC semi-Snark can be used in series, or a period-multiplying Herschel conduit can be connected to a syringe and an appropriately chosen Herschel-to-glider converter.

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

:quapole = quadpole

:quarter (c/4 diagonally, p4) The following spaceship, found by Jason Summers in September 2000. The name is due to the 25-cell minimum population. This is the smallest known c/4 spaceship other than the glider. This spaceship can also be used to make the smallest known tubstretcher.

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

:quarter diagonal A unit of measurement sometimes used for diagonal distances, especially for slow salvo glider lanes. One advantage of measurement in quarter diagonals is that gliders travel diagonally at 1qd/tick, so that the same integer value can serve as either a time or a diagonal distance measurement.

:quasar (p3) Found by Robert Wainwright, August 1971. This is related to the pulsar, and is just the smallest of an extensible series of p3 oscillators built using pulsar quadrants which are shifted with respect to each other.

    ..........OOO...OOO..........
    .............................
    ........O....O.O....O........
    ........O....O.O....O........
    ........O....O.O....O........
    ..........OOO...OOO..........
    .............................
    ........OOO.......OOO........
    ..OOO..O....O...O....O..OOO..
    .......O....O...O....O.......
    O....O.O....O...O....O.O....O
    O....O.................O....O
    O....O..OOO.......OOO..O....O
    ..OOO...................OOO..
    .............................
    ..OOO...................OOO..
    O....O..OOO.......OOO..O....O
    O....O.................O....O
    O....O.O....O...O....O.O....O
    .......O....O...O....O.......
    ..OOO..O....O...O....O..OOO..
    ........OOO.......OOO........
    .............................
    ..........OOO...OOO..........
    ........O....O.O....O........
    ........O....O.O....O........
    ........O....O.O....O........
    .............................
    ..........OOO...OOO..........

Here is the next oscillator in the series.

    ..................OOO...OOO..................
    .............................................
    ................O....O.O....O................
    ................O....O.O....O................
    ................O....O.O....O................
    ..................OOO...OOO..................
    .............................................
    ................OOO.......OOO................
    ..........OOO..O....O...O....O..OOO..........
    ...............O....O...O....O...............
    ........O....O.O....O...O....O.O....O........
    ........O....O.................O....O........
    ........O....O..OOO.......OOO..O....O........
    ..........OOO...................OOO..........
    .............................................
    ........OOO.......................OOO........
    ..OOO..O....O...................O....O..OOO..
    .......O....O...................O....O.......
    O....O.O....O...................O....O.O....O
    O....O.................................O....O
    O....O..OOO.......................OOO..O....O
    ..OOO...................................OOO..
    .............................................
    ..OOO...................................OOO..
    O....O..OOO.......................OOO..O....O
    O....O.................................O....O
    O....O.O....O...................O....O.O....O
    .......O....O...................O....O.......
    ..OOO..O....O...................O....O..OOO..
    ........OOO.......................OOO........
    .............................................
    ..........OOO...................OOO..........
    ........O....O..OOO.......OOO..O....O........
    ........O....O.................O....O........
    ........O....O.O....O...O....O.O....O........
    ...............O....O...O....O...............
    ..........OOO..O....O...O....O..OOO..........
    ................OOO.......OOO................
    .............................................
    ..................OOO...OOO..................
    ................O....O.O....O................
    ................O....O.O....O................
    ................O....O.O....O................
    .............................................
    ..................OOO...OOO..................

:quasi still life A stable constellation where the individual still lifes share dead cells, so the neighborhoods of those dead cells are changed, but all cells that used to remain dead from under-population still do so. Under Life rules, this occurs when objects are diagonally adjacent (e.g., two blocks sharing a single diagonal neighbor) or when single protruding cells in two objects such as tubs share multiple neighbors. The term is due to Mark Niemiec.

      ----------------
      Bits       Count
      ----------------
       8             6
       9            13
      10            57
      11           141
      12           465
      13          1224
      14          3956
      15         11599
      16         36538
      17        107415
      18        327250
      19        972040
      20       2957488
      21       8879327
      22      26943317
      ----------------

As the number of bits increases, the quasi still life count goes up exponentially by approximately O(3.04n), slightly more than a factor of three. By comparison, the rate for strict still lifes is about O(2.46n) while for pseudo still lifes it's around O(2.56n).

:queen bee See queen bee shuttle.

:queen bee shuttle (p30) Found by Bill Gosper in 1970. There are a number of ways to stabilize the ends. Gosper originally stabilized shuttles against one another in a square of eight shuttles. Two simpler methods are shown here; for a third see buckaroo. The queen bee shuttle is the basis of all known true p30 guns (see Gosper glider gun).

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

:queen bee shuttle pair Any arrangement of two queen bee shuttles such that the two beehives created between them are consumed in some way. There are many ways that the two shuttles can be placed, either head-to-head, or else at right angles. The most well-known and useful arrangement results in the Gosper glider gun.

Other arrangements don't create any lasting output, but create large sparks which can perturb objects (especially gliders) in various ways. For example, one arrangement of a queen bee shuttle pair was used in the original unit Life cell as a memory cell. Here an input glider is converted into a block, which remains until it is deleted by a glider on a right-angled path.

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

See p690 gun and metamorphosis II for two more examples.

:Quetzal Any Herschel track-based gun with a period below 62, which is the lowest period with a stable glider-emitting conduit. This was Dieter Leithner's name for the true p54 glider gun he built in January 1998 - a short form of Quetzalcoatlus, which expresses the fact that the gun was a very large Herschel loop that was not an emu. Shortly afterwards Leithner also built a p56 Quetzal using a mechanism found by Noam Elkies for this purpose. In October 1998 Stephen Silver constructed a p55 Quetzal using Elkies' p5 reflector of the previous month. Quetzals of periods 57-61 have since been constructed.

Some of the more recent Quetzals are not Herschel loops, but are instead short Herschel tracks firing several glider streams all but one of which is reflected back to the beginning of the track to create a new Herschel. Noam Elkies first had the idea of doing this for the p55 case, and Stephen Silver constructed the resulting gun shortly after building the original (much larger) p55 Quetzal. Jason Summers later built a p54 version, which is more complicated because the evenness of the period makes the timing problems considerably more difficult.

:Quetzalcoatlus A giant flying dinosaur after which Dieter Leithner named his p54 gun. Usually abbreviated to Quetzal, or simply Q (as in Q54, Q55, Q56, Q-gun, etc.).

:quilt = squaredance

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