Difference between revisions of "Glider synthesis"

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{{Glossary}}
{{Glossary}}
'''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 (or else it is considered “not fully functional”). [[LWSS]]es, [[MWSS]]es and [[HWSS]]es can also be used in syntheses; these spaceships can themselves be easily synthesized from gliders at any point along their trajectory, so this conversion is often left as an implicit step.
'''Glider synthesis''' (or '''glider construction''') is the construction of an object by means of [[collision]]s of [[glider]]s and glider-constructible [[spaceship]]s. 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 (or else it is considered “not fully functional”). [[LWSS]]es, [[MWSS]]es and [[HWSS]]es can also be used in syntheses; these spaceships can themselves be easily synthesized from gliders at any point along their trajectory, so this conversion is often left as an implicit step.


==Features of syntheses==
==Features of syntheses==
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* three-directional: gliders collide from all directions but one
* 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.
* 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.
* unidirectional, which assumes the initial presence of a '''target''' (usually a [[still life]] or an [[oscillator]]) to be hit with gliders. Such syntheses are also known as [[slow salvo|slow]] or [[synchronized salvo]] syntheses.
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 construction time, cost, and/or number of stages needed for 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 [[bait]] objects, 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 distance 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.
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 construction time, cost, and/or number of stages needed for 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 [[bait]] objects, 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 distance 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.


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The '''cost''' is the number of gliders expended over the course of the synthesis. Similar to the construction time, it can be defined also for individual synthesis stages. A *WSS is considered to cost 3 gliders. The discovery of the [[reverse caber tosser]] in 2018 proved that there is a universal constant upper bound on the cost to synthesise any synthesisable object; currently, the best known upper bound is {{Reverse caber tosser/Lower bound}} gliders.
The '''cost''' is the number of gliders expended over the course of the synthesis. Similar to the construction time, it can be defined also for individual synthesis stages. A *WSS is considered to cost 3 gliders. The discovery of the [[reverse caber tosser]] in 2018 proved that there is a universal constant upper bound on the cost to synthesise any synthesisable object; currently, the best known upper bound is {{Reverse caber tosser/Lower bound}} gliders.


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, [[one-time]] [[turner]]s, and [[splitter]]s.
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 [[universal construction]] [[construction arm|arms]] as well as [[one-time]] [[turner]]s and [[splitter]]s.
 
An '''incremental synthesis''' is a synthesis with multiple stages. The '''final step''' (final stage, activation step/stage) of an incremental synthesis is the step that converts a previously constructed stationary object or constellation into the target object. Finding the final step of a synthesis is often a nontrivial, complicated process.<ref name="post149546">{{LinkForumThread
|format = ref
|p      = 149546
|title  = Re: Suggested LifeWiki edits
|author = Dave Greene
|date  = August 14, 2022
}}</ref><ref name="post160135">{{LinkForumThread
|format = ref
|p      = 160135
|title  = Re: Small Spaceship Syntheses
|author = Carson Cheng
|date  = April 6, 2023
}}</ref>


==Still life syntheses==
==Still life syntheses==
In the 1990s, glider syntheses for all [[still life]]s and known [[oscillator]]s with at most 14 [[cell]]s were found by [[David Buckingham]]. Almost all of these were successfully reduced to a synthesis cost of less than 1 glider per ON cell, or "1 glider per bit".<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=&p=21500#p20597 |title=Re: 4 glider syntheses |work=ConwayLife.com forums |author=Mark D. Niemiec|date=June 20, 2015|accessdate=February 21, 2018}}</ref>
In the 1990s, glider syntheses for all [[still life]]s and known [[oscillator]]s with at most 14 [[cell]]s were found by [[David Buckingham]]. Almost all of these were successfully reduced to a synthesis cost of less than 1 glider per ON cell, or "1 glider per bit".<ref>{{LinkForumThread|p=20597|title=Re: 4 glider syntheses|author=Mark D. Niemiec|date=June 20, 2015|format=ref}}</ref>
 
A collaborative effort ending in May 2014 completed glider syntheses of all still lifes with 17 or fewer cells.<ref>{{LinkGoLNews|2014/05/constructions_known_for_all_st.html|title=Constructions Known for All Still Lifes up to 17 Bits|author=Dave Greene|date=May 23, 2014|archivedate=20180806063633}}</ref><ref>{{LinkForumThread|f=2|t=1276|title=17-bit SL Syntheses (100% Complete!)|author=Martin Grant|date=January 6, 2014|format=ref}}</ref><ref name="post11972" />  A lengthy project to complete syntheses for all 18-bit still lifes was completed in October 2019.<ref name="post83979" /> The syntheses for 19-bit still lifes were completed in February 2020,<ref name="post89061" /> 20-bit still lifes in March 2021,<ref name="post125259" /> and 21-bit still lifes in November 2022.<ref name="post153564" /> Later optimization projects reduced the maximum cost of construction for 15-bit,<ref>{{LinkForumThread|f=2|t=2441|title=15 in 15: Efficient 15-bit Synthesis Project (DONE!)|author=BlinkerSpawn|date=October 27, 2016|format=ref}}</ref><ref name="post37438" /> 16-bit,<ref>{{LinkForumThread|f=2|t=2642|title=16 in 16: Efficient 16-bit Synthesis Project|author=Bob Shemyakin|date=December 20, 2016|format=ref}}</ref><ref name="post43734" /> and 17-bit<ref name="post82560" /> still lifes to less than one glider per bit, in November 2016, May 2017, and September 2019 respectively.


A collaborative effort ending in May 2014 completed glider syntheses of all still lifes with 17 or fewer cells.<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 |author=Dave Greene |date=May 23, 2014|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 |author=Martin Grant|date=January 6, 2014 |accessdate=September 17, 2014}}</ref><ref name="post11972" />  A second, longer effort claimed to have completed all the 18-bit still lifes in November 2014,<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1467#p13607 |title=18-bit SL Syntheses (100% Complete!)|work=ConwayLife.com forums |author=Martin Grant|date=October 2, 2014|accessdate=February 21, 2018}}</ref><ref name="post14272" /> but it was later found that some of these syntheses were erroneous.{{citation needed}} The project was finally completed for real in October 2019.<ref name="post83979" /> The syntheses for 19-bit still lifes were completed in February 2020.<ref name="post89061" /> Later optimization projects reduced the maximum cost of construction for 15-bit,<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2441|title=15 in 15: Efficient 15-bit Synthesis Project (DONE!)|work=ConwayLife.com forums |author=BlinkerSpawn|date=October 27, 2016|accessdate=February 21, 2018}}</ref><ref name="post37438" /> 16-bit,<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2642 |title=16 in 16: Efficient 16-bit Synthesis Project |work=ConwayLife.com forums |author=Bob Shemyakin|date=December 20, 2016|accessdate=February 21, 2018}}</ref><ref name="post43734" /> and 17-bit<ref name="post82560" /> still lifes to less than one glider per bit, in November 2016, May 2017, and September 2019 respectively.
In September 2020, the 17-glider reverse caber-tosser proved that all synthesizable still lifes could theoretically be constructed with no more than one glider per bit.<ref name="post104484" />


The following table displays the minimum, average, and maximum costs for strict still lifes with up to 20 cells as of February 8, 2020.<ref>{{CiteCatagolue|page=syntheses|title=Syntheses|accessdate=February 8, 2020}}</ref>
The following table displays statistics about the costs (excluding RCT constructions) for strict and pseudo still lifes with up to 21 cells as of November 15, 2022.<ref>{{CiteCatagolue|page=syntheses|title=Syntheses|accessdate=November 15, 2022}}</ref>


