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:half bakery See bi-loaf.

:half fleet = ship-tie

:hammer To hammer a LWSS, MWSS or HWSS is to smash things into the rear end of it in order to transform it into a different type of spaceship. A hammer is the object used to do the hammering. In the following example by Dieter Leithner a LWSS is hammered by two more LWSS to make it into a MWSS.

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

:hammerhead A certain front end for c/2 spaceships. The central part of the hammerhead pattern is supported between two MWSS. The picture below shows a small example of a spaceship with a hammerhead front end (the front 9 columns).

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

:handshake An old MIT name for lumps of muck, from the following form (2 generations on from the stairstep hexomino):

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

:harbor (p5) Found by Dave Buckingham in September 1978. The name is by Dean Hickerson.

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

:harvester (c p4 fuse) Found by David Poyner, this was the first published example of a fuse. The name refers to the fact the it produces debris in the form of blocks which contain the same number of cells as the fuse has burnt up.

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

:hashlife A Life algorithm by Bill Gosper that is designed to take advantage of the considerable amount of repetitive behaviour in many large patterns of interest. This algorithm is described by Gosper in his paper listed in the bibliography at the end of this lexicon. Roughly speaking, the idea is to store subpatterns in a hash table so that the results of their evolution do not need to be recomputed if they arise again at some other place or time in the evolution of the full pattern. This does, however, mean that complex patterns can require substantial amounts of memory.

Hashlife provides a means of evolving repetitive patterns millions (or even billions or trillions) of generations further than normal Life algorithms can manage in a reasonable amount of time. It is not, however, suitable for showing a continuous display of the evolution of a pattern, because it works asynchronously - at any given moment it will usually have evolved different parts of the pattern through different numbers of generations.

:hassle See hassler.

:hassler An oscillator that works by hassling (repeatedly moving or changing) some object. For some examples, see Jolson, baker's dozen, toad-flipper, toad-sucker and traffic circle.

:hat (p1) Found in 1971. See also twinhat and sesquihat.

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

:heat For an oscillator or spaceship, the average number of cells which change state in each generation. For example, the heat of a glider is 4, because 2 cells are born and 2 die every generation.

For a period n oscillator with an r-cell rotor the heat is at least 2r/n and no more than r(1-(n mod 2)/n). For n=2 and n=3 these bounds are equal.

:heavyweight emulator = HW emulator

:heavyweight spaceship = HWSS

:heavyweight volcano = HW volcano

:hebdarole (p7) Found by Noam Elkies, November 1997. Compare fumarole. The smaller version shown below was found soon after by Alan Hensel using a component found by Dave Buckingham in June 1977. The top tens rows can be stabilized by their mirror image (giving an inductor) and this was the original form found by Elkies.

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

:hectic (p30) Found by Robert Wainwright in September 1984.

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

:Heisenburp device A pattern which can detect the passage of a glider without affecting the glider's path or timing. The first such device was constructed by David Bell in December 1992. The term is due to Bill Gosper.

The following is an example of the kind of reaction used at the heart of a Heisenburp device. The glider at bottom right alters the reaction of the other two gliders without itself being affected in any way.

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

:helix A convoy of standard spaceships used in a Caterpillar to move some piece of debris at the speed of the Caterpillar. The following diagram illustrates the idea.

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

:heptaplet Any 7-cell polyplet.

:heptapole (p2) The barberpole of length 7.

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

:heptomino Any 7-cell polyomino. There are 108 such objects. Those with names in common use are the B-heptomino, the Herschel and the pi-heptomino.

:Herschel (stabilizes at time 128) The following pattern which occurs at generation 20 of the B-heptomino.

	O..
	OOO
	O.O
	..O

:Herschel conduit A conduit that moves a Herschel from one place to another. See also Herschel loop.

Sixteen simple stable Herschel conduits are currently known, having been discovered from 1995 onwards by Dave Buckingham (DJB) and Paul Callahan (PBC). (Of course, the number depends on what is meant by "simple".) These are shown in the following table. In this table "steps" is the number of steps, "m" tells how the Herschel is moved (R = turned right, L = turned left, B = turned back, F = unturned, f = flipped), and "dx" and "dy" give the displacement of the centre cell of the Herschel (assumed to start in the orientation shown above).

	------------------------------------
	steps  m     dx   dy     discovery
	------------------------------------
	  64   R    -11    9   DJB, Sep 1995
	  77   Ff   -25   -8   DJB, Aug 1996
	 112   L    -12  -33   DJB, Jul 1996
	 116   F    -32    1   PBC, Feb 1997
	 117   F    -40   -6   DJB, Jul 1996
	 119   Ff   -20   14   DJB, Sep 1996
	 125   Bf     9  -17   PBC, Nov 1998
	 153   Ff   -48   -4   PBC, Feb 1997
	 156   L    -17  -41   DJB, Aug 1996
	 158   Ff   -27   -5   DJB, Jul 1996
	 166   F    -49    3   PBC, May 1997
	 176   Ff   -45    0   PBC, Oct 1997
	 190   R    -24   16   DJB, Jul 1996
	 200   Lf   -17  -40   PBC, Jun 1997
	 202   Rf    -7   32   DJB, May 1997
	 222   Bf     6  -16   PBC, Oct 1998
	------------------------------------

See also Herschel transceiver.

