LifeWiki - User contributions [en]

Talk:Mold

2025-04-27T20:38:12Z

C7X: Created page with "==Exhaustive 6x7 oscillator enumeration== Does anyone have a citation to the original enumeration showing Mold is the unique oscillator with period greater than 2 fitting in a 6x7 bounding box? There is Stephen Silver's attempt to exhaustively enumerate 6x7 patterns from March 2000 (referenced [https://conwaylife.com/forums/viewtopic.php?f=17&t=2036&p=51576#p51576 here]), but it might be better for a wiki article to have a primary source linking to the results of the enu..."

==Exhaustive 6x7 oscillator enumeration==
Does anyone have a citation to the original enumeration showing Mold is the unique oscillator with period greater than 2 fitting in a 6x7 bounding box? There is Stephen Silver's attempt to exhaustively enumerate 6x7 patterns from March 2000 (referenced [https://conwaylife.com/forums/viewtopic.php?f=17&t=2036&p=51576#p51576 here]), but it might be better for a wiki article to have a primary source linking to the results of the enumeration. [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 20:38, 27 April 2025 (UTC)

64P2H1V0

2025-04-09T03:42:18Z

C7X: Move source from my last edit

{{Spaceship
|name = 64P2H1V0
|pname = 64p2h1v0
|c = 64
|bx = 31
|by = 8
|dir = Orthogonal
|p = 2
|m = 2
|s = c/2
|z = c/2
|h = 62
|symmetry = -c
|discoverer = Dean Hickerson
|discoveryear = 1989
|rulemin = B3/S23
|rulemax = B378/S2368
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-cky/S23-cy
|isorulemax = B2n34ejqz5aceky6-k78/S234ceikqwy5-acik67c8
|plaintext = true
|rle = true
|animated = true
|viewerconfig = #C [[ TRACKLOOP 2 0 -1/2 THUMBSIZE 2 GPS 4 ]]
|apgcode = xq2_32mmgozg0igke72z1n2q1z0qgm1z31i2bsogzggqq261z1
|pentadecathlonid = 64P2H1V0.1
}}
'''64P2H1V0''' is an unnamed [[c/2 orthogonal]] [[spaceship]] discovered, along with several other {{periodS|2}} spaceships, by [[Dean Hickerson]] on July 28, {{year|1989}}. Although Hickerson does not remember which specific spaceship was discovered first, this was among the earliest.<ref>{{citation|author=[[David Bell]]|date=August 18, 1992|title=[[Spaceships in Conway's Life]] (Part 2)}}</ref> In terms of its {{cells|64|text=64 cells}}, it is the smallest period 2 spaceship,<ref name="lifeinfo_spaceships_smallest" /> this was proven by Keith Amling in 2023,<ref name="p171149" /> although there are several higher-period c/2 spaceships that are smaller like the [[LWSS]].

== See also ==
* [[Barge 2 (spaceship)]]

== References ==
<references>
<ref name="lifeinfo_spaceships_smallest">{{cite web
|url = http://pentadecathlon.com/objects/spaceships/small/smallest.php
|title = Smallest Spaceships
|work = LifeInfo
|accessdate = June 18, 2009
|archiveurl = https://web.archive.org/web/20221101074513/http://pentadecathlon.com/objects/spaceships/small/smallest.php
|archivedate = November 1, 2022
}}</ref>
<ref name="p171149">{{LinkForumThread
|format = ref
|title = Re: LLSSS min pop search results spam
|p = 171149
|author = Keith Amling
|date = November 15, 2023
}}</ref>
</references>

== External links ==
* [http://members.canb.auug.org.au/~dbell/ The home page of David Ingalls Bell] including his article, ''Spaceships in Conway's Life (Part 2)''
* {{LinkCatagolue|xq2_32mmgozg0igke72z1n2q1z0qgm1z31i2bsogzggqq261z1}}
* {{LinkPentadecathlonObject|64P2H1V0.1}}

[[Category:Unnamed periodic objects]]

64P2H1V0

2025-04-09T03:42:01Z

C7X: Add that this was proven and not just smallest known

{{Spaceship
|name = 64P2H1V0
|pname = 64p2h1v0
|c = 64
|bx = 31
|by = 8
|dir = Orthogonal
|p = 2
|m = 2
|s = c/2
|z = c/2
|h = 62
|symmetry = -c
|discoverer = Dean Hickerson
|discoveryear = 1989
|rulemin = B3/S23
|rulemax = B378/S2368
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-cky/S23-cy
|isorulemax = B2n34ejqz5aceky6-k78/S234ceikqwy5-acik67c8
|plaintext = true
|rle = true
|animated = true
|viewerconfig = #C [[ TRACKLOOP 2 0 -1/2 THUMBSIZE 2 GPS 4 ]]
|apgcode = xq2_32mmgozg0igke72z1n2q1z0qgm1z31i2bsogzggqq261z1
|pentadecathlonid = 64P2H1V0.1
}}
'''64P2H1V0''' is an unnamed [[c/2 orthogonal]] [[spaceship]] discovered, along with several other {{periodS|2}} spaceships, by [[Dean Hickerson]] on July 28, {{year|1989}}. Although Hickerson does not remember which specific spaceship was discovered first, this was among the earliest.<ref>{{citation|author=[[David Bell]]|date=August 18, 1992|title=[[Spaceships in Conway's Life]] (Part 2)}}</ref> In terms of its {{cells|64|text=64 cells}}, it is the smallest period 2 spaceship, this was proven by Keith Amling in 2023,<ref name="lifeinfo_spaceships_smallest" /><ref name="p171149" /> although there are several higher-period c/2 spaceships that are smaller like the [[LWSS]].

== See also ==
* [[Barge 2 (spaceship)]]

== References ==
<references>
<ref name="lifeinfo_spaceships_smallest">{{cite web
|url = http://pentadecathlon.com/objects/spaceships/small/smallest.php
|title = Smallest Spaceships
|work = LifeInfo
|accessdate = June 18, 2009
|archiveurl = https://web.archive.org/web/20221101074513/http://pentadecathlon.com/objects/spaceships/small/smallest.php
|archivedate = November 1, 2022
}}</ref>
<ref name="p171149">{{LinkForumThread
|format = ref
|title = Re: LLSSS min pop search results spam
|p = 171149
|author = Keith Amling
|date = November 15, 2023
}}</ref>
</references>

== External links ==
* [http://members.canb.auug.org.au/~dbell/ The home page of David Ingalls Bell] including his article, ''Spaceships in Conway's Life (Part 2)''
* {{LinkCatagolue|xq2_32mmgozg0igke72z1n2q1z0qgm1z31i2bsogzggqq261z1}}
* {{LinkPentadecathlonObject|64P2H1V0.1}}

[[Category:Unnamed periodic objects]]

2c/5 orthogonal

2025-04-09T03:13:12Z

C7X: Fix typo + add source for min pop result

{{Speed
|image = 30p5h2v0
|speed = 2c/5 orthogonal
|ss = yes
|puff = yes
|rake = yes
|gun = yes
|wick = yes
}}
'''2c/5 orthogonal''' is an orthogonal [[speed]] that is equivalent to two fifths of the speed of light.

==Spaceships==
The first 2c/5 orthogonal [[spaceship]], [[44P5H2V0]], was discovered by [[Dean Hickerson]] on July 23, {{year|1991}}. [[Robert Wainwright]] and [[David Bell]] then found some small [[tagalong]]s which could string multiple copies of this spaceship together, resulting in arbitrarily large 2c/5 spaceships. This was the only known way to create 2c/5 spaceships until the discovery of [[70P5H2V0]] by [[Hartmut Holzwart]] on December 5, {{year|1992}}. The smallest possible 2c/5 spaceship, [[30P5H2V0]], was discovered by [[Paul Tooke]] on December 7, {{year|2000}} and proved to be the smallest possible 2c/5 spaceship by [[Keith Amling]] in 2023.<ref name="post171254" />

In May 2000 David Bell and Paul Tooke found the first {{periodS|10}} 2c/5 spaceship. Tooke then found several higher-period spaceships by removing the [[trailing edge]] of larger spaceships. Methods of building 2c/5 spaceships of arbitrarily high periods were first created by David Bell and [[Jason Summers]], who constructed adjustable [[rake]]s of periods {{nowrap|205 + 10N}} and {{nowrap|410 + 5N}}, which could easily be turned into spaceships. Paul Tooke then improved this to {{nowrap|185 + 5N}} and explicitly constructed spaceships of all periods below 185.

==Puffers==
{{EmbedViewer
|pname = 2c5puffer1
|position = right
|caption = The first 2c/5 puffer constructed
}}
The first 2c/5 [[puffer]] was built by Jason Summers on February 26, {{year|1999}}.<ref>{{CiteSummersPattern|name=jslife|accessdate=October 28, 2020}}</ref> It worked by having a [[lightweight spaceship]] collide with the back of a 2c/5 spaceship. The resulting debris was then [[perturb]]ed by two passing spaceships to produce a large cloud of debris and another forward traveling lightweight spaceship some distance away. The mirror image of this initial reaction was put on the other side to create a [[glide symmetric]] period 10150 puffer.

David Bell and Paul Tooke created the first versatile 2c/5 puffer in June, 2000. By removing the back ends of spaceships Tooke then found several low period puffers including periods 10 and 15. Mostly due to Paul Tooke, all 2c/5 puffer periods are known.

===Rakes===
David Bell and Jason Summers created the first adjustable period [[rake]]s with periods {{nowrap|205 + 10N}} and {{nowrap|410 + 5N}}. Paul Tooke then improved this to {{nowrap|200 + 5N}} and later to {{nowrap|185 + 5N}}. Tooke also explicitly constructed 2c/5 rakes of all possible periods below 185 except 10 and 15, which would necessarily be [[backrake]]s.

==Wickstretchers==
On April 23, {{year|2023}} [[Matthias Merzenich]] completed a 2c/5 orthogonal [[wickstretcher]] for a period-7 wick based on a partial result by [[Keith Amling]].<ref name="post160785" />

==Guns==
In May 2000, [[Noam Elkies]] proposed that a [[glider synthesis]] could be found for [[60P5H2V0]]. The 63-glider synthesis was completed by Noam Elkies and Jason Summers in March {{year|2003}} with the help of [[Mark Niemiec]]. The synthesis allowed the construction of the first [[gun]] that fired spaceships of a speed other than [[c/4 diagonal]] or [[c/2 orthogonal]], the [[p416 60P5H2V0 gun]], built on April 11, 2003. Jason Summers built a [[p690 60P5H2V0 gun|period 690 gun]] independently later that year. Summers also constructed a period-240 c/2 orthogonal rake which fires 2c/5 spaceships.

==See also==
* {{CategoryLink|Speeds}}
* {{CategoryLink|Spaceships with speed 2c/5}}

==References==
<references>
<ref name="post160785">{{LinkForumThread
|format = ref
|title = Re: Spaceship Discussion Thread
|p = 160785
|author = Matthias Merzenich
|date = April 23, 2023
}}</ref>
<ref name="post171254">{{LinkForumThread
|format = ref
|title = Re: LLSSS min pop search results spam
|p = 171254
|author = amling
|date = November 15, 2023
}}</ref>
</references>

==External links==
* David Bell's article, "[[Spaceships in Conway's Life]] (Part 6)"
* Paul Tooke's 2c/5 puffer collection
* {{CiteLexicon|lex_g.htm#glidersynthesis|name=glider synthesis}}
* {{LinkLexicon|lex_1.htm#a-2c5spaceship|name=2c/5 spaceship}}
* {{LinkGoLNews|2008/01/new_2c5_spaceship_1.html|title=New 2c/5 Spaceship|date=January 27, 2008|author=Heinrich Koenig}}

Fountain

2025-04-08T00:47:18Z

C7X: Fix refs section

{{Oscillator
|name = Fountain
|pname = fountain
|c = 63
|bx = 19
|by = 15
|p = 4
|m = 4
|h = 38
|v = 0.68
|sv = 0.68
|symmetry = -c
|discoverer = Dean Hickerson
|discoveryear = 1994
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-a/S23-cy
|isorulemax = B2n34et5ckry6-an7c8/S234ckqw5cejkq6-ck7c8
|plaintext = true
|rle = true
|animated = yes
|apgcode = xp4_x356k3p1p3k653z354mi419939914im453zx146y3641
|viewerconfig = #C [[ GPS 1 THUMBSIZE 3 ZOOM 18 HEIGHT 500 LOOP 4 ]]
}}
'''Fountain''' is a {{period|4}} [[oscillator]] that was found on November 28, {{year|1994}} by [[Dean Hickerson]]<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> and named by [[Bill Gosper]].