{| class="wikitable" style="text-align:center"
{| class="wikitable" style="text-align:center"
! Live cells !! Count<br>({{OEIS|A019473}}) !! Min. cost !! Avg. cost !! Max. cost
! rowspan=2 | Live cells !! colspan=4 | Strict still lifes !! colspan=3 | Pseudo still lifes
|-
! Count<br>({{OEIS|A019473}}) !! Min. cost !! Avg. cost !! Max. cost !! Count<br>({{OEIS|A056613}}) !! Min. cost !! Max. cost
|-
| 4 || {{A019473|4}} || 2 || 2.500 || 3 || {{A056613|4}} || – || –
|-
|-
| {{slcells|4}} || {{A019473|4}} || 2 || 2.500 || 3
| 5 || {{A019473|5}} || 2 || 2.000 || 2 || {{A056613|5}} || – || –
|-
|-
| {{slcells|5}} || {{A019473|5}} || 2 || 2.000 || 2
| 6 || {{A019473|6}} || 2 || 3.200 || 4 || {{A056613|6}} || – || –
|-
|-
| {{slcells|6}} || {{A019473|6}} || 2 || 3.200 || 4
| 7 || {{A019473|7}} || 2 || 2.750 || 4 || {{A056613|7}} || – || –
|-
|-
| {{slcells|7}} || {{A019473|7}} || 2 || 2.750 || 4
| 8 || {{A019473|8}} || 2 || 3.556 || 4 || {{A056613|8}} || 2 || 2
|-
|-
| {{slcells|8}} || {{A019473|8}} || 2 || 3.556 || 4
| 9 || {{A019473|9}} || 3 || 4.000 || 5 || {{A056613|9}} || 3 || 3
|-
|-
| {{slcells|9}} || {{A019473|9}} || 3 || 4.000 || 5
| 10 || {{A019473|10}} || 4 || 4.360 || 5 || {{A056613|10}} || 3 || 5
|-
|-
| {{slcells|10}} || {{A019473|10}} || 4 || 4.360 || 5
| 11 || {{A019473|11}} || 4 || 4.543 || 5 || {{A056613|11}} || 3 || 6
|-
|-
| {{slcells|11}} || {{A019473|11}} || 4 || 4.913 || 7
| 12 || {{A019473|12}} || 4 || 4.983 || 7 || {{A056613|12}} || 3 || 9
|-
|-
| {{slcells|12}} || {{A019473|12}} || 4 || 5.926 || 8
| 13 || {{A019473|13}} || 4 || 5.408 || 8 || {{A056613|13}} || 4 || 9
|-
|-
| {{slcells|13}} || {{A019473|13}} || 4 || 6.571 || 9
| 14 || {{A019473|14}} || 3 || 6.019 || 9 || {{A056613|14}} || 3 || 11
|-
|-
| {{slcells|14}} || {{A019473|14}} || 3 || 7.360 || 10
| 15 || {{A019473|15}} || 4 || 6.911 || 10 || {{A056613|15}} || 4 || 12
|-
|-
| {{slcells|15}} || {{A019473|15}} || 4 || 8.517 || 12
| 16 || {{A019473|16}} || 3 || 7.880 || 13 || {{A056613|16}} || 4 || style="background-color:#ffff80;" | 23{{refn|group=n|name=RCT}}{{refn|group=n|All but 3 16-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}}
|-
|-
| {{slcells|16}} || {{A019473|16}} || 3 || 9.585 || 14
| 17 || {{A019473|17}} || 4 || 9.117 || 15 || {{A056613|17}} || 4 || style="background-color:#ffff80;" | 18{{refn|group=n|name=RCT}}{{refn|group=n|All but 2 17-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}}
|-
|-
| {{slcells|17}} || {{A019473|17}} || 4 || 10.838 || 16
| 18 || {{A019473|18}} || 4 || 10.438 || style="background-color:#ffff80;" | 28{{refn|group=n|name=RCT|{{Reverse caber tosser/Lower bound}} gliders using the [[reverse caber-tosser]]}}{{refn|group=n|All but 128 18-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}} || {{A056613|18}}|| 4 || style="background-color:#ffff80;" | 48{{refn|group=n|name=RCT}}{{refn|group=n|All but 35 18-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}}
|-
|-
| {{slcells|18}} || {{A019473|18}} || 4 || 12.420 || style="background-color:#ff8080;" | 30
| 19 || {{A019473|19}} || 4 || 11.743 || style="background-color:#ffff80;" | 46{{refn|group=n|name=RCT}}{{refn|group=n|All but 1,200 19-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}} || {{A056613|19}} || 4 || style="background-color:#ffff80;" | 41{{refn|group=n|name=RCT}}{{refn|group=n|All but 54 19-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}}
|-
|-
| {{slcells|19}} || {{A019473|19}} || 4 || 14.098 || style="background-color:#ff8080;" | 76
| 20 || {{A019473|20}} || 4 || 13.207 || style="background-color:#ffff80;" | 113{{refn|group=n|name=RCT}}{{refn|group=n|All but 5,860 20-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}} || {{A056613|20}} || 4 || style="background-color:#ffff80;" | 73{{refn|group=n|name=RCT}}{{refn|group=n|All but 279 20-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}}
|-
|-
| {{slcells|20}} || {{A019473|20}} || 4 || colspan="2" style="background-color:#c0c0c0;" | 1,867 unsynthesized
| 21 || {{A019473|21}} || 5 || 14.876 || style="background-color:#ffff80;" | 115{{refn|group=n|name=RCT}}{{refn|group=n|All but 22,839 21-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.}} || {{A056613|21}} || colspan="2" style="background-color:#c0c0c0;" | {{refn|group=n|Only 82941 of 179011 21-bit pseudo still lifes are currently tabulated on Catagolue.}}
|}
|}


==Spaceship syntheses==
In January 2022, work by [[Ilkka Törmä]] and [[Ville Salo]] demonstrated [[Unique father problem|a still life]] with 306 cells that is impossible to synthesize with gliders, [[Unique father problem#Reduction|reduced]] by [[400spartans]] to 278 on September 4, {{year|2023}}, then 236 on March 12, {{year|2024}}, meaning there is a threshold <tt>21 < n &leq; 236</tt> such that not all still lifes with <tt>&geq; n</tt> cells are constructible.
 
