Pi orbital: Difference between revisions

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|by          = 59
|by          = 59
|p            = 168
|p            = 168
|m            = 42
|h            = 270.7
|h            = 270.7
|v            = 0.91
|v            = 0.91
|sv          = 0.61
|sv          = 0.61
|symmetry    = nrc
|discoverer  = Noam Elkies
|discoverer  = Noam Elkies
|discoveryear = 1995
|discoveryear = 1995
|rulemin      = B3/S23
|rulemin      = B3/S23
|rulemax      = B3/S23
|rulemax      = B3/S23
|rulespecial  = [[Conway's Game of Life|Conway Life]]
|isorulemin  = B3/S23
|life105      = true
|isorulemax  = B3/S236ei
|life106      = true
|synthesis    = 232
|plaintext    = true
|plaintext    = true
|rle          = true
|rle          = true
|animated    = true
|animated    = true
|apgcode      = xp168_y965la8ceeeec8al56zy3888o040o11wo4xg190ggggy2ccy6szy72441x161x38841ydc2ghh4y0o8gzy3ggywo0cgy0jpu121zy311yw10jggx7fvzy5syv3408o2w321e96z697o4cw4hhg2cyv3zxvvuy0gc0oyh27dod72y4oozo4o79cwggg301z011y02o8043yagggo211sx8m8xo224gzy43y633y7p8y021w8o10201111zyq6aa5137777315aa6
|apgcode      = xp168_y965la8ceeeec8al56zy3888o040o11wo4xg190ggggy2ccy6szy72441x161x38841ydc2ghh4y0o8gzy3ggywo0cgy0jpu121zy311yw10jggx7fvzy5syv3408o2w321e96z697o4cw4hhg2cyv3zxvvuy0gc0oyh27dod72y4oozo4o79cwggg301z011y02o8043yagggo211sx8m8xo224gzy43y633y7p8y021w8o10201111zyq6aa5137777315aa6
|viewerconfig = #C [[ GPS 14 ZOOM 8 WIDTH 600 HEIGHT 600 LOOP 168 ]]
}}
}}
'''Pi orbital''' is a [[period]] [[:Category:Oscillators with period 168|168]] [[oscillator]] that was found by [[:Category:Patterns found by Noam Elkies|Noam Elkies]] in August [[:Category:Patterns found in 1995|1995]]. It works by using four [[crown]]s and four [[block]]s to turn a [[pi heptomino]] ninety degrees every 42 [[generation]]s. A second pi heptomino can be inserted to reduce the period to 84. On March 26, [[:Category:patterns found in 2009|2009]] [[Nicolay Beluchenko]] found a relatively small period [[:Category:Oscillators with period 12|12]] [[spark]]er that could replace the crowns. On April 6, [[:Category:patterns found in 2010|2010]] [[Matthias Merzenich]] discovered the [[Blocked_p4-4|Blocked p4-4]]
'''Pi orbital''' is a {{period|168}} [[oscillator]] that was found by [[Noam Elkies]] on August 22, {{year|1995}}.<ref>{{CiteSummersPattern|name=jslife|accessdate=March 14, 2020}}</ref> It consists of four 42-[[generation]] 90-degree [[pi heptomino]] turns, each using a [[crown]] and a [[block]]. A second pi heptomino can be inserted to reduce the period to 84, but no further reduction (such as {{nowrap|168 / 3 {{=}} 56}}) works.
period 4 oscillator that also supports the oscillator.
The name of the oscillator is a reference to chemical bonds and atomic orbitals in chemistry.{{refn|[https://en.wikipedia.org/wiki/Pi_bond Pi bond], [https://en.wikipedia.org/wiki/Atomic_orbital Atomic orbital] on Wikipedia}}


==Image gallery==
On March 26, {{year|2009}} [[Nicolay Beluchenko]] found a relatively small period-12 sparker, [[Eye of Sauron]], that could replace the crown.<ref>{{LinkGoLNews|2009/04/new_oscillators_5.html|title=New Oscillators|date=April 14, 2009|author=Heinrich Koenig}}</ref> On April 6, {{year|2010}} [[Matthias Merzenich]] discovered that [[blocked p4-4]] can also support the oscillator.<ref>{{LinkGoLNews|2011/01/a_plethora_of_p4_hasslers_1.html|title=A plethora of p4 hasslers|date=January 3, 2011|author=Adam P. Goucher}}</ref> Currently, the exact pi-turning reaction has not been made into a stable [[conduit]] yet.<ref name="post42551" />
{|
|-
|[[Image:piorbital_alt.png|framed|left|An alternate version of pi orbital using Nicolay Beluchenko's period 12 oscillator<br/>{{JavaRLE|alternatepiorbital|brief}}]]
|[[Image:P168.PNG‎|framed|left|Alternate form by Matthias Merzenich]]
|}


