https://www.conwaylife.com/w/api.php?action=feedcontributions&user=Rich+Holmes&feedformat=atomLifeWiki - User contributions [en]2020-04-01T08:56:11ZUser contributionsMediaWiki 1.33.0https://www.conwaylife.com/w/index.php?title=Period-24_glider_gun&diff=28400Period-24 glider gun2016-07-06T04:09:36Z<p>Rich Holmes: Jacobi's p48 image</p>
<hr />
<div>{{Requestpatternfile}}<br />
{{Gun<br />
|name = True period 24 gun<br />
|pname = trueperiod24gun<br />
|c = 335<br />
|bx = 43<br />
|by = 32<br />
|p = 24<br />
|discoverer = Noam Elkies<br />
|discoveryear = 1997<br />
|nofile = true<br />
}}<br />
'''True period 24 gun''' is a [[Gun#True-period_guns|true period]] 24 [[gun]] discovered by [[Noam Elkies|Noam D. Elkies]] in [[:Category:Patterns found in 1997|1997]].<ref name="callahan">{{cite web|url=http://www.radicaleye.com/lifepage/patterns/p24gun/p24gun.html|title=p24 "true" gun (mail digest)|author=Paul Callahan|date=February 11, 2001|accessdate=March 17, 2016}}</ref> It uses four large [[period]] [[:Category:oscillators with period 4|4]] [[oscillator]]s (two of them variants of [[fountain]], the other two adjoined by common [[casing]]) to hassle two [[T-tetromino]]s, which react together to produce gliders. The form on the right is a reduced variant found by Karel Suhajda.<ref name="jslife">{{cite web|url=http://entropymine.com/jason/life/|title=Pattern Collections, jslife/osc |author=Jason Summers|date=December 30, 2012|accessdate=March 17, 2016}}</ref><br />
<br />
No more than five days after the initial discovery, Elkies found a method to double the period of the gun, resulting in the first known period 48 glider gun.<ref name="callahan" /> A smaller version was found in 2016 by Tanner Jacobi, using [[Rich's p16]] to double the period.<ref name="jacobi">{{cite web|title=Re: Soup search results|author=Tanner Jacobi|date=2016-07-05|accessdate=2016-07-05|work=ConwayLife.com forums|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1452&start=1075#p32769}}</ref><br />
<br />
==Image gallery==<br />
{|<br />
|-<br />
|[[Image:Period24glidergun(original).png|framed|left|Original period 24 glider gun.]]<br />
|[[Image:P48-gun-smaller.png|framed|left|Period 48 glider gun.]]<br />
|}<br />
<br />
==See also==<br />
<br />
[[Period-20 glider gun]]<br />
<br />
==References==<br />
<br />
<references/></div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=File:P48-gun-smaller.png&diff=28399File:P48-gun-smaller.png2016-07-06T04:06:24Z<p>Rich Holmes: Rich Holmes uploaded a new version of &quot;File:P48-gun-smaller.png&quot;</p>
<hr />
<div>Tanner Jacobi's p48 gun</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=File:P48-gun-smaller.png&diff=28398File:P48-gun-smaller.png2016-07-06T03:58:23Z<p>Rich Holmes: Tanner Jacobi's p48 gun</p>
<hr />
<div>Tanner Jacobi's p48 gun</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Period-24_glider_gun&diff=28378Period-24 glider gun2016-07-05T16:37:08Z<p>Rich Holmes: Smaller p48</p>
<hr />
<div>{{Requestpatternfile}}<br />
{{Gun<br />
|name = True period 24 gun<br />
|pname = trueperiod24gun<br />
|c = 335<br />
|bx = 43<br />
|by = 32<br />
|p = 24<br />
|discoverer = Noam Elkies<br />
|discoveryear = 1997<br />
|nofile = true<br />
}}<br />
'''True period 24 gun''' is a [[Gun#True-period_guns|true period]] 24 [[gun]] discovered by [[Noam Elkies|Noam D. Elkies]] in [[:Category:Patterns found in 1997|1997]].<ref name="callahan">{{cite web|url=http://www.radicaleye.com/lifepage/patterns/p24gun/p24gun.html|title=p24 "true" gun (mail digest)|author=Paul Callahan|date=February 11, 2001|accessdate=March 17, 2016}}</ref> It uses four large [[period]] [[:Category:oscillators with period 4|4]] [[oscillator]]s (two of them variants of [[fountain]], the other two adjoined by common [[casing]]) to hassle two [[T-tetromino]]s, which react together to produce gliders. The form on the right is a reduced variant found by Karel Suhajda.<ref name="jslife">{{cite web|url=http://entropymine.com/jason/life/|title=Pattern Collections, jslife/osc |author=Jason Summers|date=December 30, 2012|accessdate=March 17, 2016}}</ref><br />
<br />
No more than five days after the initial discovery, Elkies found a method to double the period of the gun, resulting in the first known period 48 glider gun.<ref name="callahan" /> The period 48 gun is shown below using the reduced variant form.<ref name="jslife" /> A smaller p48 gun was found in 2016 by Tanner Jacobi, using [[Rich's p16]] to double the period.<ref name="jacobi">{{cite web|title=Re: Soup search results|author=Tanner Jacobi|date=2016-07-05|accessdate=2016-07-05|work=ConwayLife.com forums|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1452&sid=f4f6a10cc8b6e7902a977e422502bc24&start=1075#p32769}}</ref><br />
<br />
==Image gallery==<br />
{|<br />
|-<br />
|[[Image:Period24glidergun(original).png|framed|left|Original period 24 glider gun.]]<br />
|[[Image:Period48glidergun.png|framed|left|Period 48 glider gun.]]<br />
|}<br />
<br />
==See also==<br />
<br />
[[Period-20 glider gun]]<br />
<br />
==References==<br />
<br />
<references/></div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Bellman&diff=24268Bellman2016-05-02T02:31:18Z<p>Rich Holmes: </p>
<hr />
<div>Bellman, named after the character in Lewis Carroll's The Hunting of the Snark, is a program for searching for catalytic interactions in Conway's Game of Life and potentially other similar cellular automata. Results are derived directly from the automaton's evolution rule, not generated from a list of candidate catalysts as with previous searchers.<br />
<br />
== External links ==<br />
<br />
* [http://sourceforge.net/projects/bellman/ Bellman - Conway's Life pattern searcher]<br />
<br />
[[Category:Software]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Bellman&diff=24267Bellman2016-05-02T02:30:11Z<p>Rich Holmes: Initial</p>
<hr />
<div>Bellman, named after the character in Lewis Carroll's The Hunting of the Snark, is a program for searching for catalytic interactions in Conway's Game of Life and potentially other similar cellular automata. Results are derived directly from the automaton's evolution rule, not generated from a list of candidate catalysts as with previous searchers.<br />
<br />
== External links ==<br />
<br />
* [http://sourceforge.net/projects/bellman/ Bellman - Conway's Life pattern searcher]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Splitter&diff=23660Splitter2016-04-20T00:25:31Z<p>Rich Holmes: </p>
<hr />
<div>{{glossary}}<br />
{{stub}}<br />
In [[salvo|slow salvo synthesis]], a [[splitter]] is a [[constellation]] that can be hit by a [[glider]] to produce two or more output gliders.<br />
<br />
A total of 280 splitters are known that:<br />
* are slow salvo [[Glider construction|constructible]] by seven gliders<br />
* Fits in a [[bounding box]] of 10×10<br />
<br />
==See also==<br />
* [[Converter]]<br />
* [[One-time reflector]]<br />
* [[Rephaser]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Glider_synthesis&diff=23659Glider synthesis2016-04-20T00:24:50Z<p>Rich Holmes: </p>
<hr />
<div>{{Glossary}}<br />
'''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.<br />
<br />
Glider syntheses for all [[still life]]s and known [[oscillator]]s with at most 14 [[cell]]s were found by [[:Category:Patterns found by David Buckingham|David Buckingham]]. A collaborative effort then completed glider syntheses of all still lifes with 17 or fewer cells in 2014.<ref>{{cite web|url=http://pentadecathlon.com/lifeNews/2014/05/constructions_known_for_all_st.html |title=Constructions Known for All Still Lifes up to 17 Bits |work=Game of Life News |publisher=Dave Greene |accessdate=September 17, 2014}}</ref><ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1276 |title=17-bit SL Syntheses (100% Complete!) |work=ConwayLife.com forums |publisher=Martin Grant|accessdate=September 17, 2014}}</ref><br />
<br />
==Features of syntheses==<br />
Four main characterizing features of a synthesis are the ''geometry'', ''reaction speed'', ''reaction multiplicity''<!--or is there a more standard term?-->, and ''glider cost''.<br />
