From LifeWiki
(Redirected from Color of a glider)
Jump to navigation Jump to search
Pattern type Spaceship
Number of cells 5
Bounding box 3 × 3
Frequency class 1.8
Direction Diagonal
Period 4
Mod 2
Speed c/4 | c/4
Heat 4
Discovered by Richard K. Guy
Year of discovery 1969
For other meanings of the term 'glider', see Glider (disambiguation).
For other uses of 'G', see G (induction coil).

The glider (or featherweight spaceship[1]) 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.

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.[2]


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:[3]

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

The glider is often produced by randomly-generated starting patterns;[4] it is the fourth most common object on Adam P. Goucher's Catagolue.[5]

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.[6] Glider syntheses have been found for many still lifes, oscillators and spaceships, and an up-to-date list can be found on Catagolue.

Of gliders

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.[7]

An example of a colour-preserving reflector is the bumper. An example of a colour-changing reflector is the bouncer.

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.

See also


  1. "Featherweight spaceship". The Life Lexicon. Stephen Silver. Retrieved on December 3, 2018.
  2. "Does John Conway hate using Game of Life?". Numberphile (3 Mar 2014). Retrieved on 13 Jun 2016.
  3. Siobhan Roberts (2015), Genius at Play: The Curious Mind of John Horton Conway, Bloomsbury, pp. 125-126, ISBN 978-1-62040-593-2
  4. "Spontaneous appeared Spaceships out of Random Dust". Achim Flammenkamp (December 9, 1995). Retrieved on February 27, 2009.
  5. Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
  6. "Glider synthesis". The Life Lexicon. Stephen Silver. Retrieved on May 21, 2009.
  7. "Colour of a glider". The Life Lexicon. Stephen Silver. Retrieved on April 22, 2009.

External links