|View animated image|
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|Number of cells||5|
|Bounding box||3 × 3|
|Discovered by||Richard K. Guy|
|Year of discovery||1969|
- For other meanings of the term 'glider', see Glider (disambiguation).
The glider (or featherweight spaceship) is the smallest, most common, and first-discovered spaceship in Game of Life. It travels diagonally across the grid at a speed of c/4. Gliders are important because they are easily produced (by glider guns and rakes - for an example see the Gosper glider gun), can be collided with each other to form more complicated patterns (see glider synthesis), and can be used to transmit information over long distances.
The glider was found by Richard K. Guy in 1969 while Conway's group was attempting to track the evolution of the R-pentomino. It is often wrongly stated that John Conway discovered the glider, but Conway himself has said that it was Guy, a fact expounded in Conway's biography, Genius at Play:
|“||[…] They'd all head back to the department eventually and continue on the trail of the methuselah r-pentomino, hoping to happen upon an information stream. The Life computer program was still in the works, so frustration over their lack of success was exacerbated by the fact that the investigators were still working manually. Even 10 generations proved nearly impossible to document accurately without elaborate and diligent checks. In this regard, a force for good arrived in the form of Richard Guy, Mike's father, who visited nearly every summer. British-born, he had studied mathematics at Cambridge, spending much of his time playing and analyzing chess, composing endgame problems that he published in the British Chess Magazine. This led to his intensive games research, considered pivotal in the history of combinatorial game theory. He served in the Royal Air Force during the war and as a meteorologist in Iceland and Bermuda, then lectured for a time at the University of London, as well as in Singapore and in Delhi at the Indian Institute of Technology, before eventually landing at the University of Calgary. A precisian fellow—precise, careful, fastidious, conscientious—qualities of character that the Lifers on the whole lacked. Conway appointed him “blinker watcher,” a tedious task. He kept an accounting of blinkers and other debris that splintered off from center stage as the action in the spotlight evolved generation upon generation.
Late in the fall of 1969, as the group was still on the trail of the r-pentomino, the elder Guy's attention to detail paid off. The drama had been building since generation 27, when the scene split, stage left and stage right, each a microcosm of chaos unto itself. At generation 69, Guy noticed an animal that no one had ever seen before. It seemed to be wiggling, skittering, gliding its way diagonally across the board. He hollered to the others: “Come over here, there's a piece that's walking!” This was the first step toward proving Life universal. Conway christened this walking piece the “glider” (though now he wishes he'd called it the “ant”), because after two moves its position differs from the starting position by a “glide reflection,” a symmetry operation, and at generation 4 it looks exactly the same as it did at generation 0, but it has glided diagonally downward by a single place. […]
Historical note: An R-pentomino tracked past T=69 in late 1969 certainly implies that the glider, and a number of other objects such as blocks and blinkers, were first seen by Conway's group before 1970. However, for most objects it is difficult to pinpoint a definite date of discovery, so the LifeWiki and other sources traditionally use 1970 as the official figure for any objects known at the time of publication of Martin Gardner's first Scientific American article in October 1970. For many years Conway consistently "rounded up" his discovery of the Game of Life to 1970.
- Main article: List of common spaceships
- Main article: Glider synthesis
Glider synthesis is the construction of an object by means of glider collisions. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement. Glider syntheses have been found for many still lifes, oscillators and spaceships, and an up-to-date list can be found on Catagolue.
A glider can itself be synthesised with two input gliders in two ways referred to as kickback reactions.
There are also higher combinations of gliders that combine to output a greater amount of gliders than went in, which are known as over-unity reactions.
Colour of a glider
The colour of a glider is a property of the glider which remains constant while the glider is moving along a straight path, but which may change when the glider bounces off a reflector. It is an important consideration when building something using reflectors.
To define the colour of a glider, first choose some cell to be the origin. This cell is then considered to be black, and all other cells to be black or white in a checkerboard pattern (i.e. the cell with coordinates (m,n) is black if m+n is even, and white otherwise).
Then the colour of a glider is the colour of its leading cell when it is in the following phase:
Or the centre (or dot) cell for this phase:
This definition is the same for any rotated version of the above phases, but not for mirror-reflected versions. A reflected version has to be advanced by two ticks to bring it back to one of these "canonical" phases, which has the effect of moving the key cells to the opposite color.
A reflector which does not change the colour of gliders obviously cannot be used to move a glider onto a path of different colour than it started on. However, a 90-degree reflector which does change the colour of gliders is similarly limited, as the colour of the resulting glider will depend only on the direction of the glider, no matter how many reflectors are used. For maximum flexibility, therefore, both types of reflector are required.
The parity of a glider is the shape of it. Gliders come in 4 phases of 2 different shapes.
It is useful to know the parity for rephasing glider streams.
- Big glider
- Fake glider
- Glider duplicator
- Glider gun
- Infinite glider hotel
- Pure glider generator
- First natural glider
- "Featherweight spaceship". The Life Lexicon. Stephen Silver. Retrieved on December 3, 2018.
- "Does John Conway hate using Game of Life?". Numberphile (3 Mar 2014). Retrieved on 13 Jun 2016.
- Siobhan Roberts (2015), Genius at Play: The Curious Mind of John Horton Conway, Bloomsbury, pp. 125-126, ISBN 978-1-62040-593-2
- "Spontaneous appeared Spaceships out of Random Dust". Achim Flammenkamp (December 9, 1995). Retrieved on February 27, 2009.
- Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
- "Glider synthesis". The Life Lexicon. Stephen Silver. Retrieved on May 21, 2009.
- "Colour of a glider". The Life Lexicon. Stephen Silver. Retrieved on April 22, 2009.
- Glider at the Life Lexicon
- Life (B3/S23) at David Eppstein's Glider Database
- Glider at Adam P. Goucher's Catagolue
- The 1 five-bit spaceship at Mark D. Niemiec's Life Page
- 5P4H1V1.1 at Heinrich Koenig's Game of Life Object Catalogs
- Glider at Wikipedia