== Variants ==
{|style="margin:auto;width:300px;"
|{{EmbedViewer
|rle = x = 15, y = 13, rule = B3/S23
7bo2$3b2o5b2o$b2o4bo4b2o$5b2ob2o$bobo7bobo$bo2bobobobo2bo$5obobob5o$o
4bo3bo4bo$b3obobobob3o$3bob2obo2bo$8bobo$8b2o!
|position = center
|viewerconfig = #C [[ GPS 4 THUMBSIZE 2 ZOOM 16 AUTOSTART ]]
|caption = A smaller fountain that is usually interchangeable with the form in the infobox, found by [[David Eppstein]] on May 21, {{year|2000}}. It does not work with the p24 below.
|apgcode = xp4_4i28mq1e8gzvh0a0ellq23z4982dbge2
}}
|-
|{{EmbedViewer
|rle = x = 17, y = 15, rule = B3/S23
8bo2$5bo5bo$2b2o4bo4b2o$bob2ob2ob2ob2obo$bo13bo$4bo7bo$bo2bo7bo2bo$4bobo3bobo$bob3obobob3obo$o15bo$3o2bobobobo2b3o$3bobobobobobo$2obo2b2ob2o2bob2o$ob2o9b2obo!
|position = center
|viewerconfig = #C [[ GPS 4 THUMBSIZE 2 ZOOM 16 AUTOSTART ]]
|caption = A two-cell-thinner fountain with the same height and higher clearance and population.
|apgcode = xp4_cqs0o4o9n8bdzvs1w2310lmzrcu0chfaka9oz01y123032
}}
|}

== Hasslings ==
The fountain can hassle a traffic light in p24 with many variations, two of the most basic of which are shown here.
{{EmbedViewer
|rle = x = 39, y = 31, rule = B3/S23
32b2o$32bo2bo2$32bo2bo$31bo2bo$31bobo$11b2o19bo$11b2obo$15bo16b2o$12bo
19b2o$13bob2o$15b2o2$7b3o17b3o$7bobo17bobo$7b3o17b3o3$3b2o2b5o2b2o7b2o
2b5o2b2o$3bobobo3bobobo7bobobo3bobobo$4b3o5b3o9b3o5b3o$8bobo17bobo$6bo
bobobo13bobobobo$2o4b7o4b2ob2o4b7o4b2o$o2b2o4bo4b2o2bobo2b2o4bo4b2o2bo
$b3obo7bob3o3b3obo7bob3o$7b2ob2o15b2ob2o$3b2o9b2o7b2o9b2o$3bo11bo7bo
11bo$4bo9bo9bo9bo$3b2o9b2o7b2o9b2o!
|position = center
|viewerconfig = #C [[ GPS 8 THUMBSIZE 2 ZOOM 8 AUTOSTART ]]
}}

[[Robert Wainwright]] found that when hassled by [[mold]]s instead, the traffic light produces a blinker, acting as a [[factory]], two copies of which may perturb a beehive to act as a p24 heavyweight [[emulator]].<ref name="post137305" />
{{EmbedViewer
|rle = x = 34, y = 25, rule = B3/S23
6bo20bo$4b2obo18bob2o$3bo26bo$2bobo2bo18bo2bobo$2bo2bo22bo2bo$3b2o4b3o10b3o4b2o$16b2o$10bo4bo2bo4bo$16b2o3$8b3o12b3o$3b2ob7ob2o2b2ob7ob2o$3bo3bobobo3bo2bo3bobobo3bo$4b4o3b4o4b4o3b4o$6bo5bo8bo5bo$6bo5bo8bo5bo$2o3b2o5b2o6b2o5b2o3b2o$o2b5obob5o2b5obob5o2bo$b3o4b3o4b4o4b3o4b3o2$3b2o9b2o2b2o9b2o$3bo11bo2bo11bo$4bo9bo4bo9bo$3b2o9b2o2b2o9b2o!
|position = center
|viewerconfig = #C [[ GPS 8 HEIGHT 410 THUMBSIZE 2 ZOOM 12 AUTOSTART ]]
|apgcode = xp24_wo4ai1ayea1ia4ozx11y0151x4aa4x151y011zxckgks6e6skgkcwckgks6e6skgkczckgo8cf8gog8fc8oggo8cf8gog8fc8ogkczxmqy5qmwmqy5qm
}}

== See also ==
* [[Filter]]
* [[Superfountain]]

== References ==
<references>
<ref name="post137305">{{LinkForumThread
|f = 2
|t = 1437
|p = 137305
|title = Re: Oscillator Discussion Thread
|author = David Raucci
|date = November 4, 2021
|format = ref
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_f.htm#fountain}}
* {{LinkCatagolue|xp4_x356k3p1p3k653z354mi419939914im453zx146y3641}}

{{Sparker|p=4|type=dot|strength=strong}}
__NOTOC__

User:Galoomba/Longest diehards by bounding box

2025-03-02T23:46:57Z

C7X:

This table lists the longest-lasting known [[diehard]]s fitting in a n×n bounding box.

