Difference between revisions of "Glider synthesis"
(→Features of syntheses: Mention RCT) |
(spelling) |
||
(283 intermediate revisions by 24 users not shown) | |||
Line 1: | Line 1: | ||
{|style="margin-left:16px;margin-bottom:8px;width:300px;float:right;" | |||
|{{EmbedViewer | |||
|pname = loafer_synth | |||
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 14 GPS 10 THEME Book AUTOSTART T 0 PAUSE 2 T 99 PAUSE 1 LOOP 100 ]] | |||
|position = center | |||
|caption = An 8-glider synthesis of a [[loafer]] | |||
}} | |||
|} | |||
{{Glossary}} | {{Glossary}} | ||
'''Glider synthesis''' (or '''glider construction''') is the construction of an object by means of [[glider]] | '''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== | ||
Four main characterizing features of a synthesis are the ''geometry'', '' | 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: | The '''geometry''' is the number of directions of incoming gliders: | ||
Line 9: | Line 17: | ||
* 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 | 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 ''' | The '''construction time''' is simply the number of [[generation]]s it takes to complete a synthesis. For multi-stage syntheses, each stage has its own construction time. | ||
The ''' | 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. | 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 | 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 [[ | 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. | |||
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 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" | |||
! 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}} || – || – | |||
|- | |||
| 5 || {{A019473|5}} || 2 || 2.000 || 2 || {{A056613|5}} || – || – | |||
|- | |||
| 6 || {{A019473|6}} || 2 || 3.200 || 4 || {{A056613|6}} || – || – | |||
|- | |||
| 7 || {{A019473|7}} || 2 || 2.750 || 4 || {{A056613|7}} || – || – | |||
|- | |||
| 8 || {{A019473|8}} || 2 || 3.556 || 4 || {{A056613|8}} || 2 || 2 | |||
|- | |||
| 9 || {{A019473|9}} || 3 || 4.000 || 5 || {{A056613|9}} || 3 || 3 | |||
|- | |||
| 10 || {{A019473|10}} || 4 || 4.360 || 5 || {{A056613|10}} || 3 || 5 | |||
|- | |||
| 11 || {{A019473|11}} || 4 || 4.543 || 5 || {{A056613|11}} || 3 || 6 | |||
|- | |||
| 12 || {{A019473|12}} || 4 || 4.983 || 7 || {{A056613|12}} || 3 || 9 | |||
|- | |||
| 13 || {{A019473|13}} || 4 || 5.408 || 8 || {{A056613|13}} || 4 || 9 | |||
|- | |||
| 14 || {{A019473|14}} || 3 || 6.019 || 9 || {{A056613|14}} || 3 || 11 | |||
|- | |||
| 15 || {{A019473|15}} || 4 || 6.911 || 10 || {{A056613|15}} || 4 || 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.}} | |||
|- | |||
| 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.}} | |||
|- | |||
| 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.}} | |||
|- | |||
| 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.}} | |||
|- | |||
| 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.}} | |||
|- | |||
| 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.}} | |||
|} | |||
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 ≤ 236</tt> such that not all still lifes with <tt>≥ 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. | |||
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]]. | |||
<!-- NOTE: "o" and "d" stand for "orthogonal" and "diagonal" respectively; the numbers are the speeds converted into decimal form --> | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! rowspan="2" | Name !! rowspan="2" | Speed !! colspan="2" | First synthesis !! Best current synthesis | ! rowspan="2" | Name !! rowspan="2" | Speed !! colspan="2" | First synthesis !! Best current synthesis | ||
Line 37: | 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]] || 37 | ||
|- | |||
| [[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 || [[Ivan Fomichev]], [[Mark Niemiec]], [[Martin Grant]], [[Michael Simkin]] || 24 | |||
|- | |||
| [[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 | |||
|- | |||
| [[30P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2015-01-01 || [[Martin Grant]], [[Matthias Merzenich]], [[Tanner Jacobi]] || 39 | |||
|- | |- | ||
| [[25P3H1V0. | | [[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]], [[Tanner Jacobi]] || 12 | ||
|- | |- | ||
| [[ | | [[weekender]] || data-sort-value="o 0.285714" | [[2c/7 orthogonal]] || 2015-01-25 || [[Chris Cain]], [[Martin Grant]], [[Tanner Jacobi]] || 28 | ||
|- | |- | ||
| [[ | | [[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 | ||
|- | |- | ||
| [[ | | 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 | ||
|- | |- | ||
| [[copperhead]] || data-sort-value="o 0.1" | [[c/10 orthogonal]] || 2016-03-05 || [[ | | [[Pushalong 1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2015-06-12 || [[Martin Grant]] || 14 | ||
