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

Introduction | Bibliography

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

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

:IMG = intermitting glider gun

:Immigration A form of colorized Life in which there are two types of ON cell, a newly-born cell taking the type of the majority of its three parent cells and surviving cells remaining of the same type as in the previous generation.

:induction coil Any object used to stabilize an edge (or edges) without touching. The tubs used in the Gray counter are examples, as are the blocks and snakes used in the Hertz oscillator and the heptomino at the bottom of the mathematician.

:inductor Any oscillator with a row of dead cells down the middle and whose two halves are mirror images of one another, both halves being required for the oscillator to work. The classic examples are the pulsar and the tumbler. If still lifes are considered as p1 oscillators then there are numerous simple examples such as table on table, dead spark coil and cis-mirrored R-bee. Some spaceships, such as the brain, the snail and the spider use the same principle.

:infinite glider hotel A pattern by David Bell, named after Hilbert's "infinite hotel" scenario in which a hotel with an infinite number of rooms has room for more guests even if it is already full, simply by shuffling the old guests around.

In this pattern, two pairs of Corderships moving at c/12 are pulling apart such that there is an ever-lengthening glider track between them. Every 128 generations another glider is injected into the glider track, joining the gliders already circulating there. The number of gliders in the track therefore increases without limit.

The tricky part of this construction is that even though all the previously injected gliders are repeatedly flying through the injection point, that point is guaranteed to be empty when it is time for the next glider to be injected.

:infinite growth Growth of a finite pattern such that the population tends to infinity, or at least is unbounded. Sometimes the term is used for growth of something other than population (for example, length), but here we will only consider infinite population growth. The first known pattern with infinite growth in this sense was the Gosper glider gun.

An interesting question is: What is the minimum population of a pattern that exhibits infinite growth? In 1971 Charles Corderman found that a switch engine could be stabilized by a pre-block in a number of different ways, giving 11-cell patterns with infinite growth. This record stood for more than quarter of a century until Paul Callahan found, in November 1997, two 10-cell patterns with infinite growth. The following month he found the one shown below, which is much neater, being a single cluster. This produces a stabilized switch engine of the block-laying type.

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

Nick Gotts and Paul Callahan have also shown that there is no infinite growth pattern with fewer than 10 cells, so that the question has now been answered.

Also of interest is the following pattern (again found by Callahan), which is the only 5x5 pattern with infinite growth. This too emits a block-laying switch engine.

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

Following a conjecture of Nick Gotts, Stephen Silver produced, in May 1998, a pattern of width 1 which exhibits infinite growth. This pattern was very large (12470x1 in the first version, reduced to 5447x1 the following day). In October 1998 Paul Callahan did an exhaustive search, finding the smallest example, the 39x1 pattern shown below. This produces two block-laying switch engines, stability being achieved at generation 1483.

    OOOOOOOO.OOOOO...OOO......OOOOOOO.OOOOO

Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other types of growth rate are possible, quadratic growth (see breeder) being the fastest. Dean Hickerson has found many patterns with unusual growth rates, such as sawtooths and a caber tosser.

See also Fermat prime calculator.

:initials = monogram

:inline inverter The following reaction in which a p30 gun can be used to invert the presence or absence of gliders in a p30 stream, with the output glider stream being in the same direction as the input glider stream.

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

:integral = integral sign

:integral sign (p1)

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

:intentionless = elevener

:interchange (p2) A common formation of six blinkers.

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

:intermitting glider gun Despite the name, an intermitting glider gun (IMG) is more often an oscillator than a gun. There are two basic types. A type 1 IMG consists of two guns firing at one another in such a way that each gun is temporarily disabled on being hit by a glider from the other gun. A type 2 IMG consists of a single gun firing at a 180-degree glider reflector in such a way that returning gliders temporarily disable the gun.

Both types of IMG can be used to make glider guns of periods that are multiples of the base period. This is done by firing another gun across the two-way intermittent glider stream of the IMG in such a way that gliders only occasionally escape.

:island The individual polyplets of which a stable pattern consists are sometimes called islands. So, for example, a boat has only one island, while an aircraft carrier has two, a honey farm has four and the standard form of the eater3 has five.

:Iwona (stabilizes at time 28786) The following methuselah found by Andrzej Okrasinski in August 2004.

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

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