<references group=n />
 
== 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 [[c/2]] spaceships that are based on standard spaceships have been synthesized, mostly by [[Mark Niemiec]]. In June {{year|1998}}, [[Stephen Silver]] found syntheses for some of the [[Cordership]]s (although it was not until July {{year|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.
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 [[c/2]] spaceships that are based on standard spaceships have been synthesized, mostly by [[Mark Niemiec]]. In June {{year|1998}}, [[Stephen Silver]] found syntheses for some of the [[Cordership]]s (although it was not until July {{year|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 {{year|2000}}, [[Noam Elkies]] suggested that [[60P5H2V0]], a [[2c/5]] spaceship found by [[Tim Coe]] in May {{year|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 {{year|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.
In May {{year|2000}}, [[Noam Elkies]] suggested that [[60P5H2V0]], a [[2c/5]] spaceship found by [[Tim Coe]] in May {{year|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 {{year|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 [[Martin Grant]].
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]].
Line 84: Line 110:
! Date !! Discoverer !! Fewest gliders
! Date !! Discoverer !! Fewest gliders
|-
|-
| [[60P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2003-03-17 || [[Noam Elkies]] || 46
| [[60P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2003-03-17 || [[Noam Elkies]] || 37
|-
|-
| [[loafer]] || data-sort-value="o 0.142857" | [[c/7 orthogonal]] || 2013-02-17 || [[Adam P. Goucher]] || 8
| [[loafer]] || data-sort-value="o 0.142857" | [[c/7 orthogonal]] || 2013-02-17 || [[Adam P. Goucher]] || 8
|-
|-
| [[dart]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2014-12-02 || [[Martin Grant]] || 25
| [[dart]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2014-12-02 || [[Ivan Fomichev]], [[Mark Niemiec]], [[Martin Grant]], [[Michael Simkin]] || 24
|-
|-
| [[crab]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2014-12-26 || [[Martin Grant]] || 16
| [[crab]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2014-12-26 || [[Brett Berger]], [[Martin Grant]], [[Tanner Jacobi]] || 14
|-
|-
| [[Parallel HBK]] || data-sort-value="oblique" | [[(6,3)c/245912]] || 2014-12-31 || [[Michael Simkin]] || 38,380
| [[Parallel HBK]] || data-sort-value="oblique" | [[(6,3)c/245912]] || 2014-12-31 || [[Michael Simkin]] || 38,380
|-
|-
| [[30P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2015-01-01 || [[Martin Grant]] || 47
| [[30P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2015-01-01 || [[Martin Grant]], [[Matthias Merzenich]], [[Tanner Jacobi]] || 39
|-
|-
| [[25P3H1V0.1]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] ||  2015-01-06 || [[Martin Grant]] || 47
| [[25P3H1V0.1]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] ||  2015-01-06 || [[Martin Grant]] || 19
|-
|-
| [[x66]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-01-11 || [[Martin Grant]] || 12
| [[x66]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-01-11 || [[Martin Grant]], [[Tanner Jacobi]] || 12
|-
|-
| [[weekender]] || data-sort-value="o 0.285714" | [[2c/7 orthogonal]] || 2015-01-25 || [[Martin Grant]] || 59
| [[weekender]] || data-sort-value="o 0.285714" | [[2c/7 orthogonal]] || 2015-01-25 || [[Chris Cain]], [[Martin Grant]], [[Tanner Jacobi]] || 28
|-
|-
| [[pufferfish spaceship|puffership]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-02-11 || [[Chris Cain]] || 60
| [[pufferfish spaceship]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-02-11 || [[Chris Cain]] || 51
|-
|-
| [[Gemini]] || data-sort-value="oblique" | [[(2560,512)c/16849793]] || 2015-02-16 || [[Dave Greene]] || 173,449
| [[Gemini]] || data-sort-value="oblique" | [[(2560,512)c/16849793]] || 2015-02-16 || [[Dave Greene]] || 173,449
|-
|-
| half-[[X66]] with [[HWSS]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-03-08 || [[Chris Cain]] || 9
| half-[[x66]] with [[HWSS]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-03-08 || [[Adam P. Goucher]], [[praosylen]], [[Chris Cain]], [[Matthias Merzenich]] || 9
|-
|-
| [[B29]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2015-04-06 || [[Tanner Jacobi]] || 25
| [[B29]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2015-04-06 || [[Tanner Jacobi]] || 25
|-
|-
| [[Pushalong 1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-06-12 || [[Martin Grant]] || 58
| [[Pushalong 1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-06-12 || [[Martin Grant]] || 14
|-
|-
| [[30P4H2V0.4]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-09-10 || [[Tanner Jacobi]] || 85
| [[30P4H2V0]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-09-10 || [[Tanner Jacobi]] || 50
|-
|-
| [[0hd Demonoid]] || data-sort-value="d 0.000148114" | [[65c/438852 diagonal]] || 2015-12-06 || [[Chris Cain]] || 12,016
| [[0hd Demonoid]] || data-sort-value="d 0.000148114" | [[65c/438852 diagonal]] || 2015-12-06 || [[Chris Cain]] || 12,016
|-
|-
| [[copperhead]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-05 || [[Aidan F. Pierce]] || 13
| [[copperhead]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-05 || [[Tanner Jacobi]] || 13
|-
|-
| [[fireship]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-21 || [[Nico Brown]] || 18
| [[fireship]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-21 || [[Nico Brown]], [[Tanner Jacobi]] || 18
|-
|-
| [[25P3H1V0.2]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2017-12-15 || [[Martin Grant]] || 26
| [[25P3H1V0.2]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2017-12-15 || [[Martin Grant]] || 23
|-
|-
| [[Orthogonoid]] || data-sort-value="o 0.0000736475" | [[16c/217251 orthogonal]] || 2017-12-30 || [[Dave Greene]] || 37,625
| [[Orthogonoid]] || data-sort-value="o 0.0000736475" | [[16c/217251 orthogonal]] || 2017-12-30 || [[Dave Greene]] || 37,625
Line 126: Line 152:
| [[2-engine Cordership]] || data-sort-value="d 0.0833" | [[c/12 diagonal]] || 2017-12-31 || [[Dave Greene]] || 9
| [[2-engine Cordership]] || data-sort-value="d 0.0833" | [[c/12 diagonal]] || 2017-12-31 || [[Dave Greene]] || 9
|-
|-
| [[46P4H1V0]] || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2019-02-04 || [[Tanner Jacobi]] || 78
| [[46P4H1V0]] || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2019-02-04 || [[Martin Grant]], [[Tanner Jacobi]] || 46
|-
|-
| [[spider]] || data-sort-value="o 0.2" | [[c/5 orthogonal]] || 2019-03-07 || [[Martin Grant]] || 239
| [[spider]] || data-sort-value="o 0.2" | [[c/5 orthogonal]] || 2019-03-07 || [[Martin Grant]] || 205
|-
|-
| [[camelship]] || data-sort-value="oblique" | [[(3,1)c/3948264]] || 2019-05-04 || [[Dave Greene]] || 26,614
| [[camelship]] || data-sort-value="oblique" | [[(3,1)c/3948264]] || 2019-05-04 || [[Dave Greene]] || 26,614
|-
|-
| [[27P4H1V1]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2019-10-28 || [[Goldtiger997]] || 31
| [[wings]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2019-10-28 || [[Goldtiger997]], [[Tanner Jacobi]] || 31
|-
| [[orthogonal loopship]] || data-sort-value="o 0.0499977" | 1000130c/20003511 orthogonal || 2020-01-08 || [[Dave Greene]] || 56,643
|-
| [[56P6H1V0]] || data-sort-value="o 0.167" | [[c/6 orthogonal]] || 2020-03-25 || [[AforAmpere]], [[praosylen]], [[Goldtiger997]], [[Martin Grant]], [[Tanner Jacobi]] || 272
|-
| [[58P5H1V1]] || data-sort-value="d 0.2" | [[c/5 diagonal]] || 2020-04-03 || [[Adam P. Goucher]], [[BlinkerSpawn]], [[Goldtiger997]], [[Peter Naszvadi]], [[Tanner Jacobi]] || 100
|-
| [[31P8H4V0]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2020-04-10 || [[Goldtiger997]] || 36
|-
|-
| [[loopship]] || data-sort-value="o 0.0499977" | [[1000130c/20003511 orthogonal]] || 2020-01-08 || [[Dave Greene]] || 56,643
| [[70P2H1V0.1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2020-07-18 || [[Martin Grant]] || 178
|-
|-
| [[56P6H1V0]] || data-sort-value="o 0.167" | [[c/6 orthogonal]] || 2020-03-25 || [[Martin Grant]] || 311
| [[44P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2020-08-29 || [[Goldtiger997]] || 24
|-
|-
| [[58P5H1V1]] || data-sort-value="d 0.2" | [[c/5 diagonal]] || 2020-04-03 || [[Goldtiger997]] || 220
| [[55P9H3V0]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2020-09-19 || [[Goldtiger997]] || 230
|-
| [[Speed Demonoid]] || data-sort-value="d 0.1992019" | 1642811c/8246964 diagonal || 2020-09-26 || [[Dave Greene]] || 31,822
|-
| [[57P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2020-11-02 || [[Goldtiger997]] || 112
|-
| [[turtle]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2020-12-04 || [[Goldtiger997]] || 225
|-
| [[doo-dah]] || data-sort-value="o 0.285714" | [[2c/7 orthogonal]] || 2020-12-06 || [[Goldtiger997]] || 34
|-
| [[edge-repair spaceship 1]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2021-01-24 || [[bubblegum]], [[goldenratio]] || 17
|-
| {{LinkCatagolue|xq4_2534uof1u0u1fou4352zy087084048078zx3igi3x3igi3|patternname=72P4H1V0|style=raw}}<ref name="post124810" /> || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2021-03-08 || [[Tanner Jacobi]], [[Goldtiger997]] || 194
|-
| {{LinkCatagolue|xq4_y2oo7t0t7ooz2qgx8t2rgr2t8xgq2z122166y5661221|patternname=61P4H1V0|style=raw}}<ref name="post128012" /> || data-sort-value="o 0.25" | [[c/4 orthogonal]] || 2021-04-10 || [[Goldtiger997]] || 89
|-
| [[Canada Grey]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2021-07-01 || [[Goldtiger997]], [[Martin Grant]] || 427
|-
| [[self-synthesizing oblique loopship]] || data-sort-value="oblique" | (16461006,16460963)c/75568091 || 2021-08-02 || [[Goldtiger997]] || 144,221
|-
| [[Orion 2]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2022-01-10 || [[Goldtiger997]] || 57
|-
| [[33P4H1V1]] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2022-01-14 || [[Goldtiger997]], [[Mark Niemiec]]<ref name="post140292" /> || 44
|-
| [[70P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2022-01-26 || [[Goldtiger997]] || 221
|-
| [[58P8H4V0]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2022-02-25 || [[Goldtiger997]], [[Mark Niemiec]] || 47
|-
| [[SSGRL]] || data-sort-value="o 0.2419" | 15492980c/72085603 orthogonal || 2022-03-08 || [[Goldtiger997]] || 141,617
|-
| [[30P3H1V0]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2022-06-16 || [[Goldtiger997]] || 24
|-
| [[29P3H1V0]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2022-06-29 || [[Goldtiger997]] || 35
|-
| [[brain]] || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2022-11-25 || [[Goldtiger997]] || 99
|-
| Infinite families of [[waltz]] stabilisations || data-sort-value="o 0.333" | [[c/3 orthogonal]] || 2022-12-09 || [[Goldtiger997]],<ref>https://conwaylife.com/forums/viewtopic.php?f=2&t=1557&start=625#p154625</ref> [[Connor Steppie]]<ref>https://conwaylife.com/forums/viewtopic.php?f=2&t=1557&start=625#p154645</ref> || ≥28
|-
| [https://catagolue.hatsya.com/object/xq5_f930sgy1gs039fz24dcpn03330npcd42zy13iv0vi3/b3s23 66P5H2V0] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2022-12-23 || [[Goldtiger997]] || 57
|-
| [https://catagolue.hatsya.com/object/xq4_y258880638gszwu1w32gkoz34j0ozx11/b3s23 37P4H1V1] || data-sort-value="d 0.25" | [[c/4 diagonal]] || 2022-12-28 || [[Goldtiger997]] || 68
|-
| [[77P6H1V1]] || data-sort-value="d 0.167" | [[c/6 diagonal]] || 2024-01-28 || [[Goldtiger997]] || 222
|}
|}
As of June 2023, the smallest spaceships with no known syntheses are as follows:
* [[Unnamed tagalong 23P4H2V0]] supported by a LWSS: 32 cells
* [[32P4H2V0]]: 32 cells
* Unnamed tagalong 23P4H2V0 supported by a MWSS top spark: 34 cells
* Unnamed tagalong 23P4H2V0 supported by a MWSS back spark: 34 cells
* [[34P5H2V0]]: 34 cells
* [[35P4H1V1]]: 35 cells
* [[Unnamed 7WSS sidecar]]: 36 cells
* [[Canada goose]]: 36 cells
* The two ways for [[Wainwright's tagalong]] to follow a [[B29]]: 36 cells