|- | |||
| [[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 | |||
|- | |||
| [[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]], [[Tanner Jacobi]] || 18 | |||
|- | |||
| [[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 | |||
|- | |||
| [[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 || [[Martin Grant]], [[Tanner Jacobi]] || 46 | |||
|- | |||
| [[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 | |||
|- | |||
| [[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 | |||
|- | |||
| [[70P2H1V0.1]] || data-sort-value="o 0.5" | [[c/2 orthogonal]] || 2020-07-18 || [[Martin Grant]] || 178 | |||
|- | |- | ||
| [[ | | [[44P5H2V0]] || data-sort-value="o 0.4" | [[2c/5 orthogonal]] || 2020-08-29 || [[Goldtiger997]] || 24 | ||
|- | |- | ||
| [[ | | [[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 | 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> | |||
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 | 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 [[ | All 71 such syntheses can be seen below in a pattern put together by [[Jason Summers]] on January 29, {{year|2005}}: | ||
{{EmbedViewer | |||
|pname = twoglidersyntheses | |||
|position = center | |||
|caption = All 71 distinct 2-glider collisions, arranged by what they synthesize | |||
|viewerconfig = #C [[ WIDTH 1200 HEIGHT 1200 ZOOM 3 ]] | |||
}} | |||
==See also== | ==See also== | ||
*[[ | * {{CategoryLink|Patterns constructible by a given number of gliders}} | ||
*[[ | * [[Salvo]] | ||
* [[Tutorials/Glider syntheses]] | |||
* [[Shinjuku]] | |||
* [[Glider destruction]] | |||
==References== | ==References== | ||
<references /> | <references> | ||
<ref name="post11972">{{LinkForumThread | |||
|format = ref | |||
|title = Re: 17-bit SL Syntheses | |||
|p = 11972 | |||
|author = Martin Grant | |||
|date = May 17, 2014 | |||
}}</ref> | |||
<ref name="post82560">{{LinkForumThread | |||
|format = ref | |||
|title = Re: 17 in 17: Efficient 17-bit synthesis project | |||
|p = 82560 | |||
|author = Tanner Jacobi | |||
|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 name="post83979">{{LinkForumThread | |||
|format = ref | |||
|title = Re: 18-bit SL Syntheses (100% Complete!) | |||
|p = 83979 | |||
|author = Ian07 | |||
|date = October 9, 2019 | |||
}}</ref> | |||
<ref name="post89061">{{LinkForumThread | |||
|format = ref | |||
|title = Re: 19-bit still life syntheses | |||
|p = 89061 | |||
|author = Martin Grant | |||
|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 name="post37438">{{LinkForumThread | |||
|format = ref | |||
|title = Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain) | |||
|p = 37438 | |||
|author = Martin Grant | |||
|date = November 19, 2016 | |||
}}</ref> | |||
<ref name="post43734">{{LinkForumThread | |||
|format = ref | |||
|title = Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain) | |||
|p = 43734 | |||
|author = Goldtiger997 | |||
|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> | |||
</references> | |||
==External links== | ==External links== | ||
*[ | * [https://catagolue.hatsya.com/syntheses Catagolue synthesis database] | ||
*[ | * {{LinkNiemiec|lifepage.htm|title=Mark Niemiec's glider synthesis database}} | ||
*[http://pentadecathlon.com/constructions/components/components.php Heinrich Koenig's component catalog] on pentadecathlon.com | * [https://conwaylife.com/ref/DRH/life.html Dean Hickerson's Life page] with four pages of glider syntheses | ||
{{LinkLexicon|lex_g.htm#glidersynthesis}} | * [https://conwaylife.com/forums/viewtopic.php?p=46552#p46552 Martin Grant's synthesis component database], version 3 | ||
{{ | * [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}} | |||
===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
|
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 ( A019473) |
Min. cost | Avg. cost | Max. cost | Count ( 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.
- ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 15 gliders using the reverse caber-tosser
- ↑ All but 3 16-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
- ↑ All but 2 17-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
- ↑ All but 128 18-bit strict still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
- ↑ All but 35 18-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
- ↑ 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.
- ↑ All but 54 19-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
- ↑ 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.
- ↑ All but 279 20-bit pseudo still lifes can be constructed with strictly less than one glider per bit as of March 13, 2024.
- ↑ 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.
- ↑ 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.