==See also==
If the block in a turn is removed, another block will be dropped nearby. A [[block pull]] can restore it, as is shown in the final step of a [[glider synthesis]] of the p12-supported variant by [[GUYTU6J]] in December {{year|2020}}.<ref name="post117043" /> Meanwhile, that fact makes pi orbital a block [[factory]] suitable for stabilizing a [[honey farm]]-[[hassle|hassling]] [[wick]] at the same period.<ref name="post133184" /> Furthermore, sparking the [[active region]] before settling into the block creates a [[B-heptomino]],<ref name="post115599" /> and [[weld]]ing a [[BFx59H]] to the blocked p4-4 to release a [[Herschel]] is possible.<ref name="post115914" />
*[[Crown]]
{{gallery top}}
*[[Gourmet]]
{{gallery item|{{EmbedViewer
*[[Popover]]
|pname        = piorbital2
*[[Pi portraitor]]
|viewerconfig = #C [[ WIDTH 600 HEIGHT 600 THUMBSIZE 2 ZOOM 8 ]]
|position    = center
|caption      = An alternate version of pi orbital using [[Eye of Sauron]]
|style        = width:300px;
|apgcode      = xp168_yyg0e1gegggzygggy6g8882u1dd1uh4442zy2ggy811y7222t21t13z0oo0jbaafggggyl1z34747obb870fc3yx66zy135533zzyvca2248gy2gg06mlluzy433ylckgh843y169f8fgmmgf1vp6zyho40oyn7aa66zyd8o6kl4q5iii8y6cczy92999kb4l5c32zyd3043
}}}}
{{gallery item|{{EmbedViewer
|pname        = piorbital3
|viewerconfig = #C [[ WIDTH 600 HEIGHT 600 THUMBSIZE 2 ZOOM 8 ]]
|position    = center
|caption      = Alternate form by Matthias Merzenich. The form with the lowest minimum population; with one pi-heptomino, it has 197 cells
|style        = width:300px;
|apgcode      = xp84_y2okk808011188039u0ooy366zy465122222111343ydo8geicz0ooymc448gy08201uxozyp3221y22ggnwghzxccyu122qq221z6511l552zexvw18y04ahhrymcczwo4p68dyegy6ggzx11y4ggy3cc0v832aa111192alkczy911y6123x222
}}}}
{{gallery bottom}}


==External links==
On December 30, {{year|2024}}, [[KtT]] found a {{gliders|265}} synthesis.<ref name="post200637"/><ref name="j8741621325"/> The next day, [[Chris857]] lowered the cost to {{gliders|235|text=235 gliders}}.<ref name="post200687"/><ref name="j8746090993"/>
{{LinkLexicon|lex_p.htm#piorbital}}
{{LinkCatagolue|xp168_y965la8ceeeec8al56zy3888o040o11wo4xg190ggggy2ccy6szy72441x161x38841ydc2ghh4y0o8gzy3ggywo0cgy0jpu121zy311yw10jggx7fvzy5syv3408o2w321e96z697o4cw4hhg2cyv3zxvvuy0gc0oyh27dod72y4oozo4o79cwggg301z011y02o8043yagggo211sx8m8xo224gzy43y633y7p8y021w8o10201111zyq6aa5137777315aa6|format=extended}}


{{Symmetry|osc=turn90}}
== See also ==
* [[Gourmet]]
* [[p48 pi-heptomino hassler]]
* [[Pi-heptomino hasslers#p160]], a hybrid of pi orbital and a p152
* [[255P132]] - another high-period oscillator (132) that involves four 90° rotations of a [[U-turner]]
 
== References ==
<references>
<ref name="j8741621325">{{CiteCatagolueJob|job=8741621325|date=December 30, 2024}}</ref>
<ref name="j8746090993">{{CiteCatagolueJob|job=8746090993|date=December 31, 2024}}</ref>
<ref name="post42551">{{LinkForumThread
|format = ref
|title  = Re: Stable signal converters
|p      = 42551
|author = Dave Greene
|date  = April 10, 2017
}}</ref>
<ref name="post117043">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 117043
|author = GUYTU6J
|date  = December 27, 2020
}}</ref>
<ref name="post133184">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 133184
|author = Matthias Merzenich
|date  = July 7, 2021
}}</ref>
<ref name="post115599">{{LinkForumThread
|format = ref
|title  = Re: Gun Discussion Thread
|p      = 115599
|author = Aleph
|date  = December 12, 2020
}}</ref>
<ref name="post115914">{{LinkForumThread
|format = ref
|title  = Re: Gun Discussion Thread
|p      = 115914
|author = Adam P. Goucher
|date  = December 15, 2020
}}</ref>
<ref name="post200637">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 200637
|author = KtT
|date  = December 30, 2024
}}</ref>
<ref name="post200687">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 200687
|author = Chris857
|date  = December 31, 2024
}}</ref>
</references>
 
