Difference between revisions of "Integer construction"
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(Created page with "{{Glossary}} The '''integer construction''' of a pattern is a string of Life Digits, separated by an empty column, that evolves into the pattern. "Life Digits" is a Game of Life font developed by Eric Angelini in 2007. Angelini and Dean Hickerson collaborated, leading to the discovery of many integer constructions.<ref>{{cite web|url=http://oeis.org/A126803/a126803.pdf|title=Une suite pour la vie|author=Eric Angelini}}</ref><ref>{{cite web|url=https://conwayl...") |
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{{Glossary}} | {{Glossary}} | ||
The '''integer construction''' of a [[pattern]] is a string of Life Digits, separated by an empty column, that evolves into the pattern. "Life Digits" is a | The '''integer construction''' of a [[pattern]] is a string of Life Digits, separated by an empty column{{refn|group=note|Including the narrower sans-serif number 1}}, that evolves into the pattern. "Life Digits" is a digital font developed by Eric Angelini in 2007, who collaborated with [[Dean Hickerson]] to discover many integer constructions in the [[Game of Life]].<ref>{{cite web|url=http://oeis.org/A126803/a126803.pdf|title=Une suite pour la vie|author=Eric Angelini}}</ref><ref name="dh">{{cite web|url=https://conwaylife.com/ref/DRH/digits.html|title=Dean Hickerson's Life Page: Digits in Life}}</ref><ref>{{LinkGoLNews|2007/03/life_digits.html|title=Life Digits|date=March 03, 2007|author=Heinrich Koenig}}</ref><ref>{{LinkGoLNews|2007/04/life_digits_update_1.html|title=Life Digits update|date=April 03, 2007|author=Heinrich Koenig}}</ref> | ||
{{EmbedViewer | {{EmbedViewer | ||
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|position = center | |position = center | ||
|viewerconfig = #C [[ THUMBSIZE 2 ]] | |viewerconfig = #C [[ THUMBSIZE 2 ]] | ||
|caption = The Life Digits font | |caption = The Life Digits font (variable width) | ||
|style = width:300px; | |style = width:300px; | ||
}} | }} | ||
Integer constructions can be used to generate [[glider syntheses]]. For example, 1415073111111103975114 evolves into 2 gliders, which collide to form an [[eater 1]]. More complex glider syntheses can be generated by combinations of [[List_of_integer_constructions#Spaceships|integer constructions that produce spaceships]] which collide to produce the necessary gliders on the desired paths with the desired phases. An example of a 740 digit integer construction that uses this technique to produce a [[Gosper glider gun]] is show below.<ref name="dh" /> | |||
== Examples == | == Examples == | ||
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|position = center | |position = center | ||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 GPS 11 PAUSE 3 LOOP 121 AUTOSTART HEIGHT 500 ]] | |viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 GPS 11 PAUSE 3 LOOP 121 AUTOSTART HEIGHT 500 ]] | ||
|caption = Integer construction for [[LWSS]] (3207) and [[MWSS]] ( | |caption = Integer construction for [[LWSS]] (3207) and [[MWSS]] (94174). | ||
}} | }} | ||
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|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 GPS 6 PAUSE 3 LOOP 66 AUTOSTART ]] | |viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 GPS 6 PAUSE 3 LOOP 66 AUTOSTART ]] | ||
|caption = Integer construction for [[land of lakes]]. | |caption = Integer construction for [[land of lakes]]. | ||
}} | |||
|- | |||
|{{EmbedViewer | |||
|rle = x = 48, y = 44, rule = B3/S23 | |||
7b3ob3ob3ob3ob3obobob3ob3ob3obob3o$9bobobo3bo3bobobobobo3bo3bo3bobobob | |||
o$7b3ob3o3bob3obobobobob3ob3ob3obobobo$9bo3bo3bo3bobobobobo3bo3bo3bobo | |||
bobo$7b3ob3o3bob3ob3obobob3ob3ob3obob3o35$3ob3obobob3obob3ob3obobob3ob | |||
3ob3obob3o$2bo3bobobobobobo3bobobobobo3bo3bo3bobobobo$3ob3obobobobobob | |||
3obobobobob3ob3ob3obobobo$2bo3bobobobobobo3bobobobobo3bo3bo3bobobobo$ | |||