{| class="sortable wikitable"
|-
! n
! Lifetime
! Pattern
! Link
|-
| 1
|rowspan=2| 1
|rowspan=2| {{LV:Viewer|x = 1, y = 1, rule = B3/S23
o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 ZOOM 64 ]]}}
|rowspan=2|
|-
| 2
|-
| 3
| 9
| {{LV:Viewer|x = 3, y = 3, rule = B3/S23
obo$3o$o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 4
| 88
| {{LV:Viewer|x = 4, y = 4, rule = B3/S23
4o$bobo$2obo$4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 400 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 5
| 259
| {{LV:Viewer|x = 5, y = 5, rule = B3/S23
2o2bo$o2b2o$2o2bo$2bo$b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 6
|798
|{{LV:Viewer|x = 6, y = 6, rule = B3/S23
o2b3o$5bo$obobo$2bob2o$2obo$3ob2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 60 ]]
}}
|<ref name="post168418"/>
|-
| 7
|854
|{{LV:Viewer|x = 7, y = 7, rule = B3/S23
bbbbboo$ooobbob$boobbbb$ooboobb$bboobbo$bobobbo$oooobbb!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 60 ]]
}}
|<ref name="post205608"/>
|-
| 8
| 1 002
| {{LV:Viewer|x = 8, y = 7, rule = B3/S23
6bo$o5bo$4ob2o$bo4bo$2b2obobo$2o4bo$3ob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 52 ]]
}}
| <ref name="post164797"/>
|-
| 9
| 1 069
| {{LV:Viewer|x = 9, y = 8, rule = B3/S23
o2bobob2o$ob2o$o2bobob2o$5bo2bo$6bo$2b2o2bo$2b4ob2o$4b3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 48 ]]
}}
| <ref name="post164797"/>
|-
| 10
| 1 118
| {{LV:Viewer|x = 10, y = 9, rule = B3/S23
o$o$o4bo$4bobo$3bob2o$4obo3bo$5bo3bo$2o6b2o$bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 48 ]]
}}
| <ref name="post169048"/>
|-
| 11
| 1 119
| {{LV:Viewer|x = 11, y = 8, rule = B3/S23
3o$5b2o$7bo$o5bo$bob4o3bo$2bobo5bo$b2o2bo3b2o$2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 44 ]]
}}
| <ref name="post164797"/>
|-
| 12
|rowspan=4| 1 143
|rowspan=4| {{LV:Viewer|x = 12, y = 9, rule = B3/S23
5bobo$2bo3b4o$2obo5bobo$2bo3bo3b2o$obob2o2bo2bo$b3o4bo$2o4b2o2bo$3b3o$
5bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 40 ]]
}}
|rowspan=4| <ref name="post169048"/>
|-
| 13
|-
| 14
|-
| 15
|-
| 16
|rowspan=2| 1 456
|rowspan=2| {{LV:Viewer|x = 16, y = 16, rule = B3/S23
4o2bo5bo$3b3o5b2o$8b2o4bo$o2b3o2bo3bo2bo$2o2bo6b3o$o3bobo6bo$bo2b2o9b
o$b2ob2o3bobo3bo$3obo4b3o3bo$8b2o3b2o$12bob2o$10b4o$2b2o4bobob4o$2bo6b
o3b3o$3bo3b2obo3bo$2b2o4b3ob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 28 ]]
}}
|rowspan=2| <ref name="post168226"/>
|-
| 17
|-
| 18
| 2 094
| {{LV:Viewer|x = 18, y = 18, rule = B3/S23
2bo4bobo$2b2o2bob2o$3o2bo2bo5bo$2b2o3bo5bobo$2o2b3ob3o4b2o$bob2o2bobo
5bo$bobo5bo4bobo$2ob3o2bo7bo$8b2o7bo$9bo5bobo$15bobo$13b4o$8b2o2bobo$
5bo2bo3bobo$4bobobo6bo$3bobobo6b2o$2bo2bobobo3bobo$3b2o3b2o4bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 19
| 2 272
| {{LV:Viewer|x = 19, y = 19, rule = B3/S23
o4b2o7bobobo$o5bo9b2o$b2o2bo8b2obo$2bo2b2o$14bo$o2bo10b2obo$o8bobo2bo
b2o$4o5b2o5bo$2o8bo4bobo$16bo$2bob2o4b2o5bo$2bobobo2bobo3bobo$6bo2bo4b
o$5b2ob2o4bobo$3bo2bo$3b2obo8bobo$4bob2ob2o4bo$4bo2bob2o4bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 20
| 2 287
| {{LV:Viewer|x = 20, y = 19, rule = B3/S23
o4b2o8bobobo$o5bo10b2o$b2o2bo9b2obo$2bo2b2o$15bo$o2bo6bo4b2obo$o9bobo
2bob2o$4o6b2o5bo$2o14bobo$17bo$2bob2o4b2o6bo$2bobobo2bobo4bobo$6bo2bo
5bo$5b2ob2o5bobo$3bo2bo$3b2obo9bobo$4bob2ob2o5bo$4bo2bob2o5bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
|
|-
| 21
| 2 308
| {{LV:Viewer|x = 21, y = 19, rule = B3/S23
o4b2o9bobobo$o5bo11b2o$b2o2bo10b2obo$2bo2b2o$11bobo2bo$o2bo7b2o3b2obo$
o11bo3bob2o$4o14bo$2o15bobo$18bo$2bob2o4b2o7bo$2bobobo2bobo5bobo$6bo2b
o6bo$5b2ob2o6bobo$3bo2bo$3b2obo10bobo$4bob2ob2o6bo$4bo2bob2o6bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
|
|-
| 22
| 6 579
| {{LV:Viewer|x = 22, y = 21, rule = B3/S23
7bo$8bo2bo$8bobob2o$4b2o5b2ob2o$4b2o5b2ob2o$8bobob2o4bo$bo6bo2bo5bobo
$2bo4bo9bobo$3o16bo$19b2o$18bobo$2o4b2o3b2o$obo2bobo3bo3bo3b3o$2bo2bo
6b4o3bobo$2b2ob2o11bobo$5bo2bo3b4o4b2o$5bob2o3bo2bo$b2ob2obo12bo$b2ob
o2bo10bobo$5b2o11bobo$19bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 540 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 23
| 6 803
| {{LV:Viewer|x = 22, y = 23, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo4bo$11b2o4bobo$bo5b4obo6b2o$
ob4o3b3o7bo$4bo5bobo5bobo$16bo3bo$14b2o5bo$15b2o2bobo$2o16bo2bo$obo$2b
o16b3o$bo18b2o$b2o4b2o4b2o4bo$7bo3bo2bo5b2o$10bo7bobo$b2o6b3obo5bo$2b
o2b2o3b2o$bo11bo$o3bo2b2ob3o$2o5b4o2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 520 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 24
| 6 998
| {{LV:Viewer|x = 24, y = 24, rule = B3/S23
3b3ob2o$5b2o2b2o$2o4bo4bo$2o4bo4bo$5b2o2b2o9bo$3b3ob2o6b2o2bobo$14b3o
4b2o$21bo$17bo2bobo$18bo3bo$16b2o5bo$21bobo$2o18bo2bo$obo$2bo18b3o$bo
20b2o$b2o4b2o4b2o6bo$7bo3bo2bo7b2o$10bo9bobo$b2o6b3obo7bo$2bo2b2o3b2o
$bo11bo$o3bo2b2ob3o$2o5b4o2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 530 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 25
| 7 483
| {{LV:Viewer|x = 25, y = 25, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo7bo$11b2o7bobo$bo5b4obo7bobo
$ob4o3b3o10bo$4bo5bobo9b2o$21bobo2$22b3o$obo19bobo$2o3bo15bobo$5o18b2o
$obobob2o$3bob2o16bo$o2b2o8bo7bobo$bo4bo6b3o5bobo$b2ob2o10bo5bo$obob2o
bo5b3obo$o2bo9bo3bo$3b3obo6b3o$o4b2o4b3o$3obobo3bo3b2obo$bo2bobo3b2o2b
ob2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 540 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 26
| 10 320
| {{LV:Viewer|x = 26, y = 26, rule = B3/S23
11bo2b2o$11b2o3bobo$9b2o4bo2bo$9bo5bo2bo$2bob2o3bob2o3bobo3bo$o4bo5bo
2b2o5bobo$obo6bo13b2o$5o18bo$2o3b2o15bobo$2o2bo19bo$4bo20bo$o3bo18bob
o$obobo17bo2bo$obo2b2o10bobo$bobobo11bobo3b3o$bobob2o8bob2o5b2o$bo14b
o2b2o2bo$13bob2o2bo4b2o$5b2o4bo6b2o2bobo$5b2o2b2o3bo4bo3bo$7bo3b2ob2o
2bo$7b2obo3b2o2b2o$9b3o7bo$9bo2bo2bo3bo$6b2ob2ob4o2bo$6b2obo2bo4b4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 560 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 27
| 10 420
| {{LV:Viewer|x = 27, y = 26, rule = B3/S23
10bo2b2o$10b2o3bobo$8b2o4bo2bo$3bo4bo5bo2bo$o2b2o3bob2o3bobo5bo$2bo7b
o2b2o7bobo$o7bo15b2o$obobo19bo$obobo18bobo$3bo21bo$2obobo20bo$bob2o19b
obo$23bo2bo$18bobo$2b4o12bobo3b3o$4bo11bob2o5b2o$17bo2b2o2bo$14bob2o2b
o4b2o$6b2o4bo6b2o2bobo$6b2o2b2o3bo4bo3bo$8bo3b2ob2o2bo$8b2obo3b2o2b2o
$10b3o7bo$10bo2bo2bo3bo$7b2ob2ob4o2bo$7b2obo2bo4b4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 560 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 28
| 16 560
| {{LV:Viewer|x = 28, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o10bo$o13b5o$11bob
o5bo$12bob2o2bo$16b2o$3o3bo4bo11b2o$o3b3o3b2obo7bobobobo$bo2b4o3bo2bo
9bo2bo$obo2b3o3bo2bo6bobobobo$5o7b2o9bo3bo$ob2obo18b2obo$22bobo$22b2o
bobo$18bobo2bo$b2o4b2o9b2o3bo$bobo2bobo11b3o2bo$3bo2bo15bo$3b2ob2o4b2o
$6bo2bo2b2o$6bob2o8b2o2b2o$2b2ob2obo10bo3bo2b2o$2b2obo2bo5b2o2bo3bo3b
2o$6b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 620 HEIGHT 620 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 29
