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'''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 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 life]]s and known [[oscillator]]s with at most 14 [[cell]]s were found by [[:Category:Patterns found by David Buckingham|David Buckingham]].
Glider syntheses for all [[still life]]s and known [[oscillator]]s with at most 14 [[cell]]s were found by [[:Category:Patterns found by David Buckingham|David Buckingham]]. A collaborative effort then completed glider syntheses of all still lifes with 17 or fewer cells in 2014.<ref>{{cite web|url=http://pentadecathlon.com/lifeNews/2014/05/constructions_known_for_all_st.html |title=Constructions Known for All Still Lifes up to 17 Bits |work=Game of Life News |publisher=Dave Greene |accessdate=September 17, 2014}}</ref><ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1276 |title=17-bit SL Syntheses (100% Complete!) |work=ConwayLife.com forums |publisher=Martin Grant|accessdate=September 17, 2014}}</ref>
 
==Features of syntheses==
Four main characterizing features of a synthesis are the ''geometry'', ''reaction speed'', ''reaction multiplicity''<!--or is there a more standard term?-->, and ''glider cost''.
 
The '''geometry''' is the number of directions of incoming gliders:
* four-directional: gliders collide from all four directions
* three-directional: gliders collide from all directions but one
* two-directional; further divisible in head-on and 90° syntheses. All two-glider syntheses are necessarily two-directional.
* unidirectional, which assumes the initial presence of a '''target''' (usually a [[still life]] or an [[oscillator]]) to be hit with gliders.
Since gliders are themselves glider-constructible, any multidirectional synthesis can be technically downgraded to a fewer-directional one, usually at the cost of increasing the speed, multiplicity and cost of the synthesis. More challenging is finding a two- or three-directional synthesis for a particular object where few or no parts of the synthesis reactions extend outside the final pattern's [[bounding box]] in a particular direction. This is especially important for the synthesis of temporary catalysts, which will need to be placed sometimes quite close to other components without perturbing them. For especially tight locations, sometimes it will be useful to construct an [[LWSS]] (or another standard c/2 spaceship) some ways away from the synthesis nexus and let that collide with a glider in the final stages; this allows synthesis at a 45° angle, rather than a 90° angle as required for synthesis by gliders from separate directions.
 
The '''speed''' is simply the number of [[generation]]s it takes to complete a synthesis. For multi-stage syntheses, each stage has its own speed.
 
The '''multiplicity''' is the number of stages a synthesis operates in. Often a particular synthesis operation cannot be achieved by a direct collision of gliders, and a synthesis procedure instead requires first synthesizing a number of [[catalyst]]s, and then hitting these with gliders to produce the final result.
 
The '''cost''' is the number of gliders expended over the course of the synthesis. Much as speed, it can be defined also for individual synthesis stages.
 
Of particular interest is [[salvo|slow salvo synthesis]]: unidirectional synthesis where every stage has a glider cost of one. Perhaps surprisingly, anything that is glider synthesizable is also slow salvo synthesizable; a result that crucially depends on the existence of [[movable target]]s and [[splitter]]s.


==Syntheses of note==
==Syntheses of note==
[[Image:glider_synth_pentadecathlon.png|framed|right|A 3-glider synthesis of a [[pentadecathlon]].]]Perhaps the most interesting glider syntheses are those of [[spaceship]]s, because these can be used to create corresponding [[gun]]s and [[rake]]s. Many of the [[:Category:Spaceships with speed c/2|c/2]] spaceships that are based on standard spaceships have been synthesized, mostly by [[:Category:Patterns found by Mark Niemiec|Mark Niemiec]]. In June [[:Category:Patterns found in 1998|1998]], [[:Category:Patterns found by Stephen Silver|Stephen Silver]] found syntheses for some of the [[Cordership]]s (although it was not until July [[:Category:Patterns found in 1999|1999]] that [[:Category:Patterns found by Jason Summers|Jason Summers]] used this to build a Cordership gun). In May [[:Category:Patterns found in 2000|2000]], [[:Category:Patterns found by Noam Elkies|Noam Elkies]] suggested that a [[:Category:Spaceships with speed 2c/5|2c/5]] spaceship found by [[:Category:Patterns found by Tim Coe|Tim Coe]] in May [[:Category:Patterns found in 1996|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 [[:Category:Patterns found in 2003|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 [[Conway's Game of Life|Life]] of a rake which fires spaceships that travel in the same direction as the rake but more slowly.
[[Image:glider_synth_pentadecathlon.png|framed|right|A 3-glider synthesis of a [[pentadecathlon]].]]


