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 colorised 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.

:independent conduit A Herschel conduit in which the input Herschel produces its first natural glider. Compare dependent conduit.

: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 that include this kind of central gutter, 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 (see LWSS-glider bounce), 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, created in a response to a $50 prize challenge by John Conway. Martin Gardner's October 1970 article described the challenge as "Conway conjectures that no pattern can grow without limit", but Conway later explained that he had always expected that this would be disproved. The original purpose in investigating CA rules including B3/S23 was to show that a very simple two-state rule could support a universal computer and/or universal constructor. If all finite patterns could be proven to be bounded, neither of these would be possible.

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 showed in October 1997 that there is no infinite growth pattern with fewer than 10 cells, so that question has now been answered.

In October 2014, Michael Simkin discovered a three-glider collision that produces a glider-producing stabilized switch engine and thus produces infinite growth from the smallest possible number of gliders (since all 71 2-glider collisions have a finite limit population).

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

Larger patterns have since been constructed that display quadratic growth.

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 also breeder) being the fastest. Dean Hickerson has found many patterns with unusual growth rates, such as sawtooths and a caber tosser. Another pattern with superlinear but non-quadratic growth is Gotts dots.

See also Fermat prime calculator.

:initials = monogram

:inject A reaction in which a hole in a regular spaceship stream is filled partially or fully by adding a new spaceship of the same type without affecting the existing spaceships in the stream. Depending on the period of the stream, different mechanisms can be used. For adding a spaceship to an existing multi-lane convoy, see inserter.

For large period glider streams, simple reactions such as LWSS-LWSS bounce and LWSS-glider bounce suffice. If Herschel technology is used, a large number of edge shooters and transparent conduits are known. Simple examples include the NW31 Herschel-to-glider converter and the Fx119 inserter.

Shown below is an injector found by Dave Buckingham that can fill a hole in a p15 glider stream:

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

For very low-period glider streams, a GIG is a much more efficient insertion method, in the sense that fewer synchronized signals are needed. However, it has been shown that colliding gliders can complete an insertion even into a single-glider gap in a period-14 stream.

: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......................

:inserter A mechanism that can add another spaceship into a stream or convoy of other spaceships without affecting the existing spaceships. For examples see Fx119 inserter, tee, GIG, clock insertion and inject.

: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..

:intermediate target A temporary product of a partial slow salvo, elbow operation, or glider synthesis. An intermediate target is a useful step toward a desired outcome, but will not appear in the final construction.

:intermittent stream A stream of spaceships which is based on a periodic stream, but which can contain holes where some of the spaceships are not present. There is a base period for the intermittent stream such that if a spaceship arrives at a specific location, then it always does so at a generation which is a multiple of the base period. For example, the output from a period 30 glider gun where every third glider is deleted is an intermittent stream. A pseudo-random glider generator can produce a complicated intermittent stream with no obvious pattern.

Intermittent streams can be used to transmit signals, where holes in the stream can also convey information. For example, the stream can be processed by an inverter having the same period.

: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 stream of gliders in the IMG in such a way that gliders only occasionally escape.

:inverter A device which can be used to invert the presence or absence of spaceships in an intermittent stream of spaceships. The device must be a gun whose period matches the base period of the stream, since if there are no input spaceships then the device must produce spaceships as the result of the inversion. Typically the spaceships are gliders, and the inverter is made from a glider gun. Inverters provide a way to produce a NOT logic operation on a stream.

There are several ways to produce an inverter. The simplest method is to simply hit the output of a gun with the input stream to delete its spaceships, producing an output stream that is always turned 90 degrees from the input stream. An example is the northernmost p30 gun in the glider duplicator example pattern. For one way to produce an inverted output stream which is not turned, see inline inverter.

:inverting reflector See inverter.

: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..................

It has a final population of 3091 and covers an area of 413 by 364 cells, not counting the 47 gliders it produces. Its ash consists of typical stable objects and blinkers, along with the relatively rare paperclip.

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