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
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:
All 71 distinct 2-glider collisions, arranged by what they synthesize (click above to open LifeViewer) RLE: here Plaintext: here |
See also
- Patterns constructible by a given number of gliders (category)
- Salvo
- Tutorials/Glider syntheses
- Shinjuku
- Glider destruction
References
- ↑ Dave Greene (August 14, 2022). Re: Suggested LifeWiki edits (discussion thread) at the ConwayLife.com forums
- ↑ Carson Cheng (April 6, 2023). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
- ↑ Mark D. Niemiec (June 20, 2015). Re: 4 glider syntheses (discussion thread) at the ConwayLife.com forums
- ↑ Constructions Known for All Still Lifes up to 17 Bits at Game of Life News. Posted by Dave Greene on May 23, 2014.
- ↑ Martin Grant (January 6, 2014). 17-bit SL Syntheses (100% Complete!) (discussion thread) at the ConwayLife.com forums
- ↑ Martin Grant (May 17, 2014). Re: 17-bit SL Syntheses (discussion thread) at the ConwayLife.com forums
- ↑ Ian07 (October 9, 2019). Re: 18-bit SL Syntheses (100% Complete!) (discussion thread) at the ConwayLife.com forums
- ↑ Martin Grant (February 8, 2020). Re: 19-bit still life syntheses (discussion thread) at the ConwayLife.com forums
- ↑ Martin Grant (March 12, 2021). Re: 20-bit still life syntheses (discussion thread) at the ConwayLife.com forums
- ↑ May13 (November 14, 2022). Re: 21-bit still life syntheses (discussion thread) at the ConwayLife.com forums
- ↑ BlinkerSpawn (October 27, 2016). 15 in 15: Efficient 15-bit Synthesis Project (DONE!) (discussion thread) at the ConwayLife.com forums
- ↑ Martin Grant (November 19, 2016). Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain) (discussion thread) at the ConwayLife.com forums
- ↑ Bob Shemyakin (December 20, 2016). 16 in 16: Efficient 16-bit Synthesis Project (discussion thread) at the ConwayLife.com forums
- ↑ Goldtiger997 (May 24, 2017). Re: 15 in 15: Efficient 15-bit Synthesis Project (2 SLs remain) (discussion thread) at the ConwayLife.com forums
- ↑ Tanner Jacobi (September 9, 2019). Re: 17 in 17: Efficient 17-bit synthesis project (discussion thread) at the ConwayLife.com forums
- ↑ Adam P. Goucher (September 19, 2020). Re: Binary slow salvos (discussion thread) at the ConwayLife.com forums
- ↑ Adam P. Goucher. "Syntheses". Catagolue. Retrieved on November 15, 2022.
- ↑ Goldtiger997 (March 8, 2021). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
- ↑ Goldtiger997 (April 10, 2021). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
- ↑ Mark Niemiec (January 14, 2022). Re: Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
- ↑ https://conwaylife.com/forums/viewtopic.php?f=2&t=1557&start=625#p154625
- ↑ https://conwaylife.com/forums/viewtopic.php?f=2&t=1557&start=625#p154645
- ↑ Bob Shemyakin (June 16, 2014). 4 glider syntheses (discussion thread) at the ConwayLife.com forums
- ↑ Michael Simkin (October 24, 2014). Re: Making switch-engines (discussion thread) at the ConwayLife.com forums
- ↑ Luka Okanishi (March 12, 2017). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
- ↑ dani (March 27, 2022). Re: Small Quadratic Growth Patterns (discussion thread) at the ConwayLife.com forums
- ↑ dani (March 20, 2022). Re: Small Quadratic Growth Patterns (discussion thread) at the ConwayLife.com forums
External links
- Catagolue synthesis database
- Mark Niemiec's glider synthesis database at Mark D. Niemiec's Life Page
- Dean Hickerson's Life page with four pages of glider syntheses
- Martin Grant's synthesis component database, version 3
- Heinrich Koenig's component catalog on pentadecathlon.com
- Glider synthesis at the Life Lexicon
Forum threads
- Still Life Synthesis Thread (discussion thread) at the ConwayLife.com forums
- Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- Small Spaceship Syntheses (discussion thread) at the ConwayLife.com forums
- Soup-based syntheses (discussion thread) at the ConwayLife.com forums
- Randomly enumerating glider syntheses (discussion thread) at the ConwayLife.com forums
- 4 glider syntheses (discussion thread) at the ConwayLife.com forums
- Synthesis components (discussion thread) at the ConwayLife.com forums