| 16 570
| {{LV:Viewer|x = 29, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o11bo$o14b5o$12bobo
5bo$13bob2o2bo$17b2o$b3o3bo4bo11b2o$bo3b3o3b2obo7bobobobo$2bo2b4o3bo2b
o9bo2bo$bobo2b3o3bo2bo6bobobobo$b5o7b2o9bo3bo$bob2obo18b2obo$23bobo$
23b2obobo$19bobo2bo$2b2o4b2o9b2o3bo$2bobo2bobo11b3o2bo$4bo2bo15bo$4b2o
b2o4b2o$7bo2bo2b2o$7bob2o8b2o2b2o$3b2ob2obo10bo3bo2b2o$3b2obo2bo5b2o2b
o3bo3b2o$7b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 640 HEIGHT 640 ZOOM 20 ]]
}}
|
|-
| 30
| 16 660
| {{LV:Viewer|x = 30, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o10bo$o13b5o$11bobo
5bo$12bob2o2bo$16b2o$3o3bo4bo13b2o$o3b3o3b2obo9bobobobo$bo2b4o3bo2bo
11bo2bo$obo2b3o3bo2bo8bobobobo$5o7b2o11bo3bo$ob2obo20b2obo$24bobo$24b
2obobo$20bobo2bo$b2o4b2o11b2o3bo$bobo2bobo13b3o2bo$3bo2bo17bo$3b2ob2o
4b2o$6bo2bo2b2o$6bob2o8b2o2b2o$2b2ob2obo10bo3bo2b2o$2b2obo2bo5b2o2bo3b
o3b2o$6b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 640 HEIGHT 640 ZOOM 20 ]]
}}
|
|-
| 31
| 31 013
| {{LV:Viewer|x = 31, y = 31, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo$11b2o$bo5b4obo2bobo2b3o$ob4o
3b3o3bobob2o2bo$4bo5bobo3bo2b2obo$21bo3bo$15bo9b2obo$5b2o8b3o8bo2bo$b
2obo2bo7bo2bo6b2o3bo$b2ob2obo8b2o7b2o3bo$5bob2o7b2o8b2ob2o$5bo2bo3b2o
$2b2ob2o5b2o8bob5o$2bo2bo10b2o5b4o$obo2bobo7bobo8bo$2o4b2o3bo3b2o4bob
2obobo$10bobo9b2obo$11bo9b2obobobo3$2b3o6b2o4bo2bo2bobo2bo$11bobo2bob
o2bobob3o$obo3b2o5bo3bo2b3o5b2o$b3o9b2o3b2obo3b2o$2bo3bo10bo2b2ob3ob3o
$2o3b2obo9bo2bobo4b2o$obo2bo6b2ob2obob6ob4o$o2b2ob2o4b2ob4obo2b3o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 680 HEIGHT 660 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 32
|rowspan=5| 1 120 271
|rowspan=5| {{LV:Viewer|x = 32, y = 32, rule = B3/S23
obo2bob2obo9bo$2o3b2ob2obo6b3o8b2o$bo9bo5bo11bo$11b2o5bo6b2o4bo$3bo2b
2o4bo4b2o5bobo3b2o$2bo2bobo3bo9bo2bo$5obo5b3o6b3obo$2bo2bo3b3o2bo9bo4b
2o$3bo4bo2bo7b3obo4bobo$9b2o7bo2b2o5bo$2ob3o7b2o4bo6b2obo$2o2bo2bo4bob
o3b2ob2o4bobo$o6bo3bobo5bobo5bob2o$2o2bo2bobo2bo6bobo4b2obo$2bo4bo5b3o
2b2ob2o3bo2bo$3bo2bobo6bo3bobo5bob2o$5bo12bo2bo6bo$2bob3o3bo8b2o8bobo$
4bo5bo19b2o$3bo3bo2b2o$12bo10bo$12b3o7bobob2o2b2o$18bo3bobobo3b2o$16bo
6b2o2bo$12bo4b4o4b2obo$14bobo8bo2bo$14b2o5bo4b2o$2o2bo8b2o3bob2o6b3o$o
bobo7bo3bo4bobo4bo2bo$obo11bo2bo8b2o2bo$b2obo13bob2o3bo2b2o$3b2o13b4o
3b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 20 ]]
}}
|rowspan=5| <ref name="post167008"/>
|-
| 33
|-
| ...
|-
| 47
|-
| 48
|-
| 49
|rowspan=4| 149 794 021 404 732
|rowspan=4| {{LV:Viewer|x = 49, y = 49, rule = B3/S23
b2ob2o10bo2b3o12b3o10b2o$bo3bo8bo2b3o4b2o2b2obo2bo2bo7b2obo$bobo4b2o5b
o7b3o7b2ob2o8bobo$8b2o11b2o2b2o2b2o16bo$20bobo2b2o4b2o14b2o$2o9b2ob2o
14b2o15bo$3o8b2obo27b2o$obo11bo8b2o4bo6b2obobobo$obo3b2o3b2ob2o6bobo
10bobob2o$2o4bobo2b2obo6bobo11bo11b2o$3o4bo7b3o3b2o4b2o4bobo12bo$b2o
15bo8b2o4b2o11bo$17bobo18b2o6b2o$4b2ob2o9bo4b2o5b2o6bobo6bo$obo2bobo4b
2o9b2o5b2o3b2obobo5bo$2o3bobo4bo2b2o19bo2bo6b2o$bo4bo6b2obo19bo$9b2o
16b2o2bob2obobo$8bobo11b2o3bo3b2obo2bobo3b2ob2o$3bo5bo3b2o7bo5b3o3bo3b
o4b2obo$12bobo8bo7bobo14bo$2ob3o7bo8b2o2bo3bo3b3o4bo5b2o$2o2bo2bo8b2o
5bobobo3b3o2bo4b3o2bo$o6bo8b2o5bo2bobo4bo10bo2b2o$2o2bo2bobo14bobobo9b
o4bo4bo$2bo4bo5b2o10bo3b2o5b3o5b4o$3bo2bobo4b2o15bo4bo$5bo17bo5bo5b2o
9b2o$2bob3o3bo11bobo3bo17bo$4bo5bo5b2o5b2o3b2o9b2ob2o3bo$3bo3bo2b2o4b
2o21b2obo5bo$12bo31bo2b2o$12b3o10bo7bo9b2o$18bo5bobo5b3o$16bo6bobo6b3o
5b2o$12bo4b4o3bo16bo2bo$14bobo13b2o3b2o4bobobo$14b2o5bo8b2o3b2o2b2obob
obo$13b2o3bob2o18bobo2bo$12bo3bo4bobo16bo2b2o$14bo2bo21b2o$18bob2o4bo$
18b4o3bobo3b2o$2o2bo20bobo4bo$obobo21bob2o2b2ob2o$obo24bo2bob2obo$b2ob
o16b3o5bob2o3b3o$3b2o17b3o5b3o5bo$32b3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 12 ]]
}}
|rowspan=4| <ref name="post200534"/>
|-
| 50
|-
| 51
|-
| 52
|-
| 53
|rowspan=5| 2 738 059 586 423 623 206
|rowspan=5| {{LV:Viewer|x = 53, y = 53, rule = B3/S23
4b6o2b4ob4ob2o25bob2o$6bo7b4obobo2bo10b3o12b3o$10bo6bobo2bo5bo5bo2bo
14bo$5b5o6bo3bobo4bob2obo4bo11b2obo$7b2o21bobo15bob3o$4bob2o24bobo16b
2o$7bo4b2o8bo24b3ob2o$15bobobo2b3o12b2o9bo$12b2obobobo5bo12bo8bo3bo$
22b2obo9b3o10bo$bo10bob3obo3bobo3b2o4bo$obo10bo2b2o10b2o4b4o$bobo9bo2b
2ob2o16bo$bo2bo3bo4bobo2bo5b2o6b3o$b2o5bo5bobobobo3b2o6bo2bo$bo5bo6bo
2bob2o12b2o$6bo14b2o14bo8b2obo$11b2obobob2obo14bobo6bo5b2o$17bo3b2o6bo
5bobo8b2ob2obo$13b2o2bo4b2o4bobo5bo8b3obob2o$16b3o3bob2o3bo16bo4b2o$
15b2o5bob2o18bobo2bo2bo$ob3o12b2o25b2obobo$ob4o11b2o27bo2bob2o$o5bo32b
o6bo2bo2bo$bobobo2b3o3b2o13bo7b3o11b2o$2bobob4o4b2o12bo2bo4bo7b2obo4bo
$3bo2bob2o18bo2bo4b2o10b2ob2o$3bo3b3obo9bobobo4bo21bo$4b3o2b2obo4b2o2b
obo2bo6b3o7b2obo3bo$10bobo4b2o4bobo7b3o7bob2o$11bob2o6bo19bobo$12bo2bo
5bobo3b2o11bobo2b2o$13b2o6bo4bobo12bo4bo$14b5o3bo3bo4b2o3b2o7bo$15b4o
6b2o5b5o8b2o$15bobo15b3o4bob2obo$14bob2obo14bo5b2obo2bo$14bo3bobo22bob
2o$14bo2bo2b2o18b2obobo4bobo$15b2obob2o18bobo2bo5bo$17bo2b2o4b2o2bo10b
o3b2o3bobo$18bo10b2o20b2o$19b3o4bo2bo19bo2bo$obo2b2o3bo13b3o2bo21b2o$b
2o2bo4b2obo12bo2bo3b2o12b3o2bo$2bo2bob2o3b2o10bob2ob2o2b2o17bo$o5bo4bo
bo8b4obo21bo$b3obo5bob2o4bo2bo4b4o$bob2obo3bo3bo2bo3bo4bo2bo3bo$2o2bo
3b2o3bo5bo5bo4b3o$4b2o2bob2o6bo2b3o5b2o2bo$5b2o2b5o2b5obo2b7o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 12 ]]
}}
|rowspan=5| <ref name="post169209"/>
|-
| 54
|-
| ...
|-
| 58
|-
| 59
|-
| 60
| 2.7324 × 10{{sup|27284}}
| {{LV:Viewer|x = 60, y = 60, rule = B3/S23
11b6o2b4ob4ob2o25bob2o$13bo7b4obobo2bo10b3o12b3o$17bo6bobo2bo5bo5bo2bo
14bo$12b5o6bo3bobo4bob2obo4bo11b2obo$14b2o21bobo15bob3o$11bob2o24bobo
16b2o$5bo8bo14bo24b3ob2o$5b3o21b3o12b2o9bo$8bo23bo12bo8bo3bo$7b2o3bo
16b2obo9b3o10bo$12bobo14bobo3b2o4bo$11bobo21b2o4b4o$6bobo4bo30bo$7b2o
22b2o6b3o$7bo23b2o6bo2bo$15b2o3b2o2b2o14b2o$15b2o2bo2bo2bo18bo8b2obo$
3b2ob2o11bob2obo18bobo6bo5b2o$3b3o2bo3bo7bo3b2o10bo5bobo8b2ob2obo$2bo
4b2o2bobob2obobob2o6b2o3bobo5bo8b3obob2o$b3ob3o3bobobob2ob2obo6bobo3bo
16bo4b2o$b2obob2o4bo18b2o18bobo2bo2bo$bo49b2obobo$bo2b3obo44bo2bob2o$b
ob2o41bo6bo2bo2bo$21b2o13bo7b3o11b2o$4bo16b2o12bo2bo4bo7b2obo4bo$3bo
31bo2bo4b2o10b2ob2o$31b2o4bo21bo$2ob3o18b2o4bobo17b2obo3bo$2o2bo2bo16b
2o4b2o18bob2o$o6bo6b2o32bobo$2o2bo2bobo5bo11b2o5b2o11bobo2b2o$2bo4bo7b
obo8bobo4bobo12bo4bo$3bo2bobo7b2o3bo4b2o5bo4b2o3b2o7bo$5bo14bobo9b2o4b
2o3b2o7b2o$2bob3o3bo10bo25bob2obo$4bo5bo7bo10b2o9b3o4b2obo2bo$3bo3bo2b
2o5bobo8bobo9b3o7bob2o$12bo5bo4b2o3bo12bo5b2obobo4bobo$12b3o8b2o2b2o4b
2o12bobo2bo5bo$18bo14bo14bo3b2o3bobo$16bo18bo22b2o$12bo4b4o7b2o4b2o20b
o2bo$14bobo11b2o3bo24b2o$14b2o5bo4b2o6bobobob2o12b3o2bo$13b2o3bob2o4b
2o3bo3b2obobo3bo14bo$12bo3bo4bobo7bo5b3o2bo13bo$14bo2bo11b3o5bo2b4o$
18bob2o2b2obo3bobobob2ob2obo$18b4o5bo6b2o3bo$24b3o2b4ob2o3b3obo$24b2o
3b2o7bo3bo$18b2o4bobo2bobo3b2o3bob2o$22b2o9b2ob2o2bo3bo$18b3o4b2obobob
3o2bo2b2o2bo$16bob4ob3o4b2o4bob2obo$14b2o4bo2b2o2b3o2bo3b2o2bo2bo$15bo
2b2ob3obo3bobob3o2b2ob2o$18b2obob3ob8obob2obobo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 780 HEIGHT 780 ZOOM 12 ]]
}}
| <ref name="post169196"/>
|}