==Other syntheses of note==
==Other syntheses of note==
[[Image:glider_synth_pentadecathlon.png|framed|right|A 3-glider synthesis of a [[pentadecathlon]].]]
[[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 {{year|1997}} by [[Heinrich Koenig]], which came as a surprise because it was widely assumed that such a small synthesis would already be known.
A [[Three-glider collision|3-glider synthesis]] of a [[pentadecathlon]] was found in April {{year|1997}} by [[Heinrich Koenig]], which came as a surprise because it was widely assumed that such a small synthesis would already be known.
 
Along similar lines, a 3-glider synthesis of the [[bi-pond]] was discovered in June {{year|2014}} by [[Bob Shemyakin]]<ref>{{LinkForumThread|p=12276|title=4 glider syntheses|author=Bob Shemyakin|date=June 16, 2014|format=ref}}</ref>, a 3-glider synthesis of a messy [[glider-producing switch engine]] was found in October {{year|2014}} by [[Michael Simkin]]<ref>{{LinkForumThread|p=13988|title=Re: Making switch-engines|author=Michael Simkin|date=October 24, 2014|format=ref}}</ref>, and a 3-glider synthesis of a [[clean]] [[switch engine]] was discovered in March {{year|2017}} by [[Luka Okanishi]].<ref>{{LinkForumThread|p=41557|title=Re: Thread For Your Accidental Discoveries|work=ConwayLife.com forums|author=Luka Okanishi|date=March 12, 2017|format=ref}}</ref>


Along similar lines, a 3-glider synthesis of an [[infinite growth]] pattern was found in October {{year|2014}} by [[Michael Simkin]],<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?p=13988#p13988|title=Re: Making switch-engines|work=ConwayLife.com forums|author=Michael Simkin|date=October 24, 2014|accessdate=February 21, 2018}}</ref> and a 3-glider synthesis of a [[clean]] [[switch engine]] was discovered in March {{year|2017}} by [[Luka Okanishi]].<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=&p=41558#p41557|title=Re: Thread For Your Accidental Discoveries|work=ConwayLife.com forums|author=Luka Okanishi|date=March 12, 2017|accessdate=February 21, 2018}}</ref>
On March 27, {{year|2022}}, [[dani]] found that two copies of Simkin's GPSE synthesis could be combined to produce a record-breaking 6-glider synthesis<ref name="post143450" /> of a [[breeder]] which had been discovered a week earlier.<ref name="post143132" />


==2-glider syntheses==
==2-glider syntheses==
{{main|2-glider collision}}
{{main|2-glider collision}}


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]].
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 [[Two-glider octomino|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, {{year|2005}}:
All 71 such syntheses can be seen below in a pattern put together by [[Jason Summers]] on January 29, {{year|2005}}:
Line 158: Line 247:
|pname = twoglidersyntheses
|pname = twoglidersyntheses
|position = center
|position = center
|caption = All 71 distinct 2-glider collisions, arranged by what they synthesize.<br>
|caption = All 71 distinct 2-glider collisions, arranged by what they synthesize
|viewerconfig = #C [[ WIDTH 1200 HEIGHT 1200 ZOOM 3 ]]
|viewerconfig = #C [[ WIDTH 1200 HEIGHT 1200 ZOOM 3 ]]
}}
}}


==See also==
==See also==
*[[:Category:Patterns_constructible_by_a_given_number_of_gliders|List of known glider syntheses]]
* {{CategoryLink|Patterns constructible by a given number of gliders}}
*[[Salvo]]
* [[Salvo]]
*[[Tutorials/Glider syntheses]]
* [[Tutorials/Glider syntheses]]
*[[Shinjuku]]
* [[Shinjuku]]
* [[Glider destruction]]