<br />
The '''geometry''' is the number of directions of incoming gliders:<br />
* four-directional: gliders collide from all four directions<br />
* three-directional: gliders collide from all directions but one<br />
* two-directional; further divisible in head-on and 90° syntheses. All two-glider syntheses are necessarily two-directional.<br />
* unidirectional, which assumes the initial presence of a '''target''' (usually a [[still life]] or an [[oscillator]]) to be hit with gliders.<br />
Since gliders are themselves glider-constructible, any multidirectional synthesis can be technically downgraded to a fewer-directional one, usually at the cost of increasing the speed, multiplicity and cost of the synthesis. More challenging is finding a two- or three-directional synthesis for a particular object where few or no parts of the synthesis reactions extend outside the final pattern's [[bounding box]] in a particular direction. This is especially important for the synthesis of temporary catalysts, which will need to be placed sometimes quite close to other components without perturbing them. For especially tight locations, sometimes it will be useful to construct an [[LWSS]] (or another standard c/2 spaceship) some ways away from the synthesis nexus and let that collide with a glider in the final stages; this allows synthesis at a 45° angle, rather than a 90° angle as required for synthesis by gliders from separate directions.<br />
<br />
The '''speed''' is simply the number of [[generation]]s it takes to complete a synthesis. For multi-stage syntheses, each stage has its own speed.<br />
<br />
The '''multiplicity''' is the number of stages a synthesis operates in. Often a particular synthesis operation cannot be achieved by a direct collision of gliders, and a synthesis procedure instead requires first synthesizing a number of [[catalyst]]s, and then hitting these with gliders to produce the final result.<br />
<br />
The '''cost''' is the number of gliders expended over the course of the synthesis. Much as speed, it can be defined also for individual synthesis stages.<br />
<br />
Of particular interest is [[salvo|slow salvo synthesis]]: unidirectional synthesis where every stage has a glider cost of one. Perhaps surprisingly, anything that is glider synthesizable is also slow salvo synthesizable; a result that crucially depends on the existence of [[movable target]]s and [[splitter]]s.<br />
<br />
==Syntheses of note==<br />
[[Image:glider_synth_pentadecathlon.png|framed|right|A 3-glider synthesis of a [[pentadecathlon]].]]Perhaps the most interesting glider syntheses are those of [[spaceship]]s, because these can be used to create corresponding [[gun]]s and [[rake]]s. Many of the [[:Category:Spaceships with speed c/2|c/2]] spaceships that are based on standard spaceships have been synthesized, mostly by [[:Category:Patterns found by Mark Niemiec|Mark Niemiec]]. In June [[:Category:Patterns found in 1998|1998]], [[:Category:Patterns found by Stephen Silver|Stephen Silver]] found syntheses for some of the [[Cordership]]s (although it was not until July [[:Category:Patterns found in 1999|1999]] that [[:Category:Patterns found by Jason Summers|Jason Summers]] used this to build a Cordership gun). In May [[:Category:Patterns found in 2000|2000]], [[Noam Elkies]] suggested that a [[:Category:Spaceships with speed 2c/5|2c/5]] spaceship ([[60P5H2V0]]) found by [[:Category:Patterns found by Tim Coe|Tim Coe]] in May [[:Category:Patterns found in 1996|1996]] might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March [[:Category:Patterns found in 2003|2003]] that Summers and Elkies managed to find a way to perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in [[Conway's Game of Life|Life]] of a rake which fires spaceships that travel in the same direction as the rake but more slowly.<br />
<br />
During late 2014 and early 2015, a number of new spaceship syntheses were found, including the [[dart]], [[crab]], [[25P3H1V0.2]], [[30P5H2V0]], [[x66]], and [[weekender]]. [[Pushalong 1]] was reduced to glider collisions with a [[constellation]], though a full syntheses is not yet available. Most of this was due to the work of [[:Category:Patterns found by Martin Grant|Martin Grant]].<br />
<br />
A 3-glider synthesis of a [[pentadecathlon]] was found in April [[:Category:Patterns found in 1997|1997]] by [[:Category:Patterns found by Heinrich Koenig|Heinrich Koenig]], which came as a surprise because it was widely assumed that anything using just three gliders would already be known.<br />
<br />
===2-glider syntheses===<br />
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]].<br />
<br />
All 71 such syntheses can be seen below in a pattern put together by [[:Category:Patterns found by Jason Summers|Jason Summers]] on January 29, [[:Category:Patterns found in 2005|2005]].<br />
<br />
[[Image:2glidersyntheses.png|framed|center|All 71 distinct 2-glider collisions, arranged by what they synthesize.<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/patterns/twoglidersyntheses.rle click here] ]]<br />
<br />
==See also==<br />
*[[:Category:Pattern_constructible_by_a_given_number_of_gliders|List of known glider syntheses]]<br />
*[[Salvo]]<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://radicaleye.com/DRH/life.html Dean Hickerson's Life page] with four pages of glider syntheses<br />
{{LinkWeisstein|GliderSynthesis.html}}<br />
{{LinkLexicon|lex_g.htm#glidersynthesis}}</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Talk:Apgcode&diff=23655Talk:Apgcode2016-04-18T20:52:21Z<p>Rich Holmes: yl codes</p>
<hr />
<div>== yl codes ==<br />
On a brief look at apgsearch.py I see the function that produces yl codes but do not understand it, hence the unsatisfactory vagueness in this article. Someone who understands it better than me should fix it. - [[User:Rich Holmes|Rich Holmes]] ([[User talk:Rich Holmes|talk]]) 20:52, 18 April 2016 (UTC)</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Apgcode&diff=23654Apgcode2016-04-18T20:49:27Z<p>Rich Holmes: Unsatisfactory un-explanation of yl suffixes</p>
<hr />
<div>[[apgsearch]] and the search results database, [[Catagolue]], classify and denote patterns as follows. Most objects are stored as two alphanumeric strings separated by an underscore. The 'prefix' refers to everything before the underscore and may begin with:<br />
<br />
* xs denoting a [[still life]]<br />
* xp denoting an [[oscillator]]<br />
* xq denoting a [[spaceship]]<br />
* yl denoting a periodic linearly growing object, such as a [[puffer]] or [[gun]]<br />
<br />
Oversize still lifes, oscillators, and spaceships, larger than 40 by 40, have a prefix beginning with ov_s, ov_p, or ov_q, respectively.<br />
<br />
These are followed by a number. For xs or ov_s this is the [[population]] of the still life while for the others it is the [[period]] of the object.<br />
<br />
The codes for xs, xp, and xq are followed by an underscore, then a string which is a representation of the object in Extended Wechsler Format, described below. Codes for yl are followed by an underscore and additional information.<br />
<br />
Additionally, objects which apgsearch cannot classify as above are denoted by one of:<br />
<br />
* zz_EXPLOSIVE<br />
* zz_LINEAR<br />
* zz_QUADRATIC<br />
* zz_REPLICATOR<br />
* PATHOLOGICAL<br />
<br />
==Extended Wechsler Format==<br />
<br />
This is an extension of a pattern notation developed by [[Allan Wechsler]] in 1992. A string of ''n'' characters in the set {0, 1, 2, ..., 8, 9, a, b, ..., v} denotes a strip of five rows, ''n'' columns wide. Each character denotes five cells in a vertical column corresponding to the bitstrings {'00000', '00001', '00010', ..., '01000', '01001', '01010', '01011', ... '11111'}. For instance, xq4_27deee6 corresponds to a [[HWSS]]:<br />
<br />
27deee6<br />
.**....<br />
**.****<br />
.******<br />
..****.<br />
.......<br />
<br />
The character 'z' separates contiguous five-row strips. For example, xs31_0ca178b96z69d1d96 is:<br />