A 3-glider synthesis of a [[pentadecathlon]] was found in April [[:Category:Patterns found in 1997|1997]] by [[:Category:Patterns found by Heinrich Koenig|Heinrich Koenig]], which came as a surprise because it was widely assumed that anything using just three gliders would already be known.
A 3-glider synthesis of a [[pentadecathlon]] was found in April [[:Category:Patterns found in 1997|1997]] by [[:Category:Patterns found by Heinrich Koenig|Heinrich Koenig]], which came as a surprise because it was widely assumed that anything using just three gliders would already be known.
===Spaceship syntheses===
Perhaps the most interesting glider syntheses are those of [[spaceship]]s, because these can be used to create corresponding [[gun]]s and [[rake]]s. Many of the [[:Category:Spaceships with speed c/2|c/2]] spaceships that are based on standard spaceships have been synthesized, mostly by [[:Category:Patterns found by Mark Niemiec|Mark Niemiec]]. In June [[:Category:Patterns found in 1998|1998]], [[:Category:Patterns found by Stephen Silver|Stephen Silver]] found syntheses for some of the [[Cordership]]s (although it was not until July [[:Category:Patterns found in 1999|1999]] that [[:Category:Patterns found by Jason Summers|Jason Summers]] used this to build a Cordership gun).  Many larger Corderships also have known glider syntheses, and others could easily be generated using the same techniques.  In general, larger Corderships have declined in importance after the discovery of four-, three- and two-engine versions.
In May [[:Category:Patterns found in 2000|2000]], [[Noam Elkies]] suggested that a [[:Category:Spaceships with speed 2c/5|2c/5]] spaceship ([[60P5H2V0]]) found by [[:Category:Patterns found by Tim Coe|Tim Coe]] in May [[:Category:Patterns found in 1996|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 [[:Category:Patterns found in 2003|2003]] that Summers and Elkies managed to find a way to 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 [[Conway's Game of Life|Life]] of a rake which fires spaceships that travel in the same direction as the rake but more slowly.
After the [[loafer]] was discovered and synthesized in 2013, a number of new spaceship syntheses were found during a short period of time in late 2014 and early 2015, including the [[dart]], [[crab]], [[25P3H1V0.2]], [[30P5H2V0]], [[x66]], and [[weekender]].  Most of this was due to the work of [[:Category:Patterns found by Martin Grant|Martin Grant]].
{| class="wikitable"
! rowspan="2" | Name !! colspan="2" | First synthesis !! Best current synthesis
|-
! Date !! Discoverer !! Fewest gliders
|-
| [[25P3H1V0.1]] || 2015-01-06 || [[Martin Grant]] || 47
|-
| [[25P3H1V0.2]] || 2017-12-15 || [[Martin Grant]] || 26
|-
| [[30P5H2V0]] || 2015-01-01 || [[Martin Grant]] || 65
|-
| [[30P4H2V0.4]] || 2015-09-10 || [[Tanner Jacobi]] || 85
|-
| [[60P5H2V0]] || 2003-03-17 || [[Noam Elkies]] || 61
|-
| [[2-engine Cordership]] || 2017-12-31 || [[Dave Greene]] || 9
|-
| [[B29]] || 2015-04-06 || [[Tanner Jacobi]] || 25
|-
| [[copperhead]] || 2016-03-05 || [[Aidan F. Pierce]] || 14
|-
| [[crab]] || 2014-12-26 || [[Martin Grant]] || 18
|-
| [[dart]] || 2014-12-02 || [[Martin Grant]] || 25
|-
| [[fireship]] || 2016-03-21 || Nico Brown || 18
|-
| half-[[X66]] with [[HWSS]] || 2015-03-08 || [[Chris Cain]] || 9
|-
| [[loafer]] || 2013-02-17 || [[Adam P. Goucher]] || 8
|-
| [[puffership]] || 2015-02-11 || [[Chris Cain]] || 60
|-
| [[Pushalong 1]] || 2015-06-12 || [[Martin Grant]] || 77
|-
| [[weekender]] || 2015-01-25 || [[Martin Grant]] || 79
|-
| [[x66]] || 2015-01-11 || [[Martin Grant]] || 12
|-
| [[0hd Demonoid]] || 2015-12-06 || [[Chris Cain]] || 12,016
|-
| [[Orthogonoid]] || 2017-12-30 || [[Dave Greene ]] || 103,853
|-
| [[Parallel HBK]] || 2014-12-31 || [[Michael Simkin]] || 38,380
|-
| [[Gemini]] || 2015-02-16 || [[Dave Greene]] || 173,449
|}