== External links ==
* {{LinkLexicon|lex_p.htm#piorbital}}
* {{LinkCatagolue|xp168_y965la8ceeeec8al56zy3888o040o11wo4xg190ggggy2ccy6szy72441x161x38841ydc2ghh4y0o8gzy3ggywo0cgy0jpu121zy311yw10jggx7fvzy5syv3408o2w321e96z697o4cw4hhg2cyv3zxvvuy0gc0oyh27dod72y4oozo4o79cwggg301z011y02o8043yagggo211sx8m8xo224gzy43y633y7p8y021w8o10201111zyq6aa5137777315aa6|format=extended}}
* {{LinkCatagolue|xp168_yyg0e1gegggzygggy6g8882u1dd1uh4442zy2ggy811y7222t21t13z0oo0jbaafggggyl1z34747obb870fc3yx66zy135533zzyvca2248gy2gg06mlluzy433ylckgh843y169f8fgmmgf1vp6zyho40oyn7aa66zyd8o6kl4q5iii8y6cczy92999kb4l5c32zyd3043|format=extended|patternname=Pi orbital with Eye of Sauron}}
 
[[Category:Pi-heptomino hasslers|168]]
[[Category:Factories]]
__NOTOC__

Latest revision as of 21:14, 13 August 2026

Pi orbital
x = 59, y = 59, rule = B3/S23 14b2o10b2o$13bo2bo8bo2bo$13b3o2b6o2b3o$16b2o6b2o$15bo10bo$15b2obo4bob 2o$20b2o$12bo25b2o10bo$7b4o3bo4bo6bo11b2o10bo$10bo3bo2b5o2bo3b4o18bo$ 14bo2b5o2bo3bo20b2o$11bo6b3o3bo22bo$12b2o5bo7bo18bo4bo$25b2o19bo9b2o$ 48b3o5bobo$53b2obobo$53bobobo$55bo$35b2o11bo5bo2bo$7b2o26bobo10b2o4bo$ 7b2o28b2o9bo5bo3bo$35bobo16bo3bo$20b2o13b2o17bo$23bobo28bo2bo$25bo21b 3o5bo$23bo21bo7bobobo$19bo25bo4bo2b2obobo$9bo10b2o24bo9bobo$9bo38b2o6b 2o$9bo39bo$b2o6b2o38bo$obo9bo36bo$obob2o2bo4bo$bobobo7bo$3bo5b3o$bo2bo $4bo$o3bo$o3bo5bo39b2o$4bo4b2o39b2o$bo2bo5bo$3bo$bobobo$obob2o$obo5b3o $b2o9bo19b2o$7bo4bo18bo7bo5b2o$11bo22bo3b3o6bo$8b2o20bo3bo2b5o2bo$8bo 18b4o3bo2b5o2bo3bo$8bo10b2o11bo6bo4bo3b4o$8bo10b2o25bo$37b2o$32b2obo4b ob2o$32bo10bo$33b2o6b2o$30b3o2b6o2b3o$30bo2bo8bo2bo$31b2o10b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ GPS 14 ZOOM 8 WIDTH 600 HEIGHT 600 LOOP 168 ]]
View animated image
View static image
Pattern type Oscillator
Number of cells 305
Bounding box 59 × 59
Period 168 (mod: 42)
Heat 270.7
Volatility 0.91 | 0.61
Kinetic symmetry nrc
Discovered by Noam Elkies
Year of discovery 1995

Pi orbital is a period-168 oscillator that was found by Noam Elkies on August 22, 1995.[1] It consists of four 42-generation 90-degree pi heptomino turns, each using a crown and a block. A second pi heptomino can be inserted to reduce the period to 84, but no further reduction (such as 168 / 3 = 56) works. The name of the oscillator is a reference to chemical bonds and atomic orbitals in chemistry.[2]

On March 26, 2009 Nicolay Beluchenko found a relatively small period-12 sparker, Eye of Sauron, that could replace the crown.[3] On April 6, 2010 Matthias Merzenich discovered that blocked p4-4 can also support the oscillator.[4] Currently, the exact pi-turning reaction has not been made into a stable conduit yet.[5]

If the block in a turn is removed, another block will be dropped nearby. A block pull can restore it, as is shown in the final step of a glider synthesis of the p12-supported variant by GUYTU6J in December 2020.[6] Meanwhile, that fact makes pi orbital a block factory suitable for stabilizing a honey farm-hassling wick at the same period.[7] Furthermore, sparking the active region before settling into the block creates a B-heptomino,[8] and welding a BFx59H to the blocked p4-4 to release a Herschel is possible.[9]