3ob3obobob3obob3ob3obobob3ob3ob3obob3o! | |||
|position = center | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 4 GPS 20 PAUSE 3 LOOP 220 AUTOSTART ]] | |||
|caption = 3-block and 4-block [[twin bees shuttle]]s. | |||
}} | |||
|{{EmbedViewer | |||
|rle = x = 107, y = 5, rule = B3/S23 | |||
ob3ob3ob3ob3ob3ob3ob3ob3ob3obobob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3obo | |||
bob3ob3obob3o$obobobobo3bo3bobo5bo3bo3bobo3bobo3bobobobo3bo3bo3bo3bo5b | |||
obo3bo3bo3bo3bobo3bobo3bobobo$ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3bobobob | |||
3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3bob3obob3o$o3bobobo3bobo3bobo3bobo3bo | |||
5bo3bo3bobobobobobobobobobobobobobo3bobobobobobobobo3bo3bobobobobobo$o | |||
b3ob3ob3ob3ob3ob3ob3ob3ob3o3bo3bob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3bo | |||
3bob3obob3o! | |||
|position = center | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 4 GPS 30 PAUSE 3 LOOP 330 AUTOSTART ]] | |||
|caption = Trans-[[queen bee shuttle]]. | |||
}} | |||
|- | |||
|{{EmbedViewer | |||
|rle = x = 21, y = 5, rule = B3/S23 | |||
ob3obobob3ob3ob3o$obo3bobo3bobobobobo$ob3ob3ob3ob3ob3o$o3bo3bobo5bo3bo | |||
$ob3o3bob3ob3ob3o! | |||
|position = center | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 4 ]] | |||
|caption = Infinite growth: 154299 produces a [[Block-laying switch engine]] heading southeast in generation 539. | |||
}} | |||
|{{EmbedViewer | |||
|pname = p30gunintegerconstruction | |||
|position = center | |||
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 2 THEME Book ]] | |||
|caption = 740 digits that produce a [[Gosper glider gun]] in generation 4140. | |||
}} | }} | ||
|} | |} | ||
== See also == | |||
* [[List of integer constructions]] | |||
== Notes == | |||
<references group="note" /> | |||
== References == | == References == | ||
<references | <references /> | ||
== External | == External links == | ||
* {{filename|Syntheses/life-integer-constructions.rle}} from [[Golly's pattern collection]] | * {{filename|Syntheses/life-integer-constructions.rle}} from [[Golly's pattern collection]] | ||
* {{OEIS|A126803}} - Integers that die when submitted to the rules of the Game of Life | * {{OEIS|A126803}} - Integers that die when submitted to the rules of the Game of Life | ||
* {{LinkForumThread|title='Life Digits'|f=2|t=80}} | |||
__NOTOC__ | |||
Latest revision as of 18:09, 19 February 2023
The integer construction of a pattern is a string of Life Digits, separated by an empty column[note 1], that evolves into the pattern. "Life Digits" is a digital font developed by Eric Angelini in 2007, who collaborated with Dean Hickerson to discover many integer constructions in the Game of Life.[1][2][3][4]
| The Life Digits font (variable width) (click above to open LifeViewer) RLE: here Plaintext: here |
Integer constructions can be used to generate glider syntheses. For example, 1415073111111103975114 evolves into 2 gliders, which collide to form an eater 1. More complex glider syntheses can be generated by combinations of integer constructions that produce spaceships which collide to produce the necessary gliders on the desired paths with the desired phases. An example of a 740 digit integer construction that uses this technique to produce a Gosper glider gun is show below.[2]
Examples
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See also
Notes
- ↑ Including the narrower sans-serif number 1
References
- ↑ Eric Angelini. "Une suite pour la vie".
- ↑ 2.0 2.1 "Dean Hickerson's Life Page: Digits in Life".
- ↑ Life Digits at Game of Life News. Posted by Heinrich Koenig on March 03, 2007.
- ↑ Life Digits update at Game of Life News. Posted by Heinrich Koenig on April 03, 2007.
External links
- Syntheses/life-integer-constructions.rle from Golly's pattern collection
A126803 - Integers that die when submitted to the rules of the Game of Life- 'Life Digits' (discussion thread) at the ConwayLife.com forums