===2-glider syntheses===
===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 [[Polyomino#Octominoes|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]].
There are 71 distinct 2-glider collisions, of which 28 produce nothing, six produce a [[block]], five produce a [[honey farm]], three produce a [[B-heptomino]], three produce a [[pi-heptomino]], three produce a [[blinker]], three produce a [[traffic light]], two produce a [[glider]], two produce a [[pond]], two produce a [[loaf]] and a [[blinker]], one produces a [[boat]], one produces a [[beehive]], one produces a [[loaf]], one produces an [[eater 1]], one produces [[lumps of muck]], one produces a [[teardrop]], one produces an [[interchange]], one produces a traffic light and a glider, one produces an [[Polyomino#Octominoes|octomino]], one produces a [[bi-block]], one produces four blocks, one produces two blocks, one produces a blinker, loaf, [[tub]] and block, and one produces the so-called [[two-glider mess]], a [[methuselah]] stabilizing after 530 generations and 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 [[:Category:Patterns found by Jason Summers|Jason Summers]] on January 29, [[:Category:Patterns found in 2005|2005]].
All 71 such syntheses can be seen below in a pattern put together by [[:Category:Patterns found by Jason Summers|Jason Summers]] on January 29, [[:Category:Patterns found in 2005|2005]].


[[Image:2glidersyntheses.png|framed|center|All 71 distinct 2-glider collisions, arranged by what they synthesize.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=twoglidersyntheses click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=twoglidersyntheses.rle click here] ]]
[[Image:2glidersyntheses.png|framed|center|All 71 distinct 2-glider collisions, arranged by what they synthesize.<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/patterns/twoglidersyntheses.rle click here] ]]


==See also==
==See also==
*[[:Category:Pattern_constructible_by_a_given_number_of_gliders|List of known glider syntheses]]
*[[:Category:Pattern_constructible_by_a_given_number_of_gliders|List of known glider syntheses]]
*[[Salvo]]
==References==
<references />


==External links==
==External links==
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{{LinkWeisstein|GliderSynthesis.html}}
{{LinkWeisstein|GliderSynthesis.html}}
{{LinkLexicon|lex_g.htm#glidersynthesis}}
{{LinkLexicon|lex_g.htm#glidersynthesis}}
*[http://home.interserv.com/~mniemiec/objcost.htm Life Objects Sorted by Cost in Gliders] at [[Mark Niemiec]]'s webpage

Revision as of 21:50, 15 January 2018

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. A collaborative effort then completed glider syntheses of all still lifes with 17 or fewer cells in 2014.[1][2]

Features of syntheses

Four main characterizing features of a synthesis are the geometry, reaction speed, reaction multiplicity, and glider cost.

The geometry is the number of directions of incoming gliders:

  • four-directional: gliders collide from all four directions
  • three-directional: gliders collide from all directions but one
  • two-directional; further divisible in head-on and 90° syntheses. All two-glider syntheses are necessarily two-directional.
  • unidirectional, which assumes the initial presence of a target (usually a still life or an oscillator) to be hit with gliders.