== References ==
<references>
<ref name="post164797">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 164797
|author = Pyry Virtanen
|date = August 9, 2023
}}</ref>
<ref name="post167008">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 167008
|author = Tim Coe
|date = September 14, 2023
}}</ref>
<ref name="post168226">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 168226
|author = Dean Hickerson
|date = October 1, 2023
}}</ref>
<ref name="post168418">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 168418
|author = b3s23love
|date = October 3, 2023
}}</ref>
<ref name="post169048">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 169048
|author = Pyry Virtanen
|date = October 13, 2023
}}</ref>
<ref name="post169196">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 169196
|author = Tim Coe
|date = October 16, 2023
}}</ref>
<ref name="post169209">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 169209
|author = b3s23love
|date = October 16, 2023
}}</ref>
<ref name="post200534">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 200534
|author = moebius
|date = December 28, 2024
}}</ref>
<ref name="post205608">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 205608
|author = C7X
|date = March 1, 2025
}}</ref>
</references>

Boojum reflector

2025-01-25T01:23:42Z

C7X: Looks like it's referring to December 20, 2023

{{Reflector
|name = Boojum reflector
|pname = boojumreflector
|type = Stable
|colour = preserving
|c = 60
|bx = 44
|by = 32
|a = 180
|p = 202
|spartan = no
|discoverer = Dave Greene
|discoveryear = 2001
|rulemin = B3/S23
|rulemax = B3/S238
|isorulemin = B3/S23
|isorulemax = B3/S234c8
|plaintext = true
|rle = true
|viewerconfig = #C [[ HEIGHT 400 THUMBSIZE 2 ZOOM 10 GPS 20 LOOP 240 ]]
}}
The '''boojum reflector''' is a 180° [[glider]] [[reflector]] found by [[Dave Greene]] in April {{year|2001}} as a modification of [[Paul Callahan]]'s [[Herschel receiver]],<ref name="post115054" /> winning $100 bounties offered by [[Alan Hensel]] and [[Dieter Leithner]]. The name is taken from Lewis Carroll's ''The Hunting of the Snark'', referring to the fact that a small 90-degree stable reflector was really what was wanted.{{refn|group=note|180-degree reflectors have limited use in larger circuitry constructions because they cannot get a glider to wherever it needs to be. A composite 180-degree reflector can be made from two 90-degree reflectors.}}

The boojum reflector was both the smallest and fastest known [[stable reflector]], until it was superseded by the [[rectifier]] in {{year|2009}} and the [[Snark]] in {{year|2013}}.

The boojum reflector produces an unwanted [[beehive]], which is then deleted by a later glider. If the beehive is removed before the latter glider hits it, the glider will leave the reflector. This reaction can be seen in this p226 glider [[shuttle]]:

{{EmbedViewer
|pname = p226glidershuttle
|viewerconfig = #C [[ WIDTH 840 HEIGHT 560 THUMBSIZE 2 ZOOM 10 GPS 20 AUTOSTART LOOP 226 ]]
|position = center
|caption = p226 glider shuttle
|style = width:300px;
|apgcode = xp226_ya252z04s0gy033y0gn081ey7oge2zx11y033e8ifdyno8z8kkm0mmycooyc321oozx343zyzy5gyho4ozyq33g8oy8223333ycdd0d552zyr23ysooy0ggzyz08e13yhooy01074zyzyg8k8
}}

A different type of Boojum shuttle is possible by switching the output gliders and the beehive deleting gliders. The corresponding beehive-glider [[collision]] does not become nothing by itself, but the block from that boojum serves as a [[catalyst]] for the successful removal.

{{EmbedViewer
|pname = p225boojumshuttle
|viewerconfig = #C [[ WIDTH 840 HEIGHT 560 THUMBSIZE 2 ZOOM 10 GPS 20 AUTOSTART LOOP 225 ]]
|position = center
|style = width:300px;
|apgcode = xp225_yzye252zyy2egoyh33y0g0s4zyp8oys33y011ggzypgh23y7skkygmm0mk1zyp11yx343zwg8gz0ar0rqygaaey7gg33z32y2ggyq1074z8e13y0hhyh62sgzy411xg8gzya1
}}

On December 20, 2023, Luke Kiernan used [[Barrister]] to complete a boojum reflector variant with the beehive eaten by surrounding chaos.
{{EmbedViewer
|rle = x = 52, y = 32, rule = B3/S23
20b2o$20b2o5$4b2o$4bobo$7bo$5b2obo38bo$4bo2bo38bobo$4b2o17bo22bobo$b2o
bo19b2ob2o16b2ob3o$bo2bo18b2o2b2o22bo$3bo4b2o35b2ob3o$bob2o3b2o35b2ob
o$obo$o2b2o$bobo6b2o$2o2bo5bo3b2o$3b2o2b2obo4bo25b2o$7bo2bob3o26b2o4b
2o$9b2obo5b2o27bobo$17bobo29bo$17bo31b2o$16b2o23b2o$41b2o3$36bo$35bob
o$36bo!
|viewerconfig = #C [[ WIDTH 840 HEIGHT 560 THUMBSIZE 2 ZOOM 10 GPS 20 AUTOSTART T 0 PAUSE 2 LOOP 225 ]]
|position = center
|style = width:300px;
}}
==Notes==
<references group="note" />

==References==
<references>
<ref name="post115054">{{LinkForumThread
|format = ref
|p = 115054
|title = Re: History Of ConwayLife
|author = Dave Greene
|date = December 9, 2020
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_b.htm#boojumreflector}}

{{GliderNavbox}}

[[Category:Colour-preserving reflectors]]

Engineered diehard

2025-01-07T16:08:38Z

C7X: Change name /* Sawtooth-based designs */

{{stub}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|pname = diehard30273
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 ZOOM 14 ]]
|position = center
|caption = 30,273-tick diehard with bounding box {{times|32|32}} by Hickerson<ref name="post143921" />
}}
|}
{{main|Die hard#"Die hard" as a general term}}
Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes. On March 1, [[Dean Hickerson]] shared a 9044-tick {{times|32|32}} diehard in a private email to [[Dave Greene]]. After a complex series of interactions between an active reaction and various still lifes, a single [[lightweight spaceship]] is produced which eventually catches up to and collides with [[30P5H2V0]], producing a single [[loaf]]. Finally, an even slower [[25P3H1V0.1]] eventually collides with the loaf, destroying both of them.<ref name="post143573" /> On March 6, more optimized versions using different combinations of spaceships (including the especially slow [[copperhead]]) were shared, including a 14,010-tick diehard at {{times|32|32}} and an 18,477-tick diehard at {{times|36|36}}.<ref name="post143574" />

Although Hickerson's results were not initially posted publicly, a forum thread was coincidentally started a few weeks later dedicated to diehards, including engineered ones.<ref name="post143559" /> On March 31, [[Pavel Grankovskiy]] posted a 50,716-tick diehard in which a [[Simkin glider gun]] and [[pulse divider|pulse-dividing]] glider reflectors are used to slowly eat through a series of [[tub]]s. Although significantly larger than Hickerson's constructions at {{times|90|86}}, Grankovskiy's 50,716-tick diehard does not use the "spaceship-chasing" technique, meaning that throughout its evolution, the pattern only slightly exceeds its initial bounds. Using spaceship-chasing, however, the pattern's lifespan can be increased by an order of magnitude to 518,476 ticks without further increasing the bounding box.<ref name="post143605" /> [[Jiahao Yu]] optimized the bounding box of both of these patterns to {{times|87|86}},<ref name="post143624" /> as shown below.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = diehard50716
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 50,716-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = diehard518476
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 518,476-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery bottom}}