<br />
0ca178b96<br />
...**.**.<br />
..*.*.*.*<br />
.*..*...*<br />
.**..***.<br />
.........<br />
<br />
69d1d96<br />
.*****.<br />
*.....*<br />
*.*.*.*<br />
.**.**.<br />
.......<br />
<br />
The characters 'w' and 'x' are used to abbreviate '00' and '000', respectively. So xp30_w33z8kqrqk8zzzx33 is the [[trans-queen-bee-shuttle]]:<br />
<br />
0033<br />
..**<br />
..**<br />
....<br />
....<br />
....<br />
<br />
8kqrqk8<br />
...*...<br />
..***..<br />
.*...*.<br />
*.***.*<br />
.*****.<br />
<br />
[10 blank rows omitted]<br />
<br />
00033<br />
...**<br />
...**<br />
.....<br />
.....<br />
.....<br />
<br />
Note that extraneous '0's at the ends of strips are not included.<br />
<br />
Finally, the symbols {'y0', 'y1', y2', ..., 'yx', 'yy', 'yz'} correspond to runs of between 4 and 39 consecutive '0's. A good example is the [[quadpole on ship]], xp2_31a08zy0123cko:<br />
<br />
31a08<br />
**...<br />
*.*..<br />
.....<br />
..*.*<br />
.....<br />
<br />
0000123cko<br />
....*.*...<br />
.....**...<br />
.......**.<br />
.......*.*<br />
........**<br />
<br />
==Canonical form==<br />
<br />
In order to enforce a canonical form, there are further rules regarding encoding:<br />
<br />
The leftmost column and uppermost row must each contain at least one live cell. (This gives a canonical position.)<br />
<br />
Any '0's on the ends of strips are ignored, and {'00', '000', '0000', '00000', ...} are always replaced with {'w', 'x', 'y0', 'y1', 'y2', ...}.<br />
<br />
(Theoretically, runs of more than 39 zeroes should be replaced by 'yz' followed by the coding for the remaining zeroes. At the moment apgsearch labels everything larger than 40-by-40 as 'oversized' and refuses to process it.)<br />
<br />
A canonical orientation and phase must be determined. For example, with the [[caterer]] (p3 oscillator with no [[symmetry]]), there are three phases and eight orientations, so we have 24 possible encodings. Define a total order on these encodings as follows:<br />
<br />
* Prefer shorter representations to longer representations;<br />
* For representations of the same length, apply lexicographical ASCII ordering (and give preference to earlier strings).<br />
<br />
This gives, for any still-life, oscillator or spaceship, an unambiguous canonical code to represent the pattern. It has several desirable properties:<br />
<br />
Compression: it's much more compact than [[RLE]] or [[SOF]] for storing very small patterns, and often even beats the common name ('xp15_4r4z4r4' is shorter than '[[pentadecathlon]]')! <br />
<br />
Character set: it only uses digits, lowercase letters and the underscore, so can be safely used in filenames and URLs.<br />
<br />
Human-readability: the prefix means that we can instantly see whether a particular object is a still-life (and if so, what size), oscillator (and if so, what period) or spaceship (and if so, what period). It also means that the string is instantly recognised as being an encoding of an object (xp2_7 is obviously a [[blinker]], whereas the digit 7 on its own with no extra context is ambiguous).<br />
<br />
[[Category:Everything else]][[Category:File formats]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Apgcode&diff=23653Apgcode2016-04-18T20:38:03Z<p>Rich Holmes: Links</p>
<hr />
<div>[[apgsearch]] and the search results database, [[Catagolue]], classify and denote patterns as follows. Most objects are stored as two alphanumeric strings separated by an underscore. The 'prefix' refers to everything before the underscore and may begin with:<br />
<br />
* xs denoting a [[still life]]<br />
* xp denoting an [[oscillator]]<br />
* xq denoting a [[spaceship]]<br />
* yl denoting a periodic linearly growing object, such as a [[puffer]] or [[gun]]<br />
<br />
Oversize still lifes, oscillators, and spaceships, larger than 40 by 40, have a prefix beginning with ov_s, ov_p, or ov_q, respectively.<br />
<br />
These are followed by a number. For xs or ov_s this is the [[population]] of the still life while for the others it is the [[period]] of the object.<br />
<br />
The codes for xs, xp, xq, and yl are followed by an underscore, then a string which is a representation of the object in Extended Wechsler Format, described below.<br />
<br />
Additionally, objects which apgsearch cannot classify as above are denoted by one of:<br />
<br />
* zz_EXPLOSIVE<br />
* zz_LINEAR<br />
* zz_QUADRATIC<br />
* zz_REPLICATOR<br />
* PATHOLOGICAL<br />
<br />
==Extended Wechsler Format==<br />
<br />
This is an extension of a pattern notation developed by [[Allan Wechsler]] in 1992. A string of ''n'' characters in the set {0, 1, 2, ..., 8, 9, a, b, ..., v} denotes a strip of five rows, ''n'' columns wide. Each character denotes five cells in a vertical column corresponding to the bitstrings {'00000', '00001', '00010', ..., '01000', '01001', '01010', '01011', ... '11111'}. For instance, xq4_27deee6 corresponds to a [[HWSS]]:<br />
<br />
27deee6<br />
.**....<br />
**.****<br />
.******<br />
..****.<br />
.......<br />
<br />
The character 'z' separates contiguous five-row strips. For example, xs31_0ca178b96z69d1d96 is:<br />
<br />
0ca178b96<br />
...**.**.<br />
..*.*.*.*<br />
.*..*...*<br />
.**..***.<br />
.........<br />
<br />
69d1d96<br />
.*****.<br />
*.....*<br />
*.*.*.*<br />
.**.**.<br />
.......<br />
<br />
The characters 'w' and 'x' are used to abbreviate '00' and '000', respectively. So xp30_w33z8kqrqk8zzzx33 is the [[trans-queen-bee-shuttle]]:<br />
<br />
0033<br />
..**<br />
..**<br />
....<br />
....<br />
....<br />
<br />
8kqrqk8<br />
...*...<br />
..***..<br />
.*...*.<br />
*.***.*<br />
.*****.<br />
<br />
[10 blank rows omitted]<br />
<br />
00033<br />
...**<br />
...**<br />
.....<br />
.....<br />
.....<br />
<br />
Note that extraneous '0's at the ends of strips are not included.<br />
<br />
Finally, the symbols {'y0', 'y1', y2', ..., 'yx', 'yy', 'yz'} correspond to runs of between 4 and 39 consecutive '0's. A good example is the [[quadpole on ship]], xp2_31a08zy0123cko:<br />
<br />
31a08<br />
**...<br />
*.*..<br />
.....<br />
..*.*<br />
.....<br />
<br />
0000123cko<br />
....*.*...<br />
.....**...<br />
.......**.<br />
.......*.*<br />
........**<br />
<br />
==Canonical form==<br />
<br />
In order to enforce a canonical form, there are further rules regarding encoding:<br />
<br />
The leftmost column and uppermost row must each contain at least one live cell. (This gives a canonical position.)<br />
<br />
Any '0's on the ends of strips are ignored, and {'00', '000', '0000', '00000', ...} are always replaced with {'w', 'x', 'y0', 'y1', 'y2', ...}.<br />
<br />
(Theoretically, runs of more than 39 zeroes should be replaced by 'yz' followed by the coding for the remaining zeroes. At the moment apgsearch labels everything larger than 40-by-40 as 'oversized' and refuses to process it.)<br />
<br />
A canonical orientation and phase must be determined. For example, with the [[caterer]] (p3 oscillator with no [[symmetry]]), there are three phases and eight orientations, so we have 24 possible encodings. Define a total order on these encodings as follows:<br />
<br />
* Prefer shorter representations to longer representations;<br />
* For representations of the same length, apply lexicographical ASCII ordering (and give preference to earlier strings).<br />
<br />
This gives, for any still-life, oscillator or spaceship, an unambiguous canonical code to represent the pattern. It has several desirable properties:<br />
<br />
Compression: it's much more compact than [[RLE]] or [[SOF]] for storing very small patterns, and often even beats the common name ('xp15_4r4z4r4' is shorter than '[[pentadecathlon]]')! <br />
<br />
Character set: it only uses digits, lowercase letters and the underscore, so can be safely used in filenames and URLs.<br />
<br />