==References==
==References==
Line 176: Line 266:
|author = Martin Grant
|author = Martin Grant
|date  = May 17, 2014
|date  = May 17, 2014
}}</ref>
<ref name="post14272">{{LinkForumThread
|format = ref
|title  = Re: 18-bit SL Syntheses
|p      = 14272
|author = Martin Grant
|date  = November 12, 2014
}}</ref>
}}</ref>
<ref name="post82560">{{LinkForumThread
<ref name="post82560">{{LinkForumThread
Line 190: Line 273:
|author = Tanner Jacobi
|author = Tanner Jacobi
|date  = September 9, 2019
|date  = September 9, 2019
}}</ref>
<ref name="post104484">{{LinkForumThread
|format = ref
|title  = Re: Binary slow salvos
|p      = 104484
|author = Adam P. Goucher
|date  = September 19, 2020
}}</ref>
}}</ref>
<ref name="post83979">{{LinkForumThread
<ref name="post83979">{{LinkForumThread
Line 204: Line 294:
|author = Martin Grant
|author = Martin Grant
|date  = February 8, 2020
|date  = February 8, 2020
}}</ref>
<ref name="post125259">{{LinkForumThread
|format = ref
|title  = Re: 20-bit still life syntheses
|p      = 125259
|author = Martin Grant
|date  = March 12, 2021
}}</ref>
<ref name="post153564">{{LinkForumThread
|format = ref
|title  = Re: 21-bit still life syntheses
|p      = 153564
|author = May13
|date  = November 14, 2022
}}</ref>
}}</ref>
<ref name="post37438">{{LinkForumThread
<ref name="post37438">{{LinkForumThread
Line 218: Line 322:
|author = Goldtiger997
|author = Goldtiger997
|date  = May 24, 2017
|date  = May 24, 2017
}}</ref>
<ref name="post124810">{{LinkForumThread
|format = ref
|title  = Re: Small Spaceship Syntheses
|p      = 124810
|author = Goldtiger997
|date  = March 8, 2021
}}</ref>
<ref name="post128012">{{LinkForumThread
|format = ref
|title  = Re: Small Spaceship Syntheses
|p      = 128012
|author = Goldtiger997
|date  = April 10, 2021
}}</ref>
<ref name="post140292">{{LinkForumThread
|format = ref
|title  = Re: Small Spaceship Syntheses
|p      = 140292
|author = Mark Niemiec
|date  = January 14, 2022
}}</ref>
<ref name="post143450">{{LinkForumThread
|format = ref
|title  = Re: Small Quadratic Growth Patterns
|p      = 143450
|author = dani
|date  = March 27, 2022
}}</ref>
<ref name="post143132">{{LinkForumThread
|format = ref
|title  = Re: Small Quadratic Growth Patterns
|p      = 143132
|author = dani
|date  = March 20, 2022
}}</ref>
}}</ref>
</references>
</references>


==External links==
==External links==
*[https://catagolue.appspot.com/syntheses Catagolue synthesis database]
* [https://catagolue.hatsya.com/syntheses Catagolue synthesis database]
*[http://codercontest.com/mniemiec/lifepage.htm Mark Niemiec's glider synthesis database]
* {{LinkNiemiec|lifepage.htm|title=Mark Niemiec's glider synthesis database}}
*[http://radicaleye.com/DRH/life.html Dean Hickerson's Life page] with four pages of glider syntheses
* [https://conwaylife.com/ref/DRH/life.html Dean Hickerson's Life page] with four pages of glider syntheses
*[http://conwaylife.com/forums/viewtopic.php?p=46552#p46552 Martin Grant's synthesis component database], version 3
* [https://conwaylife.com/forums/viewtopic.php?p=46552#p46552 Martin Grant's synthesis component database], version 3
*[http://pentadecathlon.com/constructions/components/components.php Heinrich Koenig's component catalog] on pentadecathlon.com
* [https://web.archive.org/web/20210716021110/http://pentadecathlon.com/constructions/components/components.php Heinrich Koenig's component catalog] on [[Game of Life News|pentadecathlon.com]]
{{LinkLexicon|lex_g.htm#glidersynthesis}}
* {{LinkLexicon|lex_g.htm#glidersynthesis}}
{{LinkWeisstein|GliderSynthesis.html}}
===Forum threads===
* {{LinkForumThread|f=2|t=3267|title=Still Life Synthesis Thread}}
* {{LinkForumThread|f=2|t=1155|title=Synthesising Oscillators}}
* {{LinkForumThread|f=2|t=1557|title=Small Spaceship Syntheses}}
* {{LinkForumThread|f=2|t=3960|title=Soup-based syntheses}}
* {{LinkForumThread|f=2|t=4257|title=Randomly enumerating glider syntheses}}
* {{LinkForumThread|f=2|t=1394|title=4 glider syntheses}}
* {{LinkForumThread|f=2|t=4063|title=Synthesis components}}
 
[[Category:Synthesis| ]]
[[Category:Lists of patterns with synthesis costs]]

Latest revision as of 13:11, 13 March 2024

x = 34, y = 31, rule = B3/S23 33bo$31b2o$32b2o$9bo$bo8bo$2bo5b3o$3o3$5bo$6bo$4b3o$24bobo$25b2o$25bo 2$27bobo$27b2o$28bo$31b3o$31bo$32bo7$5b2o$6b2o$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 14 GPS 10 THEME Book AUTOSTART T 0 PAUSE 2 T 99 PAUSE 1 LOOP 100 ]]
An 8-glider synthesis of a loafer
(click above to open LifeViewer)
RLE: here Plaintext: here

Glider synthesis (or glider construction) is the construction of an object by means of collisions of gliders and glider-constructible spaceships. 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 (or else it is considered “not fully functional”). LWSSes, MWSSes and HWSSes can also be used in syntheses; these spaceships can themselves be easily synthesized from gliders at any point along their trajectory, so this conversion is often left as an implicit step.

Features of syntheses

Four main characterizing features of a synthesis are the geometry, construction time, glider cost, and number of stages.

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. Such syntheses are also known as slow or synchronized salvo syntheses.

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 construction time, cost, and/or number of stages needed for 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 bait objects, 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 distance 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 construction time is simply the number of generations it takes to complete a synthesis. For multi-stage syntheses, each stage has its own construction time.

The number of stages is a count of how many separate operations a synthesis can be divided into, with pauses of arbitrary length between the stages. 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 bait objects, 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. Similar to the construction time, it can be defined also for individual synthesis stages. A *WSS is considered to cost 3 gliders. The discovery of the reverse caber tosser in 2018 proved that there is a universal constant upper bound on the cost to synthesise any synthesisable object; currently, the best known upper bound is 15 gliders.

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 universal construction arms as well as one-time turners and splitters.

An incremental synthesis is a synthesis with multiple stages. The final step (final stage, activation step/stage) of an incremental synthesis is the step that converts a previously constructed stationary object or constellation into the target object. Finding the final step of a synthesis is often a nontrivial, complicated process.[1][2]

Still life syntheses

In the 1990s, glider syntheses for all still lifes and known oscillators with at most 14 cells were found by David Buckingham. Almost all of these were successfully reduced to a synthesis cost of less than 1 glider per ON cell, or "1 glider per bit".[3]

A collaborative effort ending in May 2014 completed glider syntheses of all still lifes with 17 or fewer cells.[4][5][6] A lengthy project to complete syntheses for all 18-bit still lifes was completed in October 2019.[7] The syntheses for 19-bit still lifes were completed in February 2020,[8] 20-bit still lifes in March 2021,[9] and 21-bit still lifes in November 2022.[10] Later optimization projects reduced the maximum cost of construction for 15-bit,[11][12] 16-bit,[13][14] and 17-bit[15] still lifes to less than one glider per bit, in November 2016, May 2017, and September 2019 respectively.