==Sawtooth-based designs==
Using a [[sawtooth]] allows for the creation of extremely long-lasting diehards. On April 7, 2022, Pavel Grankovskiy successfully constructed a diehard using a sawtooth an {{c|Sawtooths with expansion factor 121|expansion factor of 121}}. The pattern fits within a bounding box of {{times|99|101}} (just barely meeting the 10,000-cell restriction specified in the original post<ref name="post143559" />) and lasts approximately {{times|2.280624|10{{sup|870}}}} generations.<ref name="post143908" /> Further optimizations, with the help of [[toroidalet]],<ref name="post143914" /> Dean Hickerson,<ref name="post143920" /> [[EvinZL]],<ref name="post143997" /> [[Rocknlol]],<ref name="post144020" /> and [[Adam P. Goucher]]<ref name="post144030" /> increased its lifespan to {{times|~1.33616|10{{sup|1443}}}} ticks<ref name="post144027" /> and decreased its bounding box to {{times|94|98}}.<ref name="post144045" />

{{EmbedViewer
|pname = diehard1e1443
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 700 ZOOM 6 ]]
|position = center
|caption = {{times|94|98}} exponential diehard by Grankovskiy et al.
|style = width:300px;
}}

On April 9, Grankovskiy posted a concept for a pattern whose lifespan is measured via [[tetration]], the next hyperoperator after exponentiation. Originally posted in the form of a methuselah,<ref name="post144034" /> the diehard version was completed on April 11.<ref name="post144077" /> With optimization by [[Tanner Jacobi]]<ref name="post144087" /> and toroidalet,<ref name="post144162" /><ref name="post149066" /> its lifespan is somewhere between 1510 and 1610 ticks.<ref>{{Cite web|url=https://btm.qva.mybluehost.me/telling-the-tale-of-two-tetrations/|author=Brett Berger|title=Telling the tale of two tetrations|work=a blog by biggiemac42|date=April 17, 2022|accessdate=April 17, 2022}}</ref>

{{EmbedViewer
|pname = diehardtetration
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|111|90}} tetrational diehard by Grankovskiy et al.
|style = width:300px;
}}

On July 9, 2023, [[EvinZL]] proposed adding loaf-making fuse to increase the lifespan of the methuselah by extending power tower length,<ref name="post163493" /> based on the original idea of [[Tanner Jacobi]].<ref name="post148684" /> In a flurry of activity that followed after, [[toroidalet]], [[Adam P. Goucher]], [[Pavel Grankovskiy]] and [[EvinZL]] pushed the number of loaves from 15<ref name="tetrational_15_loaves" /> to approximately {{times|3.52|10{{sup|48}}}}<ref name="tetrational_1e48" />, with the latter improvement based on idea by [[Adam P. Goucher]] to use gliders from exponential part of diehard to ignite the fuse.<ref name="tetrational_exp_idea" /> This was subsequently improved to {{times|1.1|10{{sup|1046}}}}<ref name="tetrational_1e1046" /><ref name="tetrational_exp_cp4space" />.

{{EmbedViewer
|pname = diehardtetration1046
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|109|91}} tetrational diehard with a lifespan exceeding (101046)10.
|style = width:300px;
}}

On December 23, 2024, [[Tim Coe]] posted a {{times|49|49}} sawtooth-based diehard with lifetime 1237975907532, reducing the size of the sawtooth base.<ref name="post200083" />

==Double-tetrational designs==
On 15th September 2023, [[Tim Coe]] and b3s23love increased the height of the tetrational tower from {{times|1.1|10{{sup|1046}}}} to 121{{sup|{{times|8.46|10{{sup|1059}}}}}}. The following day, Tim Coe further improved this height to 121{{sup|121{{sup|121{{sup|121{{sup|498}}}}}}}}, so the height of the tetrational tower is itself a tetrational tower. This was subsequently further improved by Tim Coe, toroidalet, EvinZL, and b3s23love, culminating in a height of 121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|1356648129958673823266622201465466300}}}}}}}}}}}}}}}}}} as of the 28th September 2023. The overall lifespan of the diehard exceeds {{sup|{{sup|11}}11}}11, or 11^^^3 in Knuth's up-arrow notation. More recent designs have further improved lifespans, with the current record holder taking 17^^^3 generations to die out entirely.

{{EmbedViewer
|pname = diehardtetration17uuu3
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|116|86}} tetrational diehard with a lifespan exceeding 17↑↑↑3.
|style = width:300px;
}}

==Timetable==
In many cases, several incremental record-breaking improvements were made inside 24 hours. In the following table, the record-breaking pattern for each day is listed (with each day beginning and ending at UTC 0:00).<ref name="message1156939723001049189" />

{| class="wikitable"
! Date
! Lifespan
! Bounding box size
! Bounding box cells
! Contributor(s)
|-
!2022-02-21
|2474
|32×32
|1024
|Charity Engine
|-
!2022-03-01
|9044
|32×32
|1024
|Dean Hickerson
|-
!2022-03-06
|14010
|32×32
|1024
|Dean Hickerson
|-
!2022-03-31
|518476
|90×86
|7740
|Pavel Grankovskiy
|-
!2022-04-01
|518476
|87×86
|7482
|Jiahao Yu
|-
!2022-04-07
|2.28 × 10^870
|99×101
|9999
|Pavel Grankovskiy
|-
!2022-04-09
|1.77 × 10^1295
|94x96
|9024
|Pavel Grankovskiy, toroidalet, Rocknlol
|-
!2022-04-10
|1.476 × 10^1595
|94×99
|9306
|Pavel Grankovskiy, Dean Hickerson
|-
!2022-04-11
|11 ^^ 10
|105×95
|9975
|Pavel Grankovskiy
|-
!2022-04-13
|11 ^^ 11
|108×92
|9936
|toroidalet, Pavel Grankovskiy
|-
!2022-04-14
|11 ^^ 13
|109×91
|9919
|Pavel Grankovskiy, toroidalet, Tanner Jacobi
|-
|
|-
!2023-07-17
|121 ^^ 15
|110×90
|9900
|toroidalet, Pavgran
|-
!2023-07-18
|121 ^^ (4.98 × 10^27)
|111×90
|9990
|Pavel Grankovskiy, toroidalet, EvinZL, Adam P. Goucher
|-
!2023-07-19
|121 ^^ (5.94 × 10^54)
|109×91
|9919
|Pavel Grankovskiy, May13, toroidalet, EvinZL, Adam P. Goucher
|-
!2023-07-20
|121 ^^ (1.67 × 10^903)
|109×91
|9919
|May13, EvinZL
|-
!2023-07-23
|121 ^^ (1.10 × 10^1046)
|109×91
|9919
|Adam P. Goucher
|-
!2023-09-15
|121 ^^ (121 ^ (8.46 × 10^1059))
|108×91
|9828
|Tim Coe, b3s23love
|-
!2023-09-16
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 498)
|109×91
|9919
|Tim Coe
|-
!2023-09-19
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ (9.74 × 10^51))
|109×91
|9919
|b3s23love, toroidalet, EvinZL
|-
!2023-09-21
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 60143)
|109×91
|9919
|EvinZL, Tim Coe
|-
!2023-09-22
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 70433)
|112×89
|9968
|b3s23love, toroidalet, EvinZL
|-
!2023-09-24
|9 ^^^ 3
|112×89
|9968
|Tim Coe
|-
!2023-09-28
|11 ^^^ 3
|112×89
|9968
|toroidalet
|-
!2023-10-05
|17 ^^^ 3
|116×86
|9976
|Tim Coe, EvinZL, [https://conwaylife.com/forums/viewtopic.php?p=168589#p168589 Adam P. Goucher]
|-
!2023-10-05
|17 ^^^ 3 +
|116×86
|9976
|[https://conwaylife.com/forums/viewtopic.php?p=169264#p169264 toroidalet]
|}

==References==
<references>
<ref name="post143573">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143573
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143574">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143574
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143559">{{LinkForumThread
|format = ref
|title = (Engineered) diehards
|p = 143559
|author = squareroot12621
|date = March 30, 2022
}}</ref>
<ref name="post143605">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143605
|author = Pavel Grankovskiy
|date = March 31, 2022
}}</ref>
<ref name="post143624">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143624
|author = Jiahao Yu
|date = March 31, 2022
}}</ref>
<ref name="post143921">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143921
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143908">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143908
|author = Pavel Grankovskiy
|date = April 7, 2022
}}</ref>
<ref name="post143914">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143914
|author = toroidalet
|date = April 7, 2022
}}</ref>
<ref name="post143920">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143920
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143997">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143997
|author = EvinZL
|date = April 9, 2022
}}</ref>
<ref name="post144020">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144020
|author = Rocknlol
|date = April 10, 2022
}}</ref>
<ref name="post144030">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144030
|author = Adam P. Goucher
|date = April 10, 2022
}}</ref>
<ref name="post144027">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144027
|author = Dean Hickerson
|date = April 10, 2022
}}</ref>
<ref name="post144045">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144045
|author = toroidalet
|date = April 10, 2022
}}</ref>
<ref name="post144034">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144034
|author = Pavel Grankovskiy
|date = April 9, 2022
}}</ref>
<ref name="post144077">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144077
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144087">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144087
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144162">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144162
|author = toroidalet
|date = April 13, 2022
}}</ref>
<ref name="post149066">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 149066
|author = toroidalet
|date = August 2, 2022
}}</ref>
<ref name="post163493">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163493
|author = EvinZL
|date = July 9, 2023
}}</ref>
<ref name="post148684">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 148684
|author = Tanner Jacobi
|date = July 25, 2022
}}</ref>
<ref name="post200083">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 200083
|author = moebius
|date = December 18, 2024
}}</ref>
<ref name="tetrational_15_loaves">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163828
|author = toroidalet
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e48">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163888
|author = Adam P. Goucher
|date = July 19, 2023
}}</ref>
<ref name="tetrational_exp_idea">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163848
|author = Adam P. Goucher
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e1046">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 164085
|author = Adam P. Goucher
|date = July 23, 2023
}}</ref>
<ref name="tetrational_exp_cp4space">{{cite web|url=https://cp4space.hatsya.com/2023/07/23/miscellaneous-discoveries/|title=Miscellaneous discoveries|work=Complex Projective 4-Space|accessdate=May 23, 2023}}</ref>
<ref name="message1156939723001049189">{{CiteDiscord
|author = Adam P. Goucher
|date = September 28, 2023
|channel = cgol
|id = 1156939723001049189
}}</ref>
</references>

==External links==
* {{LinkForumThread|title=Re: (Engineered) diehards|p=144151|author=Pavel Grankovskiy|date=April 12, 2022}} (analysis of the tetrational diehard's total runtime)

[[Category:Methuselahs]]
[[Category:Gliderless methuselahs]]

User:Galoomba/Longest diehards by bounding box

2025-01-07T15:57:59Z

C7X: Improvement by same poster

This table lists the longest-lasting known [[diehard]]s fitting in a n×n bounding box.