Human-readability: the prefix means that we can instantly see whether a particular object is a still-life (and if so, what size), oscillator (and if so, what period) or spaceship (and if so, what period). It also means that the string is instantly recognised as being an encoding of an object (xp2_7 is obviously a [[blinker]], whereas the digit 7 on its own with no extra context is ambiguous).<br />
<br />
[[Category:Everything else]][[Category:File formats]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=User_talk:Rich_Holmes&diff=23652User talk:Rich Holmes2016-04-18T20:25:37Z<p>Rich Holmes: </p>
<hr />
<div>Howdy, I just wanted to say thanks a lot for the [[Symmetry]] and [[apgsearch format]] entries, it's very good to have those. [[User:Apple Bottom|Apple Bottom]] ([[User talk:Apple Bottom|talk]]) 20:00, 18 April 2016 (UTC)<br />
: And thank you for catching my typo! [[User:Rich Holmes|Rich Holmes]] ([[User talk:Rich Holmes|talk]]) 20:25, 18 April 2016 (UTC)</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Symmetry&diff=23648Symmetry2016-04-18T15:49:19Z<p>Rich Holmes: </p>
<hr />
<div>The Life transition rule, like that of any totalistic cellular automaton, is invariant under reflections and rotations. That is, the change in state of a cell remains the same if its neighborhood is rotated or reflected. This implies there are symmetries which if present in a pattern are present in all its successors. Note that the converse is not true: a pattern need not have the full symmetry of one of its successor states.<br />
<br />
Rotation symmetries include the following:<br />
<br />
* '''C1''': Symmetric under 360° rotation. This is essentially no symmetry at all.<br />
* '''C2''': Symmetric under 180° rotation. There are three possibilities:<br />
** '''C2_1''': Rotation around the center of a cell. The bounding rectangle of a C2_1 pattern is odd by odd.<br />
** '''C2_2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd.<br />
** '''C2_4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
* '''C4''': Symmetric under 90° rotation. There are two possibilities:<br />
** '''C4_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.<br />
** '''C4_4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
<br />
("C" refers to the cyclic group.)<br />
<br />
Reflection symmetries include:<br />
<br />
* '''D2''': Symmetric under reflection through a line. There are two possibilities:<br />
** '''D2_+''' The line is horizontal or vertical. There are two possibilities:<br />
*** '''D2_+1''' The line bisects a row of cells. The bounding rectangle is odd by any.<br />
*** '''D2_+2''' The line lies between two rows of cells. The bounding rectangle is even by any.<br />
** '''D2_x''' The line is diagonal.<br />
* '''D4''': Symmetric under both reflection and 180° rotation. The reflection symmetry will be with respect to two lines. There are two possibilities:<br />
** '''D4_+''': The lines are horizontal and vertical. There are three possibilities:<br />
*** '''D4_+1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.<br />
*** '''D4_+2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd.<br />
*** '''D4_+4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
** '''D4_x''' The lines are diagonal. There are two possibilities:<br />
*** '''D4_x1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.<br />
*** '''D4_x4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
* '''D8''': Symmetric under both reflection and 90° rotation. The reflection symmetry will be with respect to horizontal, vertical, and diagonal lines. There are two possibilities:<br />
** '''D8_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.<br />
** '''D8_4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
<br />
("D" refers to the dihedral group.)<br />
<br />
==References==<br />
<br />
* [http://www.conwaylife.com/forums/viewtopic.php?f=7&t=1898&start=0 Help with symmetries]<br />
<br />
<br />
[[Category: Everything else]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Symmetry&diff=23647Symmetry2016-04-18T15:44:58Z<p>Rich Holmes: Initial entry</p>
<hr />
<div>The Life transition rule, like that of any totalistic cellular automaton, is invariant under reflections and rotations. That is, the change in state of a cell remains the same if its neighborhood is rotated or reflected. This implies there are symmetries which if present in a pattern are present in all its successors. Note that the converse is not true: a pattern need not have the full symmetry of one of its successor states.<br />
<br />
Rotation symmetries include the following:<br />
<br />
* '''C1''': Symmetric under 360° rotation. This is essentially no symmetry at all.<br />
* '''C2''': Symmetric under 180° rotation. There are three possibilities:<br />
** '''C2_1''': Rotation around the center of a cell. The bounding rectangle of a C2_1 pattern is odd by odd.<br />
** '''C2_2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd.<br />
** '''C2_4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
* '''C4''': Symmetric under 90° rotation. There are two possibilities:<br />
** '''C4_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.<br />
** '''C4_4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
<br />
("C" refers to the cyclic group.)<br />
<br />
Reflection symmetries include:<br />
<br />
* '''D2''': Symmetric under reflection through a line. There are two possibilities:<br />
** '''D2_+''' The line is horizontal or vertical. There are two possibilities:<br />
*** '''D2_+1''' The line bisects a row of cells. The bounding rectangle is odd by any.<br />
*** '''D2_+2''' The line lies between two rows of cells. The bounding rectangle is even by any.<br />
** '''D2_x''' The line is diagonal.<br />
* '''D4''': Symmetric under both reflection and 180° rotation. The reflection symmetry will be with respect to two lines. There are two possibilities:<br />
** '''D4-+''': The lines are horizontal and vertical. There are three possibilities:<br />
*** '''D4_+1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.<br />
*** '''D4_+2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd.<br />
*** '''D4_+4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
** '''D4_x''' The lines are diagonal. There are two possibilities:<br />
*** '''D4_x1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.<br />
*** '''D4_x4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
* '''D8''': Symmetric under both reflection and 90° rotation. The reflection symmetry will be with respect to horizontal, vertical, and diagonal lines. There are two possibilities:<br />
** '''D8_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd.<br />
** '''D8_4''': Rotation around a corner of a cell. The bounding rectangle is even by even.<br />
<br />
("D" refers to the dihedral group.)<br />
<br />
==References==<br />
<br />
* [http://www.conwaylife.com/forums/viewtopic.php?f=7&t=1898&start=0 Help with symmetries]<br />
<br />
<br />
[[Category: Everything else]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Apgcode&diff=23646Apgcode2016-04-18T14:03:33Z<p>Rich Holmes: /* Canonical form */</p>
<hr />
<div>[[apgsearch]] and the search results database, [[Catagolue]], classify and denote patterns as follows. Most objects are stored as two alphanumeric strings separated by an underscore. The 'prefix' refers to everything before the underscore and may begin with:<br />
<br />
* xs denoting a [[still life]]<br />
* xp denoting an [[oscillator]]<br />
* xq denoting a [[spaceship]]<br />
* yl denoting a periodic linearly growing object, such as a puffer or gun<br />
<br />
Oversize still lifes, oscillators, and spaceships, larger than 40 by 40, have a prefix beginning with ov_s, ov_p, or ov_q, respectively.<br />
<br />
These are followed by a number. For xs or ov_s this is the [[population]] of the still life while for the others it is the [[period]] of the object.<br />
<br />
The codes for xs, xp, xq, and yl are followed by an underscore, then a string which is a representation of the object in Extended Wechsler Format, described below.<br />
<br />
Additionally, objects which apgsearch cannot classify as above are denoted by one of:<br />
<br />
* zz_EXPLOSIVE<br />
* zz_LINEAR<br />
