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

Introduction | Bibliography

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:dart (c/3 orthogonally, p3) Found by David Bell, May 1992.

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

:dead spark coil (p1) Compare spark coil.

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

:de Bruijn diagram = de Bruijn graph

:de Bruijn graph As applied to Life, a de Bruijn graph is a graph showing which pieces can be linked to which other pieces to form a valid part of a Life pattern of a particular kind.

For example, if we are interested in still lifes, then we could consider 2x3 rectangular pieces and the de Bruijn graph would show which pairs of these can be overlapped to form 3x3 squares in which the centre cell remains unchanged in the next generation.

David Eppstein's search program gfind is based on de Bruijn graphs.

:Deep Cell A pattern by Jared James Prince, based on David Bell's unit Life cell, in which each unit cell simulates two Life cells, in such a way that a Life universe filled with Deep Cells simulates two independent Life universes running in parallel.

In fact, a Life universe filled with Deep Cells can simulate infinitely many Life universes, as follows. Let P1, P2, P3, ... be a sequence of Life patterns. Set the Deep Cells to run a simulation of P1 in parallel with a simulation of a universe filled with Deep Cells, with these simulated Deep Cells running a simulation of P2 in parallel with another simulation of a universe filled with Deep Cells, with these doubly simulated Deep Cells simulating P3 in parallel with yet another universe of Deep Cells, and so on.

Deep Cell is available from http://psychoticdeath.com/life.htm.

:density The density of a pattern is the limit of the proportion of live cells in a (2n+1)x(2n+1) square centred on a particular cell as n tends to infinity, when this limit exists. (Note that it does not make any difference what cell is chosen as the centre cell. Also note that if the pattern is finite then the density is zero.) There are other definitions of density, but this one will do here.

In 1994 Noam Elkies proved that the maximum density of a stable pattern is 1/2, which had been the conjectured value. See the paper listed in the bibliography. Marcus Moore provided a simpler proof in 1995, and in fact proves that a still life with an m x n bounding box has at most (mn+m+n)/2 cells.

But what is the maximum average density of an oscillating pattern? The answer is conjectured to be 1/2 again, but this remains unproved. The best upper bound so far obtained is 8/13 (Hartmut Holzwart, September 1992).

The maximum possible density for a phase of an oscillating pattern is also unknown. An example with a density of 3/4 is known (see agar), but densities arbitrarily close to 1 may perhaps be possible.

:D-heptomino = Herschel

:diamond = tub

:diamond ring (p3) Found by Dave Buckingham in 1972.

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

:diehard Any pattern that vanishes, but only after a long time. The following example vanishes in 130 generations, which is probably the limit for patterns of 7 or fewer cells. Note that there is no limit for higher numbers of cells - e.g., for 8 cells we could have a glider heading towards an arbitrarily distant blinker.

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

:dinner table (p12) Found by Robert Wainwright in 1972.

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

:dirty Opposite of clean. A reaction which produces a large amount of complicated junk which is difficult to control or use is said to be dirty. Many basic puffer engines are dirty and need to be tamed by accompanying spaceships in order to produce clean output.

:diuresis (p90) Found by David Eppstein in October 1998. His original stabilization used pentadecathlons. The stabilization with complicated still lifes shown here (in two slightly different forms) was found by Dean Hickerson the following day. The name is due to Bill Gosper (see kidney).

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

:dock The following induction coil.

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

:domino The 2-cell polyomino. A number of objects, such as the HWSS and pentadecathlon, produce domino sparks.

:do-see-do The following reaction, found by David Bell in 1996, in which two gliders appear to circle around each other as they are reflected 90 degrees by a twin bees shuttle. Four copies of the reaction can be used to create a p92 glider loop which repeats the do-see-do reaction forever.

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

:double-barrelled Of a gun, emitting two streams of spaceships (or rakes). See B-52 bomber for an example.

:double block reaction A certain reaction that can be used to stabilize the twin bees shuttle (qv). This was discovered by David Bell in October 1996.

The same reaction sometimes works in other situations, as shown in the following diagram where a pair of blocks eats an R-pentomino and a LWSS. (The LWSS version was known at least as early 1994, when Paul Callahan saw it form spontaneously as a result of firing a LWSS stream at some random junk.)

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

:double caterer (p3) Found by Dean Hickerson, October 1989. Compare caterer and triple caterer.

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

:double ewe (p3) Found by Robert Wainwright before September 1971.

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

:double wing = moose antlers

:dove The following induction coil.

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

:down boat with tail = cis-boat with tail

:dragon (c/6 orthogonally, p6) This spaceship, discovered by Paul Tooke in April 2000, was the first known c/6 spaceship. All other known orthogonal c/6 spaceships are flotillas involving at least two dragons.

    .............O..OO......O..OOO
    .....O...OOOO.OOOOOO....O..OOO
    .OOOOO....O....O....OOO.......
    O......OO.O......OO.OOO..O.OOO
    .OOOOO.OOO........OOOO...O.OOO
    .....O..O..............O......
    ........OO..........OO.OO.....
    ........OO..........OO.OO.....
    .....O..O..............O......
    .OOOOO.OOO........OOOO...O.OOO
    O......OO.O......OO.OOO..O.OOO
    .OOOOO....O....O....OOO.......
    .....O...OOOO.OOOOOO....O..OOO
    .............O..OO......O..OOO

:drain trap = paperclip

:drifter A perturbation moving within a stable pattern. Dean Hickerson has written a program to search for drifters, with the hope of finding one which could be moved around a track. Because drifters can be very small, they could be packed more tightly than Herschels, and so allow the creation of oscillators of periods not yet attained, and possibly prove that Life is omniperiodic. Hickerson has found a number of components towards this end, but it has proved difficult to change the direction of movement of a drifter, and so far no complete track has been found. However, Hickerson has had success using the same search program to find eaters with novel properties, such as that used in diuresis.

:dual 1-2-3-4 = Achim's p4

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