#N Alternate pi orbital #O Nicolay Beluchenko #C An alternate version of pi orbital using a period 12 sparker found #C by Nicolay Beluchenko #C https://www.conwaylife.com/wiki/index.php?title=Pi_orbital x = 63, y = 61, rule = b3/s23 20b2o41b$18b2o2bo40b$18b5o40b$22bo40b$15b2o2b4o40b$15b2obo4b4o36b$14bo bobob2obobobo35b$14bobobob2obobobo35b$15b4o4bob2o13b2o21b$19b4o2b2o13b 2o21b$19bo43b$19b5o39b$19bo2b2o39b$20b2o34bo6b$55bo2bo4b$55bo2bo4b$55b o2bo4b$53bo3bob3ob$53b4obo4b$37b2o12b2o4bo4bo$9b2o26bobo12bob2obob3ob$ 9b2o28b2o7b3obob2obo5b$37bobo7bo4bo4b2o4b$22b2o13b2o12bob4o6b$25bobo 20b3obo3bo6b$27bo23bo2bo8b$25bo25bo2bo8b$21bo29bo2bo8b$22b2o29bo9b4$9b o53b$8bo2bo51b$8bo2bo51b$8bo2bo51b$6bo3bob3o48b$6b4obo51b$4b2o4bo4bo 47b$5bob2obob3o37b2o9b$b3obob2obo41b2o9b$o4bo4b2o51b$4bob4o53b$b3obo3b o53b$4bo2bo55b$4bo2bo55b$4bo2bo55b$6bo34b2o20b$39b2o2bo19b$39b5o19b$ 43bo19b$21b2o13b2o2b4o19b$21b2o13b2obo4b4o15b$35bobobob2obobobo14b$35b obobob2obobobo14b$36b4o4bob2o15b$40b4o2b2o15b$40bo22b$40b5o18b$40bo2b 2o18b$41b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 600 HEIGHT 600 THUMBSIZE 2 ZOOM 8 ]]
An alternate version of pi orbital using Eye of Sauron
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here
x = 47, y = 47, rule = B3/S23 13b3o3b2o$19bobo10b2o$7b2o12bo10b2o$6bo2bo11bob2o$6b3o2b7obobob2o$9b2o 8bobo$8bo10bobo20b2o$8b2obo4bo3bo21bobo$13bo25b2obobo$39bobobo$41bo$ 40bo2bo$40bo$b2o11bo25bo5bo$b2o10bobo24bo5bo$12bo3bo23bo5bo$12bo3bo24b obo$12b2ob2o24bobo$41bo$40b2o3b2o$39bo3bo2bo$40b6o$3b2o$3b2o37b2o$42b 2o$b6o$o2bo3bo$2o3b2o$5bo$3bobo24b2ob2o$3bobo24bo3bo$o5bo23bo3bo$o5bo 24bobo10b2o$o5bo25bo11b2o$6bo$3bo2bo$5bo$3bobobo$2bobob2o25bo$2bobo21b o3bo4bob2o$3b2o20bobo10bo$25bobo8b2o$22b2obobob7o2b3o$22b2obo11bo2bo$ 13b2o10bo12b2o$13b2o10bobo$26b2o3b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 600 HEIGHT 600 THUMBSIZE 2 ZOOM 8 ]]
Alternate form by Matthias Merzenich. The form with the lowest minimum population; with one pi-heptomino, it has 197 cells
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here


On December 30, 2024, KtT found a 265-glider synthesis.[10][11] The next day, Chris857 lowered the cost to 235 gliders.[12][13]

See also

References

  1. ↑ Jason Summers' jslife pattern collection. Retrieved on March 14, 2020.
  2. ↑ Pi bond, Atomic orbital on Wikipedia
  3. ↑ New Oscillators at Game of Life News. Posted by Heinrich Koenig on April 14, 2009.
  4. ↑ A plethora of p4 hasslers at Game of Life News. Posted by Adam P. Goucher on January 3, 2011.
  5. ↑ Dave Greene (April 10, 2017). Re: Stable signal converters (discussion thread) at the ConwayLife.com forums
  6. ↑ GUYTU6J (December 27, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  7. ↑ Matthias Merzenich (July 7, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  8. ↑ Aleph (December 12, 2020). Re: Gun Discussion Thread (discussion thread) at the ConwayLife.com forums
  9. ↑ Adam P. Goucher (December 15, 2020). Re: Gun Discussion Thread (discussion thread) at the ConwayLife.com forums
  10. ↑ KtT (December 30, 2024). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  11. ↑ shinjuku (#8741621325) (December 30, 2024). Job triggered by Adam P. Goucher at GitLab Catagolue project.
  12. ↑ Chris857 (December 31, 2024). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  13. ↑ shinjuku (#8746090993) (December 31, 2024). Job triggered by Adam P. Goucher at GitLab Catagolue project.
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