* zz_QUADRATIC<br />
* zz_REPLICATOR<br />
* PATHOLOGICAL<br />
<br />
==Extended Weschler Format==<br />
<br />
This is an extension of a pattern notation developed by Allan Wechsler in 1992. A string of ''n'' characters in the set {0, 1, 2, ..., 8, 9, a, b, ..., v} denotes a strip of five rows, ''n'' columns wide. Each character denotes five cells in a vertical column corresponding to the bitstrings {'00000', '00001', '00010', ..., '01000', '01001', '01010', '01011', ... '11111'}. For instance, xq4_27deee6 corresponds to a [[HWSS]]:<br />
<br />
27deee6<br />
.**....<br />
**.****<br />
.******<br />
..****.<br />
.......<br />
<br />
The character 'z' separates contiguous five-row strips. For example, xs31_0ca178b96z69d1d96 is:<br />
<br />
0ca178b96<br />
...**.**.<br />
..*.*.*.*<br />
.*..*...*<br />
.**..***.<br />
.........<br />
<br />
69d1d96<br />
.*****.<br />
*.....*<br />
*.*.*.*<br />
.**.**.<br />
.......<br />
<br />
The characters 'w' and 'x' are used to abbreviate '00' and '000', respectively. So xp30_w33z8kqrqk8zzzx33 is the [[trans-queen-bee-shuttle]]:<br />
<br />
0033<br />
..**<br />
..**<br />
....<br />
....<br />
....<br />
<br />
8kqrqk8<br />
...*...<br />
..***..<br />
.*...*.<br />
*.***.*<br />
.*****.<br />
<br />
[10 blank rows omitted]<br />
<br />
00033<br />
...**<br />
...**<br />
.....<br />
.....<br />
.....<br />
<br />
Note that extraneous '0's at the ends of strips are not included.<br />
<br />
Finally, the symbols {'y0', 'y1', y2', ..., 'yx', 'yy', 'yz'} correspond to runs of between 4 and 39 consecutive '0's. A good example is the [[quadpole on ship]], xp2_31a08zy0123cko:<br />
<br />
31a08<br />
**...<br />
*.*..<br />
.....<br />
..*.*<br />
.....<br />
<br />
0000123cko<br />
....*.*...<br />
.....**...<br />
.......**.<br />
.......*.*<br />
........**<br />
<br />
==Canonical form==<br />
<br />
In order to enforce a canonical form, there are further rules regarding encoding:<br />
<br />
The leftmost column and uppermost row must each contain at least one live cell. (This gives a canonical position.)<br />
<br />
Any '0's on the ends of strips are ignored, and {'00', '000', '0000', '00000', ...} are always replaced with {'w', 'x', 'y0', 'y1', 'y2', ...}.<br />
<br />
(Theoretically, runs of more than 39 zeroes should be replaced by 'yz' followed by the coding for the remaining zeroes. At the moment apgsearch labels everything larger than 40-by-40 as 'oversized' and refuses to process it.)<br />
<br />
A canonical orientation and phase must be determined. For example, with the caterer (p3 oscillator with no symmetry), there are three phases and eight orientations, so we have 24 possible encodings. Define a total order on these encodings as follows:<br />
<br />
* Prefer shorter representations to longer representations;<br />
* For representations of the same length, apply lexicographical ASCII ordering (and give preference to earlier strings).<br />
<br />
This gives, for any still-life, oscillator or spaceship, an unambiguous canonical code to represent the pattern. It has several desirable properties:<br />
<br />
Compression: it's much more compact than RLE or SOF for storing very small patterns, and often even beats the common name ('xp15_4r4z4r4' is shorter than 'pentadecathlon')! <br />
<br />
Character set: it only uses digits, lowercase letters and the underscore, so can be safely used in filenames and URLs.<br />
<br />
Human-readability: the prefix means that we can instantly see whether a particular object is a still-life (and if so, what size), oscillator (and if so, what period) or spaceship (and if so, what period). It also means that the string is instantly recognised as being an encoding of an object (xp2_7 is obviously a blinker, whereas the digit 7 on its own with no extra context is ambiguous).<br />
<br />
[[Category:Everything else]][[Category:File formats]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Apgcode&diff=23645Apgcode2016-04-18T14:02:12Z<p>Rich Holmes: </p>
<hr />
<div>[[apgsearch]] and the search results database, [[Catagolue]], classify and denote patterns as follows. Most objects are stored as two alphanumeric strings separated by an underscore. The 'prefix' refers to everything before the underscore and may begin with:<br />
<br />
* xs denoting a [[still life]]<br />
* xp denoting an [[oscillator]]<br />
* xq denoting a [[spaceship]]<br />
* yl denoting a periodic linearly growing object, such as a puffer or gun<br />
<br />
Oversize still lifes, oscillators, and spaceships, larger than 40 by 40, have a prefix beginning with ov_s, ov_p, or ov_q, respectively.<br />
<br />
These are followed by a number. For xs or ov_s this is the [[population]] of the still life while for the others it is the [[period]] of the object.<br />
<br />
The codes for xs, xp, xq, and yl are followed by an underscore, then a string which is a representation of the object in Extended Wechsler Format, described below.<br />
<br />
Additionally, objects which apgsearch cannot classify as above are denoted by one of:<br />
<br />
* zz_EXPLOSIVE<br />
* zz_LINEAR<br />
* zz_QUADRATIC<br />
* zz_REPLICATOR<br />
* PATHOLOGICAL<br />
<br />
==Extended Weschler Format==<br />
<br />
This is an extension of a pattern notation developed by Allan Wechsler in 1992. A string of ''n'' characters in the set {0, 1, 2, ..., 8, 9, a, b, ..., v} denotes a strip of five rows, ''n'' columns wide. Each character denotes five cells in a vertical column corresponding to the bitstrings {'00000', '00001', '00010', ..., '01000', '01001', '01010', '01011', ... '11111'}. For instance, xq4_27deee6 corresponds to a [[HWSS]]:<br />
<br />
27deee6<br />
.**....<br />
**.****<br />
.******<br />
..****.<br />
.......<br />
<br />
The character 'z' separates contiguous five-row strips. For example, xs31_0ca178b96z69d1d96 is:<br />
<br />
0ca178b96<br />
...**.**.<br />
..*.*.*.*<br />
.*..*...*<br />
.**..***.<br />
.........<br />
<br />
69d1d96<br />
.*****.<br />
*.....*<br />
*.*.*.*<br />
.**.**.<br />
.......<br />
<br />
The characters 'w' and 'x' are used to abbreviate '00' and '000', respectively. So xp30_w33z8kqrqk8zzzx33 is the [[trans-queen-bee-shuttle]]:<br />
<br />
0033<br />
..**<br />
..**<br />
....<br />
....<br />
....<br />
<br />
8kqrqk8<br />
...*...<br />
..***..<br />
.*...*.<br />
*.***.*<br />
.*****.<br />
<br />
[10 blank rows omitted]<br />
<br />
00033<br />
...**<br />
...**<br />
.....<br />
.....<br />
.....<br />
<br />
Note that extraneous '0's at the ends of strips are not included.<br />
<br />
Finally, the symbols {'y0', 'y1', y2', ..., 'yx', 'yy', 'yz'} correspond to runs of between 4 and 39 consecutive '0's. A good example is the [[quadpole on ship]], xp2_31a08zy0123cko:<br />
<br />
31a08<br />
**...<br />
*.*..<br />
.....<br />
..*.*<br />
.....<br />
<br />
0000123cko<br />
....*.*...<br />
.....**...<br />
.......**.<br />
.......*.*<br />
........**<br />
<br />
==Canonical form==<br />
<br />
In order to enforce a canonical form, there are further rules regarding encoding:<br />
<br />
The leftmost column and uppermost row must each contain at least one live cell. (This gives a canonical position.)<br />
<br />
Any '0's on the ends of strips are ignored, and {'00', '000', '0000', '00000', ...} are always replaced with {'w', 'x', 'y0', 'y1', 'y2', ...}.<br />
<br />
(Theoretically, runs of more than 39 zeroes should be replaced by 'yz' followed by the coding for the remaining zeroes. At the moment apgsearch labels everything larger than 40-by-40 as 'oversized' and refuses to process it.)<br />
<br />
A canonical orientation and phase must be determined. For example, with the caterer (p3 oscillator with no symmetry), there are three phases and eight orientations, so we have 24 possible encodings. Define a total order on these encodings as follows:<br />
<br />
- Prefer shorter representations to longer representations;<br />
- For representations of the same length, apply lexicographical ASCII ordering (and give preference to earlier strings).<br />