{| class="sortable wikitable"
|-
! n
! Lifetime
! Pattern
! Link
|-
| 1
|rowspan=2| 1
|rowspan=2| {{LV:Viewer|x = 1, y = 1, rule = B3/S23
o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 ZOOM 64 ]]}}
|rowspan=2|
|-
| 2
|-
| 3
| 9
| {{LV:Viewer|x = 3, y = 3, rule = B3/S23
obo$3o$o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 4
| 88
| {{LV:Viewer|x = 4, y = 4, rule = B3/S23
4o$bobo$2obo$4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 400 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 5
| 259
| {{LV:Viewer|x = 5, y = 5, rule = B3/S23
2o2bo$o2b2o$2o2bo$2bo$b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 6
|rowspan=2| 798
|rowspan=2| {{LV:Viewer|x = 6, y = 6, rule = B3/S23
o2b3o$5bo$obobo$2bob2o$2obo$3ob2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 60 ]]
}}
|rowspan=2| <ref name="post168418"/>
|-
| 7
|-
| 8
| 1 002
| {{LV:Viewer|x = 8, y = 7, rule = B3/S23
6bo$o5bo$4ob2o$bo4bo$2b2obobo$2o4bo$3ob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 52 ]]
}}
| <ref name="post164797"/>
|-
| 9
| 1 069
| {{LV:Viewer|x = 9, y = 8, rule = B3/S23
o2bobob2o$ob2o$o2bobob2o$5bo2bo$6bo$2b2o2bo$2b4ob2o$4b3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 48 ]]
}}
| <ref name="post164797"/>
|-
| 10
| 1 118
| {{LV:Viewer|x = 10, y = 9, rule = B3/S23
o$o$o4bo$4bobo$3bob2o$4obo3bo$5bo3bo$2o6b2o$bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 48 ]]
}}
| <ref name="post169048"/>
|-
| 11
| 1 119
| {{LV:Viewer|x = 11, y = 8, rule = B3/S23
3o$5b2o$7bo$o5bo$bob4o3bo$2bobo5bo$b2o2bo3b2o$2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 44 ]]
}}
| <ref name="post164797"/>
|-
| 12
|rowspan=4| 1 143
|rowspan=4| {{LV:Viewer|x = 12, y = 9, rule = B3/S23
5bobo$2bo3b4o$2obo5bobo$2bo3bo3b2o$obob2o2bo2bo$b3o4bo$2o4b2o2bo$3b3o$
5bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 40 ]]
}}
|rowspan=4| <ref name="post169048"/>
|-
| 13
|-
| 14
|-
| 15
|-
| 16
|rowspan=2| 1 456
|rowspan=2| {{LV:Viewer|x = 16, y = 16, rule = B3/S23
4o2bo5bo$3b3o5b2o$8b2o4bo$o2b3o2bo3bo2bo$2o2bo6b3o$o3bobo6bo$bo2b2o9b
o$b2ob2o3bobo3bo$3obo4b3o3bo$8b2o3b2o$12bob2o$10b4o$2b2o4bobob4o$2bo6b
o3b3o$3bo3b2obo3bo$2b2o4b3ob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 28 ]]
}}
|rowspan=2| <ref name="post168226"/>
|-
| 17
|-
| 18
| 2 094
| {{LV:Viewer|x = 18, y = 18, rule = B3/S23
2bo4bobo$2b2o2bob2o$3o2bo2bo5bo$2b2o3bo5bobo$2o2b3ob3o4b2o$bob2o2bobo
5bo$bobo5bo4bobo$2ob3o2bo7bo$8b2o7bo$9bo5bobo$15bobo$13b4o$8b2o2bobo$
5bo2bo3bobo$4bobobo6bo$3bobobo6b2o$2bo2bobobo3bobo$3b2o3b2o4bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 19
| 2 272
| {{LV:Viewer|x = 19, y = 19, rule = B3/S23
o4b2o7bobobo$o5bo9b2o$b2o2bo8b2obo$2bo2b2o$14bo$o2bo10b2obo$o8bobo2bo
b2o$4o5b2o5bo$2o8bo4bobo$16bo$2bob2o4b2o5bo$2bobobo2bobo3bobo$6bo2bo4b
o$5b2ob2o4bobo$3bo2bo$3b2obo8bobo$4bob2ob2o4bo$4bo2bob2o4bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 20
| 2 287
| {{LV:Viewer|x = 20, y = 19, rule = B3/S23
o4b2o8bobobo$o5bo10b2o$b2o2bo9b2obo$2bo2b2o$15bo$o2bo6bo4b2obo$o9bobo
2bob2o$4o6b2o5bo$2o14bobo$17bo$2bob2o4b2o6bo$2bobobo2bobo4bobo$6bo2bo
5bo$5b2ob2o5bobo$3bo2bo$3b2obo9bobo$4bob2ob2o5bo$4bo2bob2o5bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
|
|-
| 21
| 2 308
| {{LV:Viewer|x = 21, y = 19, rule = B3/S23
o4b2o9bobobo$o5bo11b2o$b2o2bo10b2obo$2bo2b2o$11bobo2bo$o2bo7b2o3b2obo$
o11bo3bob2o$4o14bo$2o15bobo$18bo$2bob2o4b2o7bo$2bobobo2bobo5bobo$6bo2b
o6bo$5b2ob2o6bobo$3bo2bo$3b2obo10bobo$4bob2ob2o6bo$4bo2bob2o6bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
|
|-
| 22
| 6 579
| {{LV:Viewer|x = 22, y = 21, rule = B3/S23
7bo$8bo2bo$8bobob2o$4b2o5b2ob2o$4b2o5b2ob2o$8bobob2o4bo$bo6bo2bo5bobo
$2bo4bo9bobo$3o16bo$19b2o$18bobo$2o4b2o3b2o$obo2bobo3bo3bo3b3o$2bo2bo
6b4o3bobo$2b2ob2o11bobo$5bo2bo3b4o4b2o$5bob2o3bo2bo$b2ob2obo12bo$b2ob
o2bo10bobo$5b2o11bobo$19bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 540 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 23
| 6 803
| {{LV:Viewer|x = 22, y = 23, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo4bo$11b2o4bobo$bo5b4obo6b2o$
ob4o3b3o7bo$4bo5bobo5bobo$16bo3bo$14b2o5bo$15b2o2bobo$2o16bo2bo$obo$2b
o16b3o$bo18b2o$b2o4b2o4b2o4bo$7bo3bo2bo5b2o$10bo7bobo$b2o6b3obo5bo$2b
o2b2o3b2o$bo11bo$o3bo2b2ob3o$2o5b4o2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 520 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 24
| 6 998
| {{LV:Viewer|x = 24, y = 24, rule = B3/S23
3b3ob2o$5b2o2b2o$2o4bo4bo$2o4bo4bo$5b2o2b2o9bo$3b3ob2o6b2o2bobo$14b3o
4b2o$21bo$17bo2bobo$18bo3bo$16b2o5bo$21bobo$2o18bo2bo$obo$2bo18b3o$bo
20b2o$b2o4b2o4b2o6bo$7bo3bo2bo7b2o$10bo9bobo$b2o6b3obo7bo$2bo2b2o3b2o
$bo11bo$o3bo2b2ob3o$2o5b4o2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 530 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 25
| 7 483
| {{LV:Viewer|x = 25, y = 25, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo7bo$11b2o7bobo$bo5b4obo7bobo
$ob4o3b3o10bo$4bo5bobo9b2o$21bobo2$22b3o$obo19bobo$2o3bo15bobo$5o18b2o
$obobob2o$3bob2o16bo$o2b2o8bo7bobo$bo4bo6b3o5bobo$b2ob2o10bo5bo$obob2o
bo5b3obo$o2bo9bo3bo$3b3obo6b3o$o4b2o4b3o$3obobo3bo3b2obo$bo2bobo3b2o2b
ob2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 540 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 26
| 10 320
| {{LV:Viewer|x = 26, y = 26, rule = B3/S23
11bo2b2o$11b2o3bobo$9b2o4bo2bo$9bo5bo2bo$2bob2o3bob2o3bobo3bo$o4bo5bo
2b2o5bobo$obo6bo13b2o$5o18bo$2o3b2o15bobo$2o2bo19bo$4bo20bo$o3bo18bob
o$obobo17bo2bo$obo2b2o10bobo$bobobo11bobo3b3o$bobob2o8bob2o5b2o$bo14b
o2b2o2bo$13bob2o2bo4b2o$5b2o4bo6b2o2bobo$5b2o2b2o3bo4bo3bo$7bo3b2ob2o
2bo$7b2obo3b2o2b2o$9b3o7bo$9bo2bo2bo3bo$6b2ob2ob4o2bo$6b2obo2bo4b4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 560 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 27
| 10 420
| {{LV:Viewer|x = 27, y = 26, rule = B3/S23
10bo2b2o$10b2o3bobo$8b2o4bo2bo$3bo4bo5bo2bo$o2b2o3bob2o3bobo5bo$2bo7b
o2b2o7bobo$o7bo15b2o$obobo19bo$obobo18bobo$3bo21bo$2obobo20bo$bob2o19b
obo$23bo2bo$18bobo$2b4o12bobo3b3o$4bo11bob2o5b2o$17bo2b2o2bo$14bob2o2b
o4b2o$6b2o4bo6b2o2bobo$6b2o2b2o3bo4bo3bo$8bo3b2ob2o2bo$8b2obo3b2o2b2o
$10b3o7bo$10bo2bo2bo3bo$7b2ob2ob4o2bo$7b2obo2bo4b4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 560 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 28
| 16 560
| {{LV:Viewer|x = 28, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o10bo$o13b5o$11bob
o5bo$12bob2o2bo$16b2o$3o3bo4bo11b2o$o3b3o3b2obo7bobobobo$bo2b4o3bo2bo
9bo2bo$obo2b3o3bo2bo6bobobobo$5o7b2o9bo3bo$ob2obo18b2obo$22bobo$22b2o
bobo$18bobo2bo$b2o4b2o9b2o3bo$bobo2bobo11b3o2bo$3bo2bo15bo$3b2ob2o4b2o
$6bo2bo2b2o$6bob2o8b2o2b2o$2b2ob2obo10bo3bo2b2o$2b2obo2bo5b2o2bo3bo3b
2o$6b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 620 HEIGHT 620 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 29
| 16 570
| {{LV:Viewer|x = 29, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o11bo$o14b5o$12bobo
5bo$13bob2o2bo$17b2o$b3o3bo4bo11b2o$bo3b3o3b2obo7bobobobo$2bo2b4o3bo2b
o9bo2bo$bobo2b3o3bo2bo6bobobobo$b5o7b2o9bo3bo$bob2obo18b2obo$23bobo$
23b2obobo$19bobo2bo$2b2o4b2o9b2o3bo$2bobo2bobo11b3o2bo$4bo2bo15bo$4b2o
b2o4b2o$7bo2bo2b2o$7bob2o8b2o2b2o$3b2ob2obo10bo3bo2b2o$3b2obo2bo5b2o2b
o3bo3b2o$7b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 640 HEIGHT 640 ZOOM 20 ]]
}}
|
|-
| 30
| 16 660
| {{LV:Viewer|x = 30, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o10bo$o13b5o$11bobo
5bo$12bob2o2bo$16b2o$3o3bo4bo13b2o$o3b3o3b2obo9bobobobo$bo2b4o3bo2bo
11bo2bo$obo2b3o3bo2bo8bobobobo$5o7b2o11bo3bo$ob2obo20b2obo$24bobo$24b
2obobo$20bobo2bo$b2o4b2o11b2o3bo$bobo2bobo13b3o2bo$3bo2bo17bo$3b2ob2o
4b2o$6bo2bo2b2o$6bob2o8b2o2b2o$2b2ob2obo10bo3bo2b2o$2b2obo2bo5b2o2bo3b
o3b2o$6b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 640 HEIGHT 640 ZOOM 20 ]]
}}
|
|-
| 31
| 31 013
| {{LV:Viewer|x = 31, y = 31, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo$11b2o$bo5b4obo2bobo2b3o$ob4o
3b3o3bobob2o2bo$4bo5bobo3bo2b2obo$21bo3bo$15bo9b2obo$5b2o8b3o8bo2bo$b
2obo2bo7bo2bo6b2o3bo$b2ob2obo8b2o7b2o3bo$5bob2o7b2o8b2ob2o$5bo2bo3b2o
$2b2ob2o5b2o8bob5o$2bo2bo10b2o5b4o$obo2bobo7bobo8bo$2o4b2o3bo3b2o4bob
2obobo$10bobo9b2obo$11bo9b2obobobo3$2b3o6b2o4bo2bo2bobo2bo$11bobo2bob
o2bobob3o$obo3b2o5bo3bo2b3o5b2o$b3o9b2o3b2obo3b2o$2bo3bo10bo2b2ob3ob3o
$2o3b2obo9bo2bobo4b2o$obo2bo6b2ob2obob6ob4o$o2b2ob2o4b2ob4obo2b3o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 680 HEIGHT 660 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 32
|rowspan=5| 1 120 271
|rowspan=5| {{LV:Viewer|x = 32, y = 32, rule = B3/S23
obo2bob2obo9bo$2o3b2ob2obo6b3o8b2o$bo9bo5bo11bo$11b2o5bo6b2o4bo$3bo2b
2o4bo4b2o5bobo3b2o$2bo2bobo3bo9bo2bo$5obo5b3o6b3obo$2bo2bo3b3o2bo9bo4b
2o$3bo4bo2bo7b3obo4bobo$9b2o7bo2b2o5bo$2ob3o7b2o4bo6b2obo$2o2bo2bo4bob
o3b2ob2o4bobo$o6bo3bobo5bobo5bob2o$2o2bo2bobo2bo6bobo4b2obo$2bo4bo5b3o
2b2ob2o3bo2bo$3bo2bobo6bo3bobo5bob2o$5bo12bo2bo6bo$2bob3o3bo8b2o8bobo$
4bo5bo19b2o$3bo3bo2b2o$12bo10bo$12b3o7bobob2o2b2o$18bo3bobobo3b2o$16bo
6b2o2bo$12bo4b4o4b2obo$14bobo8bo2bo$14b2o5bo4b2o$2o2bo8b2o3bob2o6b3o$o
bobo7bo3bo4bobo4bo2bo$obo11bo2bo8b2o2bo$b2obo13bob2o3bo2b2o$3b2o13b4o
3b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 20 ]]
}}
|rowspan=5| <ref name="post167008"/>
|-
| 33
|-
| ...
|-
| 47
|-
| 48
|-
| 49
|rowspan=4| 149 794 021 404 732
|rowspan=4| {{LV:Viewer|x = 49, y = 49, rule = B3/S23
b2ob2o10bo2b3o12b3o10b2o$bo3bo8bo2b3o4b2o2b2obo2bo2bo7b2obo$bobo4b2o5b
o7b3o7b2ob2o8bobo$8b2o11b2o2b2o2b2o16bo$20bobo2b2o4b2o14b2o$2o9b2ob2o
14b2o15bo$3o8b2obo27b2o$obo11bo8b2o4bo6b2obobobo$obo3b2o3b2ob2o6bobo
10bobob2o$2o4bobo2b2obo6bobo11bo11b2o$3o4bo7b3o3b2o4b2o4bobo12bo$b2o
15bo8b2o4b2o11bo$17bobo18b2o6b2o$4b2ob2o9bo4b2o5b2o6bobo6bo$obo2bobo4b
2o9b2o5b2o3b2obobo5bo$2o3bobo4bo2b2o19bo2bo6b2o$bo4bo6b2obo19bo$9b2o
16b2o2bob2obobo$8bobo11b2o3bo3b2obo2bobo3b2ob2o$3bo5bo3b2o7bo5b3o3bo3b
o4b2obo$12bobo8bo7bobo14bo$2ob3o7bo8b2o2bo3bo3b3o4bo5b2o$2o2bo2bo8b2o
5bobobo3b3o2bo4b3o2bo$o6bo8b2o5bo2bobo4bo10bo2b2o$2o2bo2bobo14bobobo9b
o4bo4bo$2bo4bo5b2o10bo3b2o5b3o5b4o$3bo2bobo4b2o15bo4bo$5bo17bo5bo5b2o
9b2o$2bob3o3bo11bobo3bo17bo$4bo5bo5b2o5b2o3b2o9b2ob2o3bo$3bo3bo2b2o4b
2o21b2obo5bo$12bo31bo2b2o$12b3o10bo7bo9b2o$18bo5bobo5b3o$16bo6bobo6b3o
5b2o$12bo4b4o3bo16bo2bo$14bobo13b2o3b2o4bobobo$14b2o5bo8b2o3b2o2b2obob
obo$13b2o3bob2o18bobo2bo$12bo3bo4bobo16bo2b2o$14bo2bo21b2o$18bob2o4bo$
18b4o3bobo3b2o$2o2bo20bobo4bo$obobo21bob2o2b2ob2o$obo24bo2bob2obo$b2ob
o16b3o5bob2o3b3o$3b2o17b3o5b3o5bo$32b3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 12 ]]
}}
|rowspan=4| <ref name="post200534"/>
|-
| 50
|-
| 51
|-
| 52
|-
| 53
|rowspan=5| 2 738 059 586 423 623 206
|rowspan=5| {{LV:Viewer|x = 53, y = 53, rule = B3/S23
4b6o2b4ob4ob2o25bob2o$6bo7b4obobo2bo10b3o12b3o$10bo6bobo2bo5bo5bo2bo
14bo$5b5o6bo3bobo4bob2obo4bo11b2obo$7b2o21bobo15bob3o$4bob2o24bobo16b
2o$7bo4b2o8bo24b3ob2o$15bobobo2b3o12b2o9bo$12b2obobobo5bo12bo8bo3bo$
22b2obo9b3o10bo$bo10bob3obo3bobo3b2o4bo$obo10bo2b2o10b2o4b4o$bobo9bo2b
2ob2o16bo$bo2bo3bo4bobo2bo5b2o6b3o$b2o5bo5bobobobo3b2o6bo2bo$bo5bo6bo
2bob2o12b2o$6bo14b2o14bo8b2obo$11b2obobob2obo14bobo6bo5b2o$17bo3b2o6bo
5bobo8b2ob2obo$13b2o2bo4b2o4bobo5bo8b3obob2o$16b3o3bob2o3bo16bo4b2o$
15b2o5bob2o18bobo2bo2bo$ob3o12b2o25b2obobo$ob4o11b2o27bo2bob2o$o5bo32b
o6bo2bo2bo$bobobo2b3o3b2o13bo7b3o11b2o$2bobob4o4b2o12bo2bo4bo7b2obo4bo
$3bo2bob2o18bo2bo4b2o10b2ob2o$3bo3b3obo9bobobo4bo21bo$4b3o2b2obo4b2o2b
obo2bo6b3o7b2obo3bo$10bobo4b2o4bobo7b3o7bob2o$11bob2o6bo19bobo$12bo2bo
5bobo3b2o11bobo2b2o$13b2o6bo4bobo12bo4bo$14b5o3bo3bo4b2o3b2o7bo$15b4o
6b2o5b5o8b2o$15bobo15b3o4bob2obo$14bob2obo14bo5b2obo2bo$14bo3bobo22bob
2o$14bo2bo2b2o18b2obobo4bobo$15b2obob2o18bobo2bo5bo$17bo2b2o4b2o2bo10b
o3b2o3bobo$18bo10b2o20b2o$19b3o4bo2bo19bo2bo$obo2b2o3bo13b3o2bo21b2o$b
2o2bo4b2obo12bo2bo3b2o12b3o2bo$2bo2bob2o3b2o10bob2ob2o2b2o17bo$o5bo4bo
bo8b4obo21bo$b3obo5bob2o4bo2bo4b4o$bob2obo3bo3bo2bo3bo4bo2bo3bo$2o2bo
3b2o3bo5bo5bo4b3o$4b2o2bob2o6bo2b3o5b2o2bo$5b2o2b5o2b5obo2b7o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 12 ]]
}}
|rowspan=5| <ref name="post169209"/>
|-
| 54
|-
| ...
|-
| 58
|-
| 59
|-
| 60
| 2.7324 × 10{{sup|27284}}
| {{LV:Viewer|x = 60, y = 60, rule = B3/S23
11b6o2b4ob4ob2o25bob2o$13bo7b4obobo2bo10b3o12b3o$17bo6bobo2bo5bo5bo2bo
14bo$12b5o6bo3bobo4bob2obo4bo11b2obo$14b2o21bobo15bob3o$11bob2o24bobo
16b2o$5bo8bo14bo24b3ob2o$5b3o21b3o12b2o9bo$8bo23bo12bo8bo3bo$7b2o3bo
16b2obo9b3o10bo$12bobo14bobo3b2o4bo$11bobo21b2o4b4o$6bobo4bo30bo$7b2o
22b2o6b3o$7bo23b2o6bo2bo$15b2o3b2o2b2o14b2o$15b2o2bo2bo2bo18bo8b2obo$
3b2ob2o11bob2obo18bobo6bo5b2o$3b3o2bo3bo7bo3b2o10bo5bobo8b2ob2obo$2bo
4b2o2bobob2obobob2o6b2o3bobo5bo8b3obob2o$b3ob3o3bobobob2ob2obo6bobo3bo
16bo4b2o$b2obob2o4bo18b2o18bobo2bo2bo$bo49b2obobo$bo2b3obo44bo2bob2o$b
ob2o41bo6bo2bo2bo$21b2o13bo7b3o11b2o$4bo16b2o12bo2bo4bo7b2obo4bo$3bo
31bo2bo4b2o10b2ob2o$31b2o4bo21bo$2ob3o18b2o4bobo17b2obo3bo$2o2bo2bo16b
2o4b2o18bob2o$o6bo6b2o32bobo$2o2bo2bobo5bo11b2o5b2o11bobo2b2o$2bo4bo7b
obo8bobo4bobo12bo4bo$3bo2bobo7b2o3bo4b2o5bo4b2o3b2o7bo$5bo14bobo9b2o4b
2o3b2o7b2o$2bob3o3bo10bo25bob2obo$4bo5bo7bo10b2o9b3o4b2obo2bo$3bo3bo2b
2o5bobo8bobo9b3o7bob2o$12bo5bo4b2o3bo12bo5b2obobo4bobo$12b3o8b2o2b2o4b
2o12bobo2bo5bo$18bo14bo14bo3b2o3bobo$16bo18bo22b2o$12bo4b4o7b2o4b2o20b
o2bo$14bobo11b2o3bo24b2o$14b2o5bo4b2o6bobobob2o12b3o2bo$13b2o3bob2o4b
2o3bo3b2obobo3bo14bo$12bo3bo4bobo7bo5b3o2bo13bo$14bo2bo11b3o5bo2b4o$
18bob2o2b2obo3bobobob2ob2obo$18b4o5bo6b2o3bo$24b3o2b4ob2o3b3obo$24b2o
3b2o7bo3bo$18b2o4bobo2bobo3b2o3bob2o$22b2o9b2ob2o2bo3bo$18b3o4b2obobob
3o2bo2b2o2bo$16bob4ob3o4b2o4bob2obo$14b2o4bo2b2o2b3o2bo3b2o2bo2bo$15bo
2b2ob3obo3bobob3o2b2ob2o$18b2obob3ob8obob2obobo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 780 HEIGHT 780 ZOOM 12 ]]
}}
| <ref name="post169196"/>
|}

