Glider synthesis

Glider synthesis (or glider construction) 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 for all still lifes and known oscillators with at most 14 cells were found by David Buckingham.

Syntheses of note

A 3-glider synthesis of a pentadecathlon.

Perhaps the most interesting glider syntheses are those of spaceships, because these can be used to create corresponding guns and rakes. Many of the c/2 spaceships that are based on standard spaceships have been synthesized, mostly by Mark Niemiec. In June 1998, Stephen Silver found syntheses for some of the Corderships (although it was not until July 1999 that Jason Summers used this to build a Cordership gun). In May 2000, Noam Elkies suggested that a 2c/5 spaceship found by Tim Coe in May 1996 might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March 2003 that Summers and Elkies managed to find a way perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in Life of a rake which fires spaceships that travel in the same direction as the rake but more slowly.

A 3-glider synthesis of a pentadecathlon was found in April 1997 by Heinrich Koenig, which came as a surprise because it was widely assumed that anything using just three gliders would already be known.

2-glider syntheses

There are 71 distinct 2-glider collisions, 28 of which produce nothing, six of which produce a block, five of which produce a honey farm, three of which produce a B-heptomino, three of which produce a pi-heptomino, three of which produce a blinker, three of which produce a traffic light, two of which produce a glider, two of which produce a pond, two of which produce a loaf and a blinker, one of which produces a boat, one of which produces a beehive, one of which produces a loaf, one of which produces an eater 1, one of which produces lumps of muck, one of which produces a teardrop, one of which produces an interchange, one of which produces a traffic light and a glider, one of which produces an octomino, one of which produces a bi-block, one of which produces four blocks, one of which produces two block, one of which produces a blinker, loaf, tub and block, and one of which produces a mess consisting of four gliders, eight blinkers (including a traffic light), four blocks, a beehive and a ship.

All 71 such syntheses can be seen below in a pattern put together by Jason Summers on January 29, 2005.

All 71 distinct 2-glider collisions, arranged by what they synthesize.
Manipulate via Java: click here
Download RLE: click here

See also

• List of known glider syntheses

External links

• Glider synthesis at the Life Lexicon