<br />
This gives, for any still-life, oscillator or spaceship, an unambiguous canonical code to represent the pattern. It has several desirable properties:<br />
<br />
Compression: it's much more compact than RLE or SOF for storing very small patterns, and often even beats the common name ('xp15_4r4z4r4' is shorter than 'pentadecathlon')! <br />
<br />
Character set: it only uses digits, lowercase letters and the underscore, so can be safely used in filenames and URLs.<br />
<br />
Human-readability: the prefix means that we can instantly see whether a particular object is a still-life (and if so, what size), oscillator (and if so, what period) or spaceship (and if so, what period). It also means that the string is instantly recognised as being an encoding of an object (xp2_7 is obviously a blinker, whereas the digit 7 on its own with no extra context is ambiguous).<br />
<br />
[[Category:Everything else]][[Category:File formats]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Apgcode&diff=23644Apgcode2016-04-18T14:01:28Z<p>Rich Holmes: Initial version</p>
<hr />
<div>[[apgsearch]] and the search results database, [[Catagolue]], classify and denote patterns as follows. Most objects are stored as two alphanumeric strings separated by an underscore. The 'prefix' refers to everything before the underscore and may begin with:<br />
<br />
* xs denoting a [[still life]]<br />
* xp denoting an [[oscillator]]<br />
* xq denoting a [[spaceship]]<br />
* yl denoting a periodic linearly growing object, such as a puffer or gun<br />
<br />
Oversize still lifes, oscillators, and spaceships, larger than 40 by 40, have a prefix beginning with ov_s, ov_p, or ov_q, respectively.<br />
<br />
These are followed by a number. For xs or ov_s this is the [[population]] of the still life while for the others it is the [[period]] of the object.<br />
<br />
The codes for xs, xp, xq, and yl are followed by an underscore, then a string which is a representation of the object in Extended Wechsler Format, described below.<br />
<br />
Additionally, objects which apgsearch cannot classify as above are denoted by one of:<br />
<br />
* zz_EXPLOSIVE<br />
* zz_LINEAR<br />
* zz_QUADRATIC<br />
* zz_REPLICATOR<br />
* PATHOLOGICAL<br />
<br />
==Extended Weschler Format==<br />
<br />
This is an extension of a pattern notation developed by Allan Wechsler in 1992. A string of _n_ characters in the set {0, 1, 2, ..., 8, 9, a, b, ..., v} denotes a strip of five rows, _n_ columns wide. Each character denotes five cells in a vertical column corresponding to the bitstrings {'00000', '00001', '00010', ..., '01000', '01001', '01010', '01011', ... '11111'}. For instance, xq4_27deee6 corresponds to a [[HWSS]]:<br />
<br />
27deee6<br />
.**....<br />
**.****<br />
.******<br />
..****.<br />
.......<br />
<br />
The character 'z' separates contiguous five-row strips. For example, xs31_0ca178b96z69d1d96 is:<br />
<br />
0ca178b96<br />
...**.**.<br />
..*.*.*.*<br />
.*..*...*<br />
.**..***.<br />
.........<br />
<br />
69d1d96<br />
.*****.<br />
*.....*<br />
*.*.*.*<br />
.**.**.<br />
.......<br />
<br />
The characters 'w' and 'x' are used to abbreviate '00' and '000', respectively. So xp30_w33z8kqrqk8zzzx33 is the [[trans-queen-bee-shuttle]]:<br />
<br />
0033<br />
..**<br />
..**<br />
....<br />
....<br />
....<br />
<br />
8kqrqk8<br />
...*...<br />
..***..<br />
.*...*.<br />
*.***.*<br />
.*****.<br />
<br />
[10 blank rows omitted]<br />
<br />
00033<br />
...**<br />
...**<br />
.....<br />
.....<br />
.....<br />
<br />
Note that extraneous '0's at the ends of strips are not included.<br />
<br />
Finally, the symbols {'y0', 'y1', y2', ..., 'yx', 'yy', 'yz'} correspond to runs of between 4 and 39 consecutive '0's. A good example is the [[quadpole on ship]], xp2_31a08zy0123cko:<br />
<br />
31a08<br />
**...<br />
*.*..<br />
.....<br />
..*.*<br />
.....<br />
<br />
0000123cko<br />
....*.*...<br />
.....**...<br />
.......**.<br />
.......*.*<br />
........**<br />
<br />
==Canonical form==<br />
<br />
In order to enforce a canonical form, there are further rules regarding encoding:<br />
<br />
The leftmost column and uppermost row must each contain at least one live cell. (This gives a canonical position.)<br />
<br />
Any '0's on the ends of strips are ignored, and {'00', '000', '0000', '00000', ...} are always replaced with {'w', 'x', 'y0', 'y1', 'y2', ...}.<br />
<br />
(Theoretically, runs of more than 39 zeroes should be replaced by 'yz' followed by the coding for the remaining zeroes. At the moment apgsearch labels everything larger than 40-by-40 as 'oversized' and refuses to process it.)<br />
<br />
A canonical orientation and phase must be determined. For example, with the caterer (p3 oscillator with no symmetry), there are three phases and eight orientations, so we have 24 possible encodings. Define a total order on these encodings as follows:<br />
<br />
- Prefer shorter representations to longer representations;<br />
- For representations of the same length, apply lexicographical ASCII ordering (and give preference to earlier strings).<br />
<br />
This gives, for any still-life, oscillator or spaceship, an unambiguous canonical code to represent the pattern. It has several desirable properties:<br />
<br />
Compression: it's much more compact than RLE or SOF for storing very small patterns, and often even beats the common name ('xp15_4r4z4r4' is shorter than 'pentadecathlon')! <br />
<br />
Character set: it only uses digits, lowercase letters and the underscore, so can be safely used in filenames and URLs.<br />
<br />
Human-readability: the prefix means that we can instantly see whether a particular object is a still-life (and if so, what size), oscillator (and if so, what period) or spaceship (and if so, what period). It also means that the string is instantly recognised as being an encoding of an object (xp2_7 is obviously a blinker, whereas the digit 7 on its own with no extra context is ambiguous).<br />
<br />
[[Category:Everything else]][[Category:File formats]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Stable_reflector&diff=23574Stable reflector2016-04-16T16:05:45Z<p>Rich Holmes: </p>
<hr />
<div>A '''stable reflector''' is a [[reflector]] composed entirely of [[still life]]s. That is, it is a collection of still lifes that can reflect some type of [[spaceship]] (usually a [[glider]]) without suffering permanent damage. Stable reflectors are special in that, if they satisfy certain conditions, they can be used to construct [[oscillator]]s of all sufficiently large periods. It was known for some time that stable reflectors were possible (see [[universal constructor]]), but no one was able to construct an [[stable reflector 1|explicit example]] until [[Paul Callahan]] did so in October [[:Category:Patterns found in 1996|1996]].<br />
<br />
==Types of stable reflectors==<br />
There are several distinct categories of stable reflector:<br />
<br />
* 'Create-then-remove' reflector - A reflector that temporarily creates an unwanted still-life and later destroys it.<br />
* 'Destroy-then-rebuild' reflector - A reflector that temporarily destroys a necessary still-life and later reconstructs it.<br />
* Direct reflector - A reflector that does not contain a Herschel track.<br />
<br />
===Repeat time===<br />
The '''repeat time''', also called the '''recovery time''' or '''compression''' of a stable reflector is the number of generations after the acceptance of one spaceship required for the reflector to be able to reflect the next spaceship.<br />
<br />
===Staged-recovery systems===<br />
The staged-recovery system was invented by Dave Greene, when he incorporated it into his [[highway robber]] and stable [[Heisenburp]] patterns. In 2009, Adam P. Goucher built two 'Create-then-remove' reflectors using a staged-recovery system.<br />
<br />
==History==<br />