In September 2020, the 17-glider reverse caber-tosser proved that all synthesizable still lifes could theoretically be constructed with no more than one glider per bit.[16]

The following table displays statistics about the costs (excluding RCT constructions) for strict and pseudo still lifes with up to 21 cells as of November 15, 2022.[17]

Live cells Strict still lifes Pseudo still lifes
Count
(OEISicon light 11px.png A019473)		 Min. cost Avg. cost Max. cost Count
(OEISicon light 11px.png A056613)		 Min. cost Max. cost
4 2 2 2.500 3 0 – –
5 1 2 2.000 2 0 – –
6 5 2 3.200 4 0 – –
7 4 2 2.750 4 0 – –
8 9 2 3.556 4 1 2 2
9 10 3 4.000 5 1 3 3
10 25 4 4.360 5 7 3 5
11 46 4 4.543 5 16 3 6
12 121 4 4.983 7 55 3 9
13 240 4 5.408 8 110 4 9
14 619 3 6.019 9 279 3 11
15 1,353 4 6.911 10 620 4 12
16 3,286 3 7.880 13 1,645 4 23[n 1][n 2]
17 7,773 4 9.117 15 4,067 4 18[n 1][n 3]
18 19,044 4 10.438 28[n 1][n 4] 10,843 4 48[n 1][n 5]
19 45,759 4 11.743 46[n 1][n 6] 27,250 4 41[n 1][n 7]
20 112,243 4 13.207 113[n 1][n 8] 70,637 4 73[n 1][n 9]
21 273,188 5 14.876 115[n 1][n 10] 179,011 [n 11]

In January 2022, work by Ilkka Törmä and Ville Salo demonstrated a still life with 306 cells that is impossible to synthesize with gliders, reduced by 400spartans to 278 on September 4, 2023, then 236 on March 12, 2024, meaning there is a threshold 21 < n ≤ 236 such that not all still lifes with ≥ n cells are constructible.

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 15 gliders using the reverse caber-tosser
  2. ↑ All but 3 16-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  3. ↑ All but 2 17-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  4. ↑ All but 128 18-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  5. ↑ All but 35 18-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  6. ↑ All but 1,200 19-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  7. ↑ All but 54 19-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  8. ↑ All but 5,860 20-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  9. ↑ All but 279 20-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  10. ↑ All but 22,839 21-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
  11. ↑ Only 82941 of 179011 21-bit pseudo still lifes are currently tabulated on Catagolue.

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 60P5H2V0, 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 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 Speed First synthesis Best current synthesis
Date Discoverer Fewest gliders
60P5H2V0 2c/5 orthogonal 2003-03-17 Noam Elkies 37
loafer c/7 orthogonal 2013-02-17 Adam P. Goucher 8
dart c/3 orthogonal 2014-12-02 Ivan Fomichev, Mark Niemiec, Martin Grant, Michael Simkin 24
crab c/4 diagonal 2014-12-26 Brett Berger, Martin Grant, Tanner Jacobi 14
Parallel HBK (6,3)c/245912 2014-12-31 Michael Simkin 38,380
30P5H2V0 2c/5 orthogonal 2015-01-01 Martin Grant, Matthias Merzenich, Tanner Jacobi 39
25P3H1V0.1 c/3 orthogonal 2015-01-06 Martin Grant 19
x66 c/2 orthogonal 2015-01-11 Martin Grant, Tanner Jacobi 12
weekender 2c/7 orthogonal 2015-01-25 Chris Cain, Martin Grant, Tanner Jacobi 28
pufferfish spaceship c/2 orthogonal 2015-02-11 Chris Cain 51
Gemini (2560,512)c/16849793 2015-02-16 Dave Greene 173,449
half-x66 with HWSS c/2 orthogonal 2015-03-08 Adam P. Goucher, praosylen, Chris Cain, Matthias Merzenich 9
B29 c/4 diagonal 2015-04-06 Tanner Jacobi 25
Pushalong 1 c/2 orthogonal 2015-06-12 Martin Grant 14
30P4H2V0 c/2 orthogonal 2015-09-10 Tanner Jacobi 50
0hd Demonoid 65c/438852 diagonal 2015-12-06 Chris Cain 12,016
copperhead c/10 orthogonal 2016-03-05 Tanner Jacobi 13
fireship c/10 orthogonal 2016-03-21 Nico Brown, Tanner Jacobi 18
25P3H1V0.2 c/3 orthogonal 2017-12-15 Martin Grant 23
Orthogonoid 16c/217251 orthogonal 2017-12-30 Dave Greene 37,625
2-engine Cordership c/12 diagonal 2017-12-31 Dave Greene 9
46P4H1V0 c/4 orthogonal 2019-02-04 Martin Grant, Tanner Jacobi 46
spider c/5 orthogonal 2019-03-07 Martin Grant 205
camelship (3,1)c/3948264 2019-05-04 Dave Greene 26,614
wings c/4 diagonal 2019-10-28 Goldtiger997, Tanner Jacobi 31
orthogonal loopship 1000130c/20003511 orthogonal 2020-01-08 Dave Greene 56,643
56P6H1V0 c/6 orthogonal 2020-03-25 AforAmpere, praosylen, Goldtiger997, Martin Grant, Tanner Jacobi 272
58P5H1V1 c/5 diagonal 2020-04-03 Adam P. Goucher, BlinkerSpawn, Goldtiger997, Peter Naszvadi, Tanner Jacobi 100
31P8H4V0 c/2 orthogonal 2020-04-10 Goldtiger997 36
70P2H1V0.1 c/2 orthogonal 2020-07-18 Martin Grant 178
44P5H2V0 2c/5 orthogonal 2020-08-29 Goldtiger997 24
55P9H3V0 c/3 orthogonal 2020-09-19 Goldtiger997 230
Speed Demonoid 1642811c/8246964 diagonal 2020-09-26 Dave Greene 31,822
57P5H2V0 2c/5 orthogonal 2020-11-02 Goldtiger997 112
turtle c/3 orthogonal 2020-12-04 Goldtiger997 225
doo-dah 2c/7 orthogonal 2020-12-06 Goldtiger997 34
edge-repair spaceship 1 c/3 orthogonal 2021-01-24 bubblegum, goldenratio 17
72P4H1V0[18] c/4 orthogonal 2021-03-08 Tanner Jacobi, Goldtiger997 194
61P4H1V0[19] c/4 orthogonal 2021-04-10 Goldtiger997 89
Canada Grey c/2 orthogonal 2021-07-01 Goldtiger997, Martin Grant 427
self-synthesizing oblique loopship (16461006,16460963)c/75568091 2021-08-02 Goldtiger997 144,221
Orion 2 c/4 diagonal 2022-01-10 Goldtiger997 57
33P4H1V1 c/4 diagonal 2022-01-14 Goldtiger997, Mark Niemiec[20] 44
70P5H2V0 2c/5 orthogonal 2022-01-26 Goldtiger997 221
58P8H4V0 c/2 orthogonal 2022-02-25 Goldtiger997, Mark Niemiec 47
SSGRL 15492980c/72085603 orthogonal 2022-03-08 Goldtiger997 141,617
30P3H1V0 c/3 orthogonal 2022-06-16 Goldtiger997 24
29P3H1V0 c/3 orthogonal 2022-06-29 Goldtiger997 35
brain c/3 orthogonal 2022-11-25 Goldtiger997 99
Infinite families of waltz stabilisations c/3 orthogonal 2022-12-09 Goldtiger997,[21] Connor Steppie[22] ≥28
66P5H2V0 2c/5 orthogonal 2022-12-23 Goldtiger997 57
37P4H1V1 c/4 diagonal 2022-12-28 Goldtiger997 68
77P6H1V1 c/6 diagonal 2024-01-28 Goldtiger997 222

As of June 2023, the smallest spaceships with no known syntheses are as follows:

Other 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 such a small synthesis would already be known.

