Glider

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Glider
bob$2bo$3o! #C [[ THEME 6 GRID GRIDMAJOR 0 THUMBLAUNCH AUTOSTART ]] #C [[ TRACKLOOP 4 1/4 1/4 THUMBSIZE 3 GPS 4 ]]
Pattern type Spaceship
Number of cells 5
Bounding box 3×3
Direction Diagonal
Period 4
Mod 2
Speed c/4
Heat 4
Discovered by Richard K. Guy
Year of discovery 1970
For other meanings of the term 'glider', see Glider (disambiguation).

The glider (or featherweight spaceship) is the smallest, most common, and first-discovered spaceship. It travels diagonally across the Life grid at a speed of c/4. Gliders are important because they are easily produced (for an example see the Gosper glider gun), can be collided with each other to form more complicated objects (see glider synthesis), and can be used to transmit information over long distances.

Its name is due in part to the fact that it is glide symmetric; however, John Conway has stated he regrets calling it a glider, saying it looks more like an ant walking across the plane.[1]

Discovery

The glider was found by Richard K. Guy in 1970 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:[2]

[...] 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. [...]

Commonness

The glider is often produced by randomly-generated starting patterns;[3] it is the fourth most common object on Adam P. Goucher's Catagolue.[4]

Glider synthesis

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.[5]

Glider syntheses for all still lifes with at most 18 cells[6][7] and known oscillators with at most 14 cells have been explicitly constructed.

Colour of a glider

The colour (or parity) of a glider is a property of the glider which remains constant while the glider is moving along a straight path, but which can be changed 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 white, and all other cells to be black or white in a checkerboard pattern (i.e. the cell with coordinates (m,n) is white if m+n is even, and black otherwise). Then the colour of a glider is the colour of its leading cell when it is in a phase which can be rotated to look like this image.

A reflector which does not change the colour of gliders obviously can not 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.[8]

See also

References

  1. "Does John Conway hate using Game of Life?". Numberphile (3 Mar 2014). Retrieved on 13 Jun 2016.
  2. Siobhan Roberts (2015), Genius at Play: The Curious Mind of John Horton Conway, Bloomsbury, pp. 125-126, ISBN 978-1-62040-593-2
  3. "Spontaneous appeared Spaceships out of Random Dust". Achim Flammenkamp (December 9, 1995). Retrieved on February 27, 2009.
  4. Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
  5. "Glider synthesis". The Life Lexicon. Stephen Silver. Retrieved on May 21, 2009.
  6. "Constructions Known for All Still Lifes up to 17 Bits". Game of Life News. Dave Greene. Retrieved on September 17, 2014.
  7. "18-bit SL Syntheses (100% Complete!)".
  8. "Colour of a glider". The Life Lexicon. Stephen Silver. Retrieved on April 22, 2009.

External links

  • Glider at Eric Weisstein's Treasure Trove of Life
  • 5P4H1V1.1 at Heinrich Koenig's Game of Life Object Catalogs
  • Glider at Wikipedia