Before 2013, all known stable reflectors were quite slow. Callahan's original reflector has a repeat time of 4840, soon improved to 1686 and then 894 and then 850. In November 1996, [[Dean Hickerson]] managed to reduce the repeat time to 747 using a specialised Herschel-to-glider [[conduit]]. [[David Buckingham]] reduced it to 672 in May [[:Category:Patterns found in 1997|1997]] using a somewhat different method; he used a boat as the 'bait' catalyst, which is converted, on impact, directly into a Herschel, which rebuilds the initial boat. In October 1997, [[Stephen Silver]] reduced the time to 623 by a method closer to the original; instead of using a boat and [[conduit 1]] to convert the R-pentomino into a Herschel, Silver used a loaf. In November 1998, Callahan reduced this to 575 with a new initial reaction based on a beehive, rather than a block. A small modification by Silver a few days later [[Silver's reflector|brought this down to 497]].<br />
<br />
In 2009, Adam P. Goucher used a staged-recovery system to delete the beehive much quicker, lowering the repeat time to 466. In 2012 'Guam' used a new conduit to reduce the repeat time further, to 444<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=2&t=279&start=525#p7102 |title=new stable glider reflector (and glider to Herschel converter) |author=Guam |date=September 29th, 2012 |accessdate=September 30,2014}}</ref>. When the [[Snark]] was discovered, it became possible to cut down the repeat time to 386 ticks.<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=2&t=148&start=50#p8496 |title=386-tick G-to-H |author=Martin Grant |date=July 11th, 2013 |accessdate=September 30,2014}}</ref><br />
<br />
In April [[:Category:Patterns found in 2001|2001]], [[Dave Greene]] found a 180-degree stable glider reflector with a repeat time of only 202 known as the [[boojum reflector]].<br />
<br />
In [[:Category:Patterns found in 2009|2009]], [[Adam P. Goucher]] constructed a 180-degree stable glider reflector with a repeat time of only 106, known as the [[rectifier]].<br />
<br />
In April, [[:Category:patterns found in 2013|2013]] [[Mike Playle]] found a small 90-degree reflector with a repeat time of 43 generations, known as the [[snark]].<br />
<br />
===Prizes===<br />
In 2001, Dave Greene's discovery of the boojum reflector won two long-standing prize offers of $100 each from [[Alan Hensel]] and [[Dietrich Leithner]], for a stable reflector fitting inside a 50x50 bounding box. Greene offered two follow-up $50 prizes for stable reflectors:<br />
<br />
* Find a stable glider reflector that fits inside a 50&times;50 bounding box.<br />
* Find a stable glider reflector that fits inside a 35&times;35 bounding box.<br />
<br />
Matthias Merzenich offered two similar $50 prizes for stable reflectors:<br />
<br />
* Find a stable glider reflector with a repeat time of 100 generations or less.<br />
* Find a stable glider reflector with a repeat time of 61 generations or less.<br />
<br />
Mike Playle won all four prizes with his discovery of his small stable reflector in April, 2013. Playle then offered a new prize of $100 USD for a similarly small and fast stable reflector that changes the glider's color (since the [[Snark]] is a color-preserving reflector):<br />
<br />
* Find a color-changing stable glider reflector that's at most 25x25, with a repeat time of 50 generations or less.<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=2&t=1082#p7843 |title=Just the place for a Snark! |author=Mike Playle |date=April 27, 2013 |accessdate=September 30, 2014}}</ref><br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
<br />
* {{Cite web|url=https://groups.google.com/d/msg/comp.theory.cell-automata/sHpFoieXvk4/NQRWMvcD76oJ|title=Still-life glider reflector found|author=Paul Callahan|date=November 16, 1996|accessdate=May 11, 2013}}<br />
* A detailed summary of stable technology, 1996-2009. [http://www.calcyman.co.uk/life/stable.htm]<br />
* A complete list of notable stable reflectors. [http://www.calcyman.co.uk/life/reflectors.htm]<br />
<br />
[[Category:glossary]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Stable_reflector&diff=23573Stable reflector2016-04-16T16:05:10Z<p>Rich Holmes: rm redundant text</p>
<hr />
<div>A '''stable reflector''' is a [[reflector]] composed entirely of [[still life]]s. That is, it is a collection of still lifes that can reflect some type of [[spaceship]] (usually a [[glider]]) without suffering permanent damage. Stable reflectors are special in that, if they satisfy certain conditions, they can be used to construct [[oscillator]]s of all sufficiently large periods. It was known for some time that stable reflectors were possible (see [[universal constructor]]), but no one was able to construct an [[stable reflector 1|explicit example]] until [[Paul Callahan]] did so in October [[:Category:Patterns found in 1996|1996]].<br />
<br />
==Types of stable reflectors==<br />
There are several distinct categories of stable reflector:<br />
<br />
* 'Create-then-remove' reflector - A reflector that temporarily creates an unwanted still-life and later destroys it.<br />
* 'Destroy-then-rebuild' reflector - A reflector that temporarily destroys a necessary still-life and later reconstructs it.<br />
* Direct reflector - A reflector that does not contain a Herschel track.<br />
<br />
===Repeat time===<br />
The '''repeat time''', also called the '''recovery time''' or '''compression''' of a stable reflector is the number of generations after the acceptance of one spaceship required for the reflector to be able to reflect the next spaceship.<br />
<br />
===Staged-recovery systems===<br />
The staged-recovery system was invented by Dave Greene, when he incorporated it into his [[highway robber]] and stable [[Heisenburp]] patterns. In 2009, Adam P. Goucher built two 'Create-then-remove' reflectors using a staged-recovery system.<br />
<br />
==History==<br />
Before 2013, all known stable reflectors were quite slow. Callahan's original reflector has a repeat time of 4840, soon improved to 1686 and then 894 and then 850. In November 1996, [[Dean Hickerson]] managed to reduce the repeat time to 747 using a specialised Herschel-to-glider [[conduit]]. [[David Buckingham]] reduced it to 672 in May [[:Category:Patterns found in 1997|1997]] using a somewhat different method; he used a boat as the 'bait' catalyst, which is converted, on impact, directly into a Herschel, which rebuilds the initial boat. In October 1997, [[Stephen Silver]] reduced the time to 623 by a method closer to the original; instead of using a boat and [[conduit 1]] to convert the R-pentomino into a Herschel, Silver used a loaf. In November 1998, Callahan reduced this to 575 with a new initial reaction based on a beehive, rather than a block. A small modification by Silver a few days later [[Silver's reflector|brought this down to 497]].<br />
<br />
In 2009, Adam P. Goucher used a staged-recovery system to delete the beehive much quicker, lowering the repeat time to 466. In 2012 'Guam' used a new conduit to reduce the repeat time further, to 444<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=2&t=279&start=525#p7102 |title=new stable glider reflector (and glider to Herschel converter) |author=Guam |date=September 29th, 2012 |accessdate=September 30,2014}}</ref>. When the [[Snark]] was discovered, it became possible to cut down the repeat time to 386 ticks.<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=2&t=148&start=50#p8496 |title=386-tick G-to-H |author=Martin Grant |date=July 11th, 2013 |accessdate=September 30,2014}}</ref><br />
<br />
In April [[:Category:Patterns found in 2001|2001]], [[Dave Greene]] found a 180-degree stable glider reflector with a repeat time of only 202 known as the [[boojum reflector]].<br />
<br />
In [[:Category:Patterns found in 2009|2009]], [[Adam P. Goucher]] constructed a 180-degree stable glider reflector with a repeat time of only 106, known as the [[rectifier]].<br />
<br />
In April, [[:Category:patterns found in 2013|2013]] [[Mike Playle]] found a small 90-degree reflector with a repeat time of 43 generations, known as the [[snark]].<br />
<br />
===Prizes===<br />