Along similar lines, a 3-glider synthesis of the bi-pond was discovered in June 2014 by Bob Shemyakin[23], a 3-glider synthesis of a messy glider-producing switch engine was found in October 2014 by Michael Simkin[24], and a 3-glider synthesis of a clean switch engine was discovered in March 2017 by Luka Okanishi.[25]

On March 27, 2022, dani found that two copies of Simkin's GPSE synthesis could be combined to produce a record-breaking 6-glider synthesis[26] of a breeder which had been discovered a week earlier.[27]

2-glider syntheses

Main article: 2-glider collision

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:

x = 379, y = 369, rule = B3/S23 154bo36bo18bo$58bo18bo19bo16bo19bo18bo19bo16bo18bo36bo$57bo18bo19bo16b o19bo19b3o16bo17b3o16b3o15bo17bo$57b3o16b3o17b3o14b3o17b3o36b3o51bo18b 3o$226b3o4$190bo$58b3o17b3o89bo18b2o55bo$58bo19bo20bo17bo20bo13b2o15b 2o18bobo14b2o20bo16b2o$59bo19bo18b2o16b2o19b2o13bobo14bobo34bobo18b2o 16bobo$98bobo15bobo18bobo12bo53bo20bobo$bo4bo3bobo3bobobo2bo3bo3bo3bo 4bo4bobo2$bobo2bo2bo3bo4bo4bo3bo3bo3bobo2bo2bo2$bo2bobo2bo3bo4bo4bobob o3bo3bo2bobo2bo2bobo2$bo4bo2bo3bo4bo4bo3bo3bo3bo4bo2bo4bo266bo$269bo 22bo21bo62bo$bo4bo3bobo5bo4bo3bo3bo3bo4bo4bobo182bo15bo21bo22bo22b3o 18bo22bo17bo$229bo15bo22b3o20b3o40bo22bo18b3o$86bo16bo17bo16bo16bo15bo 17bo16bo22b3o13b3o86b3o20b3o$66bo18bo16bo17bo16bo16bo15bo17bo16bo$65bo 19b3o14b3o15b3o14b3o14b3o13b3o15b3o14b3o$65b3o4$224b3o15b3o59b2o$76b3o 16b3o16b3o15b3o15b3o14b3o16b3o15b3o19bo17bo11b2o23b2o20bobo20b2o40b2o$ 54b3o21bo18bo18bo17bo17bo16bo18bo17bo18bo17bo13b2o23b2o21bo21b2o12b2o 26b2o$56bo20bo18bo18bo17bo17bo16bo18bo17bo50bo24bo44bo15b2o24bo$55bo 285bo23$106bo157bo$74bo30bo157bo38bo$2bobo4bo6bo3bo4bo2bo3bo2bobobo2bo bo28bo15bo15b3o119bobobo2bo28b3o14bo20bo$46bo26b3o12bo190bo21b3o$2bo3b o2bo6bo3bobo2bo2bo2bo3bo6bo45b3o138bo4bo44b3o$46bo$2bobo4bo6bo3bo2bobo 2bobo4bobobo2bobo184bo4bo2$2bo3bo2bo6bo3bo4bo2bo2bo3bo6bo2bo183bo4bo$ 305b3o$2bobo4bobobo2bo3bo4bo2bo3bo2bobobo2bo3bo61b2o119bo4bobobo44bo 21bo$108bobo146b2o23b2o22bo$66b2o21b2o17bo149b2o22bobo$65bobo21bobo 165bo$67bo21bo17$84bo15bo39bo153bo24bo19bo$bobo4bo7bobo4bobo3bo3bo28bo 20bo15bo39bo88bo3bo2bobobo20bo16bo15bo24bo19bo$61bo21b3o13b3o15bo21b3o 17bo99bo16bo16b3o22b3o17b3o$bo3bo2bo6bo3bo2bo3bo2bo2bo28b3o52bo41bo69b o3bo2bo23b3o14b3o$116b3o39b3o$bobo4bo6bo3bo2bo6bobo196bobobo2bobobo2$b o3bo2bo6bo3bo2bo3bo2bo2bo195bo3bo2bo2$bobo4bobobo3bobo4bobo3bo3bo85b3o 106bo3bo2bo$54b3o62bo17b2o16bo103bo35b2o35b2o$56bo21b2o15b2o23bo16bobo 14b2o102b2o16b2o17bobo11b2o22b2o$55bo23b2o15b2o39bo16bobo101bobo15bobo 16bo14b2o20bo$78bo16bo180bo32bo6$73b2o19b2o$74bo20bo152b2o$249bo7$64bo 233bo$63bo20bo194bo17bo$63b3o17bo166bo27bo18b3o$2bobo3bo6bo3bobo4bobob o2bobo47b3o143bobo17bo28b3o$37bo211b3o$o7bo6bo3bo3bo2bo6bo195bo3bo$37b o275b2o$o2bobo2bo6bo3bo3bo2bobobo2bobo193bobo82bo$256b2o$o4bo2bo6bo3bo 3bo2bo6bo2bo192bo3bo23bo$80bo$2bobo3bobobo2bo3bobo4bobobo2bo3bo20b2o 19b2o148bobo18bo42b2o$57bobo19bobo167b2o13b2o26bobo$59bo189bobo13b2o 27bo$264bo14$252b2o24b2o$253bo25bo$258bo15bo$257bo15bo26bo$61bo195b3o 13b3o23bo$obo5bobo5bo4bobobo34bo167bobo4bo63b3o$60b3o169bo45bo24b3o$o 3bo2bo3bo3bobo5bo204bo6bo41b2o24bo$232bo44bobo24bo$obo4bo3bo2bo3bo4bo 204bobo4bo19b2o37b2o$254bobo38bo$o3bo2bo3bo2bobobo4bo204bo6bo20bo2$obo 5bobo3bo3bo4bo204bo6bo2$53b2o$54b2o$53bo18$3bo3bo3bo3bo3bo2bobobo30bo 169bo6bobo3bo5bo18bo$56bo207bo$3bo3bo3bo3bo3bo2bo33b3o168bo5bo3bo2bobo bobo17b3o2$3bobobo3bo3bo3bo2bobobo200bo5bo3bo2bo2bo2bo2$3bo3bo3bo4bobo 3bo204bo5bo3bo2bo5bo2$3bo3bo3bo5bo4bobobo32b3o165bobobo2bobo3bo5bo$59b o203bo$60bo201b2o$262bobo17$67bo$66bo$4bo6bobo5bo4bobobo37b3o157bobobo 2bobobo4bo4bobo4bobo4bobo5bobo3bobo$251bo13bo13bo17bo$4bo5bo3bo3bobo3b o203bo4bo7bobo3bo6bo3bo2bo6bo3bo2bo20bo$251bo13bo13bo16b3o$4bo5bo3bo2b o3bo2bobobo199bo4bobobo2bo3bo2bobo4bo3bo2bobo4bo3bo2bobo2$4bo5bo3bo2bo bobo2bo203bo4bo6bobobo2bo2bo3bo3bo2bo2bo3bo3bo2bo2$4bobobo2bobo3bo3bo 2bo203bo4bobobo2bo3bo2bo3bo2bobo4bo3bo3bobo3bo$58b2o239bo$57bobo238b2o $59bo238bobo16$59bo$58bo$58b3o264bo$3bobobo4bo4bobobo2bobobo2bobo193bo 3bo4bo2bobobo2bobobo2bobo5bobo3bo3bo4bo4bo4bo4bobo3bobobo22bo$35bo221b o66b3o$3bo7bobo5bo4bo6bo195bo3bobo2bo4bo4bo6bo6bo3bo2bo3bo3bobo3bobo2b o2bo7bo$35bo221bo$3bobobo2bo3bo4bo4bobobo2bobo193bo3bo2bobo4bo4bobobo 2bobo4bo6bobobo2bo3bo2bo2bobo2bo2bobo2bobobo$57bo$3bo6bobobo4bo4bo6bo 2bo21b2o169bo3bo4bo4bo4bo6bo2bo3bo3bo2bo3bo2bobobo2bo4bo2bo4bo2bo26b3o $56bobo265bo$3bobobo2bo3bo4bo4bobobo2bo3bo191bo3bo4bo4bo4bobobo2bo3bo 3bobo3bo3bo2bo3bo2bo4bo4bobo3bobobo23bo11$305b2o$306bo9$55bo16bo237bo$ 2bobo5bobo3bo4bo2bobo27bo16bo155bobobo2bo14bobo3bo6bo3bobo4bobobo2bobo 26bo$6bo47b3o14b3o210bo24b3o$2bo6bo3bo2bobo2bo2bo3bo200bo4bo7bo4bo7bo 6bo3bo3bo2bo6bo$6bo277bo$2bobo4bo3bo2bo2bobo2bo3bo200bo4bo5bobobo2bo2b obo2bo6bo3bo3bo2bobobo2bobo2$2bo6bo3bo2bo4bo2bo3bo200bo4bo7bo4bo4bo2bo 6bo3bo3bo2bo6bo2bo26b3o$310bo$2bo7bobo3bo4bo2bobo46bo155bo4bobobo10bob o3bobobo2bo3bobo4bobobo2bo3bo26bo$50b2o20b2o$51b2o19bobo$50bo19$2bobo 5bo7bobo4bo7bobo4bobo3bo3bo2$2bo3bo3bo7bo3bo2bo6bo3bo2bo3bo2bo2bo28bo 239bo$77bo239bo$2bobo5bo2bobo2bobo4bo6bo3bo2bo6bobo28b3o237b3o$229bobo 4bobo3bobobo3bobo3bo5bo3bo3bo4bo3bobo$2bo3bo3bo7bo3bo2bo6bo3bo2bo3bo2b o2bo$228bo3bo2bo3bo4bo4bo3bo2bobobobo3bo3bobo2bo2bo3bo$2bobo5bo7bobo4b obobo3bobo4bobo3bo3bo$228bo3bo2bo8bo4bo3bo2bo2bo2bo3bo3bo2bobo2bo3bo$ 77b3o$77bo150bo3bo2bo3bo4bo4bo3bo2bo5bo3bo3bo4bo2bo3bo$78bo$229bobo4bo bo5bo5bobo3bo5bo3bo3bo4bo3bobo26b2o$307bobo$309bo7$276b2o37b2o$277bo 38bo6$112bo13bo$2bo6bobo5bo4bobobo9bobo4bo6bo3bo4bo2bo3bo2bobobo2bobo 32bo13bo$80bo30b3o11b3o$2bo5bo3bo3bobo3bo8bo4bo3bo2bo6bo3bobo2bo2bo2bo 3bo6bo$80bo$2bo5bo3bo2bo3bo2bobobo2bobobo2bobo4bo6bo3bo2bobo2bobo4bobo bo2bobo2$2bo5bo3bo2bobobo2bo8bo4bo3bo2bo6bo3bo4bo2bo2bo3bo6bo2bo2$2bob obo2bobo3bo3bo2bo13bobo4bobobo2bo3bo4bo2bo3bo2bobobo2bo3bo$107b2o21b2o 195bo$107bobo20bobo193bo$107bo22bo98bobobo9bobo3bo6bo3bobo4bobobo2bobo 7bo5bo2bobobo3bobo3bobo16b3o$278bo$233bo7bo7bo6bo3bo3bo2bo6bo9bobobobo 2bo6bo5bo$278bo$229bobobo2bobo2bo2bobo2bo6bo3bo3bo2bobobo2bobo7bo2bo2b o2bobobo3bobo3bobo2$229bo11bo4bo2bo6bo3bo3bo2bo6bo2bo6bo5bo2bo10bo5bo$ 324bo$229bobobo9bobo3bobobo2bo3bobo4bobobo2bo3bo5bo5bo2bobobo3bobo3bob o13b2o$323bobo7$69bo$68bo$46bo21b3o34bo$3bo5bo3bo3bobo4bobo18bo58bo$ 45b3o56b3o$3bobobobo3bo2bo6bo3bo2$3bo2bo2bo3bo3bobo3bo2$3bo5bo3bo6bo2b o3bo19b3o$47bo24b2o17b3o177b2o32b2o$3bo5bo3bo3bobo4bobo21bo23bobo18bo 178bo33bo$72bo19bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 1200 HEIGHT 1200 ZOOM 3 ]]
All 71 distinct 2-glider collisions, arranged by what they synthesize
(click above to open LifeViewer)
RLE: here Plaintext: here