Since gliders are themselves glider-constructible, any multidirectional synthesis can be technically downgraded to a fewer-directional one, usually at the cost of increasing the speed, multiplicity and cost of the synthesis. More challenging is finding a two- or three-directional synthesis for a particular object where few or no parts of the synthesis reactions extend outside the final pattern's bounding box in a particular direction. This is especially important for the synthesis of temporary catalysts, which will need to be placed sometimes quite close to other components without perturbing them. For especially tight locations, sometimes it will be useful to construct an LWSS (or another standard c/2 spaceship) some ways away from the synthesis nexus and let that collide with a glider in the final stages; this allows synthesis at a 45° angle, rather than a 90° angle as required for synthesis by gliders from separate directions.

The speed is simply the number of generations it takes to complete a synthesis. For multi-stage syntheses, each stage has its own speed.

The multiplicity is the number of stages a synthesis operates in. Often a particular synthesis operation cannot be achieved by a direct collision of gliders, and a synthesis procedure instead requires first synthesizing a number of catalysts, and then hitting these with gliders to produce the final result.

The cost is the number of gliders expended over the course of the synthesis. Much as speed, it can be defined also for individual synthesis stages.

Of particular interest is slow salvo synthesis: unidirectional synthesis where every stage has a glider cost of one. Perhaps surprisingly, anything that is glider synthesizable is also slow salvo synthesizable; a result that crucially depends on the existence of movable targets and splitters.

Syntheses of note

A 3-glider synthesis of a pentadecathlon.

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.

Spaceship syntheses

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). Many larger Corderships also have known glider syntheses, and others could easily be generated using the same techniques. In general, larger Corderships have declined in importance after the discovery of four-, three- and two-engine versions.

In May 2000, Noam Elkies suggested that a 2c/5 spaceship (60P5H2V0) 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 to 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.

After the loafer was discovered and synthesized in 2013, a number of new spaceship syntheses were found during a short period of time in late 2014 and early 2015, including the dart, crab, 25P3H1V0.2, 30P5H2V0, x66, and weekender. Most of this was due to the work of Martin Grant.

Name First synthesis Best current synthesis
Date Discoverer Fewest gliders
25P3H1V0.1 2015-01-06 Martin Grant 47
25P3H1V0.2 2017-12-15 Martin Grant 26
30P5H2V0 2015-01-01 Martin Grant 65
30P4H2V0.4 2015-09-10 Tanner Jacobi 85
60P5H2V0 2003-03-17 Noam Elkies 61
2-engine Cordership 2017-12-31 Dave Greene 9
B29 2015-04-06 Tanner Jacobi 25
copperhead 2016-03-05 Aidan F. Pierce 14
crab 2014-12-26 Martin Grant 18
dart 2014-12-02 Martin Grant 25
fireship 2016-03-21 Nico Brown 18
half-X66 with HWSS 2015-03-08 Chris Cain 9
loafer 2013-02-17 Adam P. Goucher 8
puffership 2015-02-11 Chris Cain 60
Pushalong 1 2015-06-12 Martin Grant 77
weekender 2015-01-25 Martin Grant 79
x66 2015-01-11 Martin Grant 12
0hd Demonoid 2015-12-06 Chris Cain 12,016
Orthogonoid 2017-12-30 Dave Greene 103,853
Parallel HBK 2014-12-31 Michael Simkin 38,380
Gemini 2015-02-16 Dave Greene 173,449

2-glider syntheses

There are 71 distinct 2-glider collisions, of which 28 produce nothing, six produce a block, five produce a honey farm, three produce a B-heptomino, three produce a pi-heptomino, three produce a blinker, three produce a traffic light, two produce a glider, two produce a pond, two produce a loaf and a blinker, one produces a boat, one produces a beehive, one produces a loaf, one produces an eater 1, one produces lumps of muck, one produces a teardrop, one produces an interchange, one produces a traffic light and a glider, one produces an octomino, one produces a bi-block, one produces four blocks, one produces two blocks, one produces a blinker, loaf, tub and block, and one produces the so-called two-glider mess, a methuselah stabilizing after 530 generations and 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.
Download RLE: click here

See also

References

  1. "Constructions Known for All Still Lifes up to 17 Bits". Game of Life News. Dave Greene. Retrieved on September 17, 2014.
  2. "17-bit SL Syntheses (100% Complete!)". ConwayLife.com forums. Martin Grant. Retrieved on September 17, 2014.

External links

Template:LinkWeisstein