In 2001, [[Dave Greene]]'s discovery of the boojum reflector won two long-standing prize offers of $100 each from [[Alan Hensel]] and [[Dietrich Leithner]], for a stable reflector fitting inside a 50x50 bounding box. Greene offered two follow-up $50 prizes for stable reflectors:<br />
<br />
* Find a stable glider reflector that fits inside a 50&times;50 bounding box.<br />
* Find a stable glider reflector that fits inside a 35&times;35 bounding box.<br />
<br />
Matthias Merzenich offered two similar $50 prizes for stable reflectors:<br />
<br />
* Find a stable glider reflector with a repeat time of 100 generations or less.<br />
* Find a stable glider reflector with a repeat time of 61 generations or less.<br />
<br />
Mike Playle won all four prizes with his discovery of his small stable reflector in April, 2013. Playle then offered a new prize of $100 USD for a similarly small and fast stable reflector that changes the glider's color (since the [[Snark]] is a color-preserving reflector):<br />
<br />
* Find a color-changing stable glider reflector that's at most 25x25, with a repeat time of 50 generations or less.<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=2&t=1082#p7843 |title=Just the place for a Snark! |author=Mike Playle |date=April 27, 2013 |accessdate=September 30, 2014}}</ref><br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
<br />
* {{Cite web|url=https://groups.google.com/d/msg/comp.theory.cell-automata/sHpFoieXvk4/NQRWMvcD76oJ|title=Still-life glider reflector found|author=Paul Callahan|date=November 16, 1996|accessdate=May 11, 2013}}<br />
* A detailed summary of stable technology, 1996-2009. [http://www.calcyman.co.uk/life/stable.htm]<br />
* A complete list of notable stable reflectors. [http://www.calcyman.co.uk/life/reflectors.htm]<br />
<br />
[[Category:glossary]]</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Period-61_glider_gun&diff=23572Period-61 glider gun2016-04-16T15:56:13Z<p>Rich Holmes: Description</p>
<hr />
<div>{{Gun|p=61|name=Period-61 glider gun|pname=period61glidergun|c=5403|bx=366|by=287|discoverer=AbhpzTa|discoveryear=2016|rle=true|animated=true}}<br />
{{stub}}<br />
'''Period-61 glider gun''' is the first [[Gun#True-period_guns|true period]]-61 glider gun discovered by 'AbhpzTa' in April [[:Category:Patterns found in 2016|2016]]<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?p=29965|title=p61 gun|author=AbhpzTa|date=April 13, 2016|accessdate=April 13, 2016}}</ref>. It is a [[quetzal]] using a [[lightweight spaceship]] stream as a glider-to-Herschel converter, as well as a small stable Herschel-to-2 glider converter.<br />
<br />
==References==<br />
<br />
<references/></div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=LifeWiki_talk:Game_of_Life_Status_page&diff=23553LifeWiki talk:Game of Life Status page2016-04-15T15:05:59Z<p>Rich Holmes: This page is hard to find</p>
<hr />
<div>Nothing links to this page. It's not in any categories. What would be a good way to remedy this? - [[User:Rich Holmes|Rich Holmes]] ([[User talk:Rich Holmes|talk]]) 15:05, 15 April 2016 (UTC)</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Talk:Conduit_1&diff=23551Talk:Conduit 12016-04-15T12:08:41Z<p>Rich Holmes: Redirection</p>
<hr />
<div>Would it not make more sense for [[Herschel conduit]] to redirect to [[Conduit#Herschel_conduits]] rather than here? - [[User:Rich Holmes|Rich Holmes]] ([[User talk:Rich Holmes|talk]]) 12:08, 15 April 2016 (UTC)</div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=Salvo&diff=23433Salvo2016-04-10T14:26:19Z<p>Rich Holmes: Link to color definition</p>
<hr />
<div>{{Glossary}}<br />
A '''salvo''' is a collection of [[spaceship]]s (usually [[glider]]s) that are all coming from the same direction.<ref>{{Cite web|url=http://b3s23life.blogspot.com/2006/02/new-results-from-glue-2.html|title=New results from Glue 2|author=Dave Greene|date=February 24, 2006|accessdate=June 13, 2009|publisher=Conway's Life: Work in Progress}}</ref> A salvo is generally aimed at a target to produce a specific [[reaction]] -- for example, in a [[sliding-block memory]] or a [[slide gun]], a salvo might move a [[block]] or other [[still life]] a step closer to the salvo source, or a step farther away. Or two or more salvos may collide with each other to [[Glider synthesis|construct]] a complex object.<br />
<br />
A '''slow salvo''' is a salvo in which the spaceships are far enough apart that any collision reaction affecting the n<sup>th</sup> spaceship has settled down by the time the (n+1)<sup>st</sup> spaceship arrives.<br />
<br />
A '''P1 slow salvo''' is a slow salvo in which the intermediate settled-down stages are all period 1 (i.e., stable.) It is conjectured that any glider-constructible object can be produced by a P1 slow salvo aimed at a single block or other small still life -- though the number of gliders needed may be very large.<br />
<br />
Conversely, a '''P2 slow salvo''' may have intermediate stages containing P2 oscillators, allowing constructions with significantly fewer gliders on average. P3 and higher slow salvos are technically possible, but higher periods do not appear to make much difference to construction efficiency in Life, where higher-period oscillators only appears rarely.<br />
<br />
A '''monochromatic slow salvo''' is a slow salvo which contains only gliders of a single [[glider#Colour of a glider|color]].<ref>{{Cite web|url=http://conwaylife.com/forums/viewtopic.php?f=11&t=1346&p=11688#p11688|title=Re: Serizawa - Linear Self Replicator.|author=Dave Greene|date=April 18, 2014|accessdate=July 29, 2014}}</ref> For example, [[half-baked knightship]]s reconstruct their glider seed constellations using monochromatic slow salvos.<br />
<br />
Similarly, a '''monoparity slow salvo''' is a slow salvo which contains only gliders of the same shape -- i.e., even or odd parity. The intermediate targets for this type of slow salvo can be P1 or P2, but P2 targets have two completely separate and non-interchangeable phases. A phase-0 blinker is a different target than a phase-1 blinker, for example, and the two targets would require completely different construction recipes. Even-step variants of the [[engineless Caterpillar]] use slow salvos that are both monochromatic and monoparity.<ref>{{Cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1448&start=150#p20789|title=Re: David Bell's engineless caterpillar idea revisited|author=Michael Simkin|date=June 26, 2015|accessdate=August 4, 2015}}</ref><br />
==References==<br />
<references /></div>Rich Holmeshttps://www.conwaylife.com/w/index.php?title=OCA:Day_%26_Night&diff=21598OCA:Day & Night2015-11-09T22:29:21Z<p>Rich Holmes: dead link</p>
<hr />
<div>{{ambox|text=Please do not move this page and its [[{{TALKPAGENAMEE}}|talk page]] until this system is updated by [[User:Nathaniel|Nathaniel]].<br />
<br />
[[User:Zhuyifei1999|Zhuyifei1999]] 07:50, 11 March 2013 (CDT)}}<br />
<br />
{{Rule|name=Day & Night|imgname=Day&night|s=34678|b=3678|char=Stable}}<br />
'''Day & Night''' is a [[Life-like cellular automaton]] in which cells survive from one generation to the next if they have 3, 6, 7, or 8 neighbours, and are born if they have 3, 4, 6, 7, or 8 neighbours. Day & Night is the most well-known self-complementary rule. That is, if all grid cells have their on/off state exchanged, the history of the pattern is the inverse of the history of the original. [[Nathan Thompson]] explored the rule starting in April, 1997, and [[David Bell]] discussed the rule in detail the following November.<br />
<br />
==External links==<br />
<br />
* {{cite web<br />
| author = David I. Bell<br />
| year = 1997<br />
| url = http://www.tip.net.au/~dbell/articles/DayNight.zip<br />
| title = Day & Night - An Interesting Variant of Life<br />
| work = See also Bell's [http://www.tip.net.au/~dbell/archive/b3678s34678.tar.gz Day & Night pattern archive]}}<br />
<br />
* {{cite web<br />
| author = Pete Carlton<br />
| url = http://www.ocf.berkeley.edu/~pcarlton/CA.html<br />
| title = Pete's Game of Life Page: B3678 S34678}}[dead link]</div>Rich Holmes