See also

References

  1. ↑ Dave Greene (August 14, 2022). Re: Suggested LifeWiki edits (discussion thread) at the ConwayLife.com forums
  2. ↑ Carson Cheng (April 6, 2023). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
  3. ↑ Mark D. Niemiec (June 20, 2015). Re: 4 glider syntheses (discussion thread) at the ConwayLife.com forums
  4. ↑ Constructions Known for All Still Lifes up to 17 Bits at Game of Life News. Posted by Dave Greene on May 23, 2014.
  5. ↑ Martin Grant (January 6, 2014). 17-bit SL Syntheses (100% Complete!) (discussion thread) at the ConwayLife.com forums
  6. ↑ Martin Grant (May 17, 2014). Re: 17-bit SL Syntheses (discussion thread) at the ConwayLife.com forums
  7. ↑ Ian07 (October 9, 2019). Re: 18-bit SL Syntheses (100% Complete!) (discussion thread) at the ConwayLife.com forums
  8. ↑ Martin Grant (February 8, 2020). Re: 19-bit still life syntheses (discussion thread) at the ConwayLife.com forums
  9. ↑ Martin Grant (March 12, 2021). Re: 20-bit still life syntheses (discussion thread) at the ConwayLife.com forums
  10. ↑ May13 (November 14, 2022). Re: 21-bit still life syntheses (discussion thread) at the ConwayLife.com forums
  11. ↑ BlinkerSpawn (October 27, 2016). 15 in 15: Efficient 15-bit Synthesis Project (DONE!) (discussion thread) at the ConwayLife.com forums
  12. ↑ Martin Grant (November 19, 2016). Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain) (discussion thread) at the ConwayLife.com forums
  13. ↑ Bob Shemyakin (December 20, 2016). 16 in 16: Efficient 16-bit Synthesis Project (discussion thread) at the ConwayLife.com forums
  14. ↑ Goldtiger997 (May 24, 2017). Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain) (discussion thread) at the ConwayLife.com forums
  15. ↑ Tanner Jacobi (September 9, 2019). Re: 17 in 17: Efficient 17-bit synthesis project (discussion thread) at the ConwayLife.com forums
  16. ↑ Adam P. Goucher (September 19, 2020). Re: Binary slow salvos (discussion thread) at the ConwayLife.com forums
  17. ↑ Adam P. Goucher. "Syntheses". Catagolue. Retrieved on November 15, 2022.
  18. ↑ Goldtiger997 (March 8, 2021). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
  19. ↑ Goldtiger997 (April 10, 2021). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
  20. ↑ Mark Niemiec (January 14, 2022). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
  21. ↑ https://conwaylife.com/forums/viewtopic.php?f=2&t=1557&start=625#p154625
  22. ↑ https://conwaylife.com/forums/viewtopic.php?f=2&t=1557&start=625#p154645
  23. ↑ Bob Shemyakin (June 16, 2014). 4 glider syntheses (discussion thread) at the ConwayLife.com forums
  24. ↑ Michael Simkin (October 24, 2014). Re: Making switch-engines (discussion thread) at the ConwayLife.com forums
  25. ↑ Luka Okanishi (March 12, 2017). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
  26. ↑ dani (March 27, 2022). Re: Small Quadratic Growth Patterns (discussion thread) at the ConwayLife.com forums
  27. ↑ dani (March 20, 2022). Re: Small Quadratic Growth Patterns (discussion thread) at the ConwayLife.com forums

External links

Forum threads

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