:Herschel loop A cyclic Herschel track. Although no loop of length less than 256 generations has been constructed it is possible to make oscillators of smaller periods by putting more than one Herschel in the track. In this way oscillators, and in most cases guns, of all periods from 54 onwards can now be constructed (although the p55 case is a bit strange, shooting itself with gliders in order to stabilize itself). See also emu and omniperiodic.

:Herschel receiver A pattern found by Paul Callahan in 1996, as part of the first stable glider reflector. Used as a receiver, it converts two parallel input gliders (with path separations of 2, 5, or 6) to an R-pentomino, which is then converted to a Herschel by one of two known mechanisms (the first of which was found by Dave Buckingham way back in 1972, and the second by Stephen Silver in October 1997). The version using Buckingham's R-to-Herschel converter is shown below.

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

:Herschel track A track for Herschels. See also B track.

:Herschel transceiver An adjustable Herschel conduit made up of a Herschel transmitter and a Herschel receiver. The intermediate stage consists of two gliders on parallel tracks, so the transmitter and receiver can be separated by any required distance. The conduit may be stable, or may contain low-period oscillators.

:Herschel transmitter Any Herschel-to-glider converter that produces two gliders on parallel tracks which can be used as input to a Herschel receiver. If the gliders are far enough apart, a suitably oriented mirror image of the receiver will also work: the first glider triggers the receiver and the second glider deletes the extra beehive.

The following diagram shows a stable Herschel transmitter found by Paul Callahan in May 1997:

	......OO...........
	.....O.O...........
	...OOO.............
	..O...O......O.....
	..OO.OO......OOO...
	.............O.O...
	...............O...
	...................
	...................
	OO.O...............
	O.OO...............
	...................
	...................
	...................
	...............OO..
	...............O...
	................OOO
	..................O
Examples of small reversible p6 and p7 transmitters are also known.

:Hertz oscillator (p8) Compare negentropy, and also cauldron. Found by Conway's group in 1970.

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

:hexadecimal = beehive and dock

:hexaplet Any 6-cell polyplet.

:hexapole (p2) The barberpole of length 6.

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

:hexomino Any 6-cell polyomino. There are 35 such objects. For some examples see century, stairstep hexomino, table, toad and Z-hexomino.

:H-heptomino Name given by Conway to the following heptomino. After one generation this is the same as the I-heptomino.

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

:hive = beehive

:hivenudger (c/2 orthogonally, p4) A spaceship found by Hartmut Holzwart in July 1992. (The name is due to Bill Gosper.) It consists of a pre-beehive escorted by four LWSS. In fact any LWSS can be replaced by a MWSS or a HWSS, so that there are 45 different single-hive hivenudgers.

	OOOO.....O..O
	O...O...O....
	O.......O...O
	.O..O...OOOO.
	.............
	.....OO......
	.....OO......
	.....OO......
	.............
	.O..O...OOOO.
	O.......O...O
	O...O...O....
	OOOO.....O..O
Wider versions can be made by stabilizing the front of the extended "pre-beehive", as in the line puffer shown below.
	.........O.O..................
	........O..O..................
	.......OO.....................
	......O...O...................
	.....OOO.O....................
	..OO..........................
	.O...OOOOO.......OOOO.....O..O
	O...O............O...O...O....
	O.....OO.........O.......O...O
	OOO...OOOO........O..O...OOOO.
	.O.......O....................
	.OO...................OO......
	.O.O..................OO......
	.OO..OO.O........O.O..OO......
	..O.OOO.O...O.OOOO.O..OO......
	.........OO.O.OO..O...OO...OOO
	....OOOOOO.OO...OOOO..OO...OOO
	.....O....OOO......O..OO...OOO
	......OO.....OO..OO...OO......
	.......O..O.....OOOO..OO......
	........O.O.OO.....O..OO......
	......................OO......
	..............................
	..................O..O...OOOO.
	.................O.......O...O
	.................O...O...O....
	.................OOOO.....O..O

:honeycomb (p1)

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

:honey farm (p1) A common formation of four beehives.

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

:hook Another term for a bookend. It is also used for other hook-shaped things, such as occur in the eater1 and the hook with tail, for example.

:hook with tail (p1) For a long time this was the smallest still life without a well-established name. It is now a vital component of the smallest known HWSS gun, where it acts as a rock.

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

:houndstooth agar The p2 agar that results from tiling the plane with the following pattern.

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

:house The following induction coil. It is generation 3 of the pi-heptomino. See spark coil and dead spark coil.

	.OOO.
	O...O
	OO.OO

:hustler (p3) Found by Robert Wainwright, June 1971.

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

:hustler II (p4)

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

:HW emulator (p4) Found by Robert Wainwright in June 1980. See also emulator.

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

:HWSS (c/2 orthogonally, p4) A heavyweight spaceship, the fourth most common spaceship. Found by Conway in 1970. See also LWSS and MWSS.

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

:HWSS emulator = HW emulator

:HW volcano (p5) A p5 domino sparker, found by Dean Hickerson in February 1995. There are at least two known forms for this, one of which is shown below.

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

:hybrid grey ship A grey ship containing more than one type of region of density 1/2, usually a combination of a with-the-grain grey ship and an against-the-grain grey ship.


Introduction | 1-9 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | Bibliography