== References ==
<references>
<ref name="post164797">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 164797
|author = Pyry Virtanen
|date = August 9, 2023
}}</ref>
<ref name="post167008">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 167008
|author = Tim Coe
|date = September 14, 2023
}}</ref>
<ref name="post168226">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 168226
|author = Dean Hickerson
|date = October 1, 2023
}}</ref>
<ref name="post168418">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 168418
|author = b3s23love
|date = October 3, 2023
}}</ref>
<ref name="post169048">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 169048
|author = Pyry Virtanen
|date = October 13, 2023
}}</ref>
<ref name="post169196">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 169196
|author = Tim Coe
|date = October 16, 2023
}}</ref>
<ref name="post169209">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 169209
|author = b3s23love
|date = October 16, 2023
}}</ref>
<ref name="post200534">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 200534
|author = moebius
|date = December 28, 2024
}}</ref>
</references>

User:Galoomba/Longest diehards by bounding box

2025-01-07T15:52:57Z

C7X: Whoops, b3s23love's reduction wasn't exactly equivalent. Sorry

This table lists the longest-lasting known [[diehard]]s fitting in a n×n bounding box.

{| class="sortable wikitable"
|-
! n
! Lifetime
! Pattern
! Link
|-
| 1
|rowspan=2| 1
|rowspan=2| {{LV:Viewer|x = 1, y = 1, rule = B3/S23
o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 ZOOM 64 ]]}}
|rowspan=2|
|-
| 2
|-
| 3
| 9
| {{LV:Viewer|x = 3, y = 3, rule = B3/S23
obo$3o$o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 4
| 88
| {{LV:Viewer|x = 4, y = 4, rule = B3/S23
4o$bobo$2obo$4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 400 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 5
| 259
| {{LV:Viewer|x = 5, y = 5, rule = B3/S23
2o2bo$o2b2o$2o2bo$2bo$b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 6
|rowspan=2| 798
|rowspan=2| {{LV:Viewer|x = 6, y = 6, rule = B3/S23
o2b3o$5bo$obobo$2bob2o$2obo$3ob2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 60 ]]
}}
|rowspan=2| <ref name="post168418"/>
|-
| 7
|-
| 8
| 1 002
| {{LV:Viewer|x = 8, y = 7, rule = B3/S23
6bo$o5bo$4ob2o$bo4bo$2b2obobo$2o4bo$3ob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 52 ]]
}}
| <ref name="post164797"/>
|-
| 9
| 1 069
| {{LV:Viewer|x = 9, y = 8, rule = B3/S23
o2bobob2o$ob2o$o2bobob2o$5bo2bo$6bo$2b2o2bo$2b4ob2o$4b3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 48 ]]
}}
| <ref name="post164797"/>
|-
| 10
| 1 118
| {{LV:Viewer|x = 10, y = 9, rule = B3/S23
o$o$o4bo$4bobo$3bob2o$4obo3bo$5bo3bo$2o6b2o$bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 48 ]]
}}
| <ref name="post169048"/>
|-
| 11
| 1 119
| {{LV:Viewer|x = 11, y = 8, rule = B3/S23
3o$5b2o$7bo$o5bo$bob4o3bo$2bobo5bo$b2o2bo3b2o$2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 44 ]]
}}
| <ref name="post164797"/>
|-
| 12
|rowspan=4| 1 143
|rowspan=4| {{LV:Viewer|x = 12, y = 9, rule = B3/S23
5bobo$2bo3b4o$2obo5bobo$2bo3bo3b2o$obob2o2bo2bo$b3o4bo$2o4b2o2bo$3b3o$
5bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 40 ]]
}}
|rowspan=4| <ref name="post169048"/>
|-
| 13
|-
| 14
|-
| 15
|-
| 16
|rowspan=2| 1 456
|rowspan=2| {{LV:Viewer|x = 16, y = 16, rule = B3/S23
4o2bo5bo$3b3o5b2o$8b2o4bo$o2b3o2bo3bo2bo$2o2bo6b3o$o3bobo6bo$bo2b2o9b
o$b2ob2o3bobo3bo$3obo4b3o3bo$8b2o3b2o$12bob2o$10b4o$2b2o4bobob4o$2bo6b
o3b3o$3bo3b2obo3bo$2b2o4b3ob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 28 ]]
}}
|rowspan=2| <ref name="post168226"/>
|-
| 17
|-
| 18
| 2 094
| {{LV:Viewer|x = 18, y = 18, rule = B3/S23
2bo4bobo$2b2o2bob2o$3o2bo2bo5bo$2b2o3bo5bobo$2o2b3ob3o4b2o$bob2o2bobo
5bo$bobo5bo4bobo$2ob3o2bo7bo$8b2o7bo$9bo5bobo$15bobo$13b4o$8b2o2bobo$
5bo2bo3bobo$4bobobo6bo$3bobobo6b2o$2bo2bobobo3bobo$3b2o3b2o4bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 19
| 2 272
| {{LV:Viewer|x = 19, y = 19, rule = B3/S23
o4b2o7bobobo$o5bo9b2o$b2o2bo8b2obo$2bo2b2o$14bo$o2bo10b2obo$o8bobo2bo
b2o$4o5b2o5bo$2o8bo4bobo$16bo$2bob2o4b2o5bo$2bobobo2bobo3bobo$6bo2bo4b
o$5b2ob2o4bobo$3bo2bo$3b2obo8bobo$4bob2ob2o4bo$4bo2bob2o4bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 20
| 2 287
| {{LV:Viewer|x = 20, y = 19, rule = B3/S23
o4b2o8bobobo$o5bo10b2o$b2o2bo9b2obo$2bo2b2o$15bo$o2bo6bo4b2obo$o9bobo
2bob2o$4o6b2o5bo$2o14bobo$17bo$2bob2o4b2o6bo$2bobobo2bobo4bobo$6bo2bo
5bo$5b2ob2o5bobo$3bo2bo$3b2obo9bobo$4bob2ob2o5bo$4bo2bob2o5bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
|
|-
| 21
| 2 308
| {{LV:Viewer|x = 21, y = 19, rule = B3/S23
o4b2o9bobobo$o5bo11b2o$b2o2bo10b2obo$2bo2b2o$11bobo2bo$o2bo7b2o3b2obo$
o11bo3bob2o$4o14bo$2o15bobo$18bo$2bob2o4b2o7bo$2bobobo2bobo5bobo$6bo2b
o6bo$5b2ob2o6bobo$3bo2bo$3b2obo10bobo$4bob2ob2o6bo$4bo2bob2o6bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
|
|-
| 22
| 6 579
| {{LV:Viewer|x = 22, y = 21, rule = B3/S23
7bo$8bo2bo$8bobob2o$4b2o5b2ob2o$4b2o5b2ob2o$8bobob2o4bo$bo6bo2bo5bobo
$2bo4bo9bobo$3o16bo$19b2o$18bobo$2o4b2o3b2o$obo2bobo3bo3bo3b3o$2bo2bo
6b4o3bobo$2b2ob2o11bobo$5bo2bo3b4o4b2o$5bob2o3bo2bo$b2ob2obo12bo$b2ob
o2bo10bobo$5b2o11bobo$19bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 540 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 23
| 6 803
| {{LV:Viewer|x = 22, y = 23, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo4bo$11b2o4bobo$bo5b4obo6b2o$
ob4o3b3o7bo$4bo5bobo5bobo$16bo3bo$14b2o5bo$15b2o2bobo$2o16bo2bo$obo$2b
o16b3o$bo18b2o$b2o4b2o4b2o4bo$7bo3bo2bo5b2o$10bo7bobo$b2o6b3obo5bo$2b
o2b2o3b2o$bo11bo$o3bo2b2ob3o$2o5b4o2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 520 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 24
| 6 998
| {{LV:Viewer|x = 24, y = 24, rule = B3/S23
3b3ob2o$5b2o2b2o$2o4bo4bo$2o4bo4bo$5b2o2b2o9bo$3b3ob2o6b2o2bobo$14b3o
4b2o$21bo$17bo2bobo$18bo3bo$16b2o5bo$21bobo$2o18bo2bo$obo$2bo18b3o$bo
20b2o$b2o4b2o4b2o6bo$7bo3bo2bo7b2o$10bo9bobo$b2o6b3obo7bo$2bo2b2o3b2o
$bo11bo$o3bo2b2ob3o$2o5b4o2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 530 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 25
| 7 483
| {{LV:Viewer|x = 25, y = 25, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo7bo$11b2o7bobo$bo5b4obo7bobo
$ob4o3b3o10bo$4bo5bobo9b2o$21bobo2$22b3o$obo19bobo$2o3bo15bobo$5o18b2o
$obobob2o$3bob2o16bo$o2b2o8bo7bobo$bo4bo6b3o5bobo$b2ob2o10bo5bo$obob2o
bo5b3obo$o2bo9bo3bo$3b3obo6b3o$o4b2o4b3o$3obobo3bo3b2obo$bo2bobo3b2o2b
ob2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 540 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 26
| 10 320
| {{LV:Viewer|x = 26, y = 26, rule = B3/S23
11bo2b2o$11b2o3bobo$9b2o4bo2bo$9bo5bo2bo$2bob2o3bob2o3bobo3bo$o4bo5bo
2b2o5bobo$obo6bo13b2o$5o18bo$2o3b2o15bobo$2o2bo19bo$4bo20bo$o3bo18bob
o$obobo17bo2bo$obo2b2o10bobo$bobobo11bobo3b3o$bobob2o8bob2o5b2o$bo14b
o2b2o2bo$13bob2o2bo4b2o$5b2o4bo6b2o2bobo$5b2o2b2o3bo4bo3bo$7bo3b2ob2o
2bo$7b2obo3b2o2b2o$9b3o7bo$9bo2bo2bo3bo$6b2ob2ob4o2bo$6b2obo2bo4b4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 560 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 27
| 10 420
| {{LV:Viewer|x = 27, y = 26, rule = B3/S23
10bo2b2o$10b2o3bobo$8b2o4bo2bo$3bo4bo5bo2bo$o2b2o3bob2o3bobo5bo$2bo7b
o2b2o7bobo$o7bo15b2o$obobo19bo$obobo18bobo$3bo21bo$2obobo20bo$bob2o19b
obo$23bo2bo$18bobo$2b4o12bobo3b3o$4bo11bob2o5b2o$17bo2b2o2bo$14bob2o2b
o4b2o$6b2o4bo6b2o2bobo$6b2o2b2o3bo4bo3bo$8bo3b2ob2o2bo$8b2obo3b2o2b2o
$10b3o7bo$10bo2bo2bo3bo$7b2ob2ob4o2bo$7b2obo2bo4b4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 560 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 28
| 16 560
| {{LV:Viewer|x = 28, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o10bo$o13b5o$11bob
o5bo$12bob2o2bo$16b2o$3o3bo4bo11b2o$o3b3o3b2obo7bobobobo$bo2b4o3bo2bo
9bo2bo$obo2b3o3bo2bo6bobobobo$5o7b2o9bo3bo$ob2obo18b2obo$22bobo$22b2o
bobo$18bobo2bo$b2o4b2o9b2o3bo$bobo2bobo11b3o2bo$3bo2bo15bo$3b2ob2o4b2o
$6bo2bo2b2o$6bob2o8b2o2b2o$2b2ob2obo10bo3bo2b2o$2b2obo2bo5b2o2bo3bo3b
2o$6b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 620 HEIGHT 620 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 29
| 16 570
| {{LV:Viewer|x = 29, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o11bo$o14b5o$12bobo
5bo$13bob2o2bo$17b2o$b3o3bo4bo11b2o$bo3b3o3b2obo7bobobobo$2bo2b4o3bo2b
o9bo2bo$bobo2b3o3bo2bo6bobobobo$b5o7b2o9bo3bo$bob2obo18b2obo$23bobo$
23b2obobo$19bobo2bo$2b2o4b2o9b2o3bo$2bobo2bobo11b3o2bo$4bo2bo15bo$4b2o
b2o4b2o$7bo2bo2b2o$7bob2o8b2o2b2o$3b2ob2obo10bo3bo2b2o$3b2obo2bo5b2o2b
o3bo3b2o$7b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 640 HEIGHT 640 ZOOM 20 ]]
}}
|
|-
| 30
| 16 660
| {{LV:Viewer|x = 30, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o10bo$o13b5o$11bobo
5bo$12bob2o2bo$16b2o$3o3bo4bo13b2o$o3b3o3b2obo9bobobobo$bo2b4o3bo2bo
11bo2bo$obo2b3o3bo2bo8bobobobo$5o7b2o11bo3bo$ob2obo20b2obo$24bobo$24b
2obobo$20bobo2bo$b2o4b2o11b2o3bo$bobo2bobo13b3o2bo$3bo2bo17bo$3b2ob2o
4b2o$6bo2bo2b2o$6bob2o8b2o2b2o$2b2ob2obo10bo3bo2b2o$2b2obo2bo5b2o2bo3b
o3b2o$6b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 640 HEIGHT 640 ZOOM 20 ]]
}}
|
|-
| 31
| 31 013
| {{LV:Viewer|x = 31, y = 31, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo$11b2o$bo5b4obo2bobo2b3o$ob4o
3b3o3bobob2o2bo$4bo5bobo3bo2b2obo$21bo3bo$15bo9b2obo$5b2o8b3o8bo2bo$b
2obo2bo7bo2bo6b2o3bo$b2ob2obo8b2o7b2o3bo$5bob2o7b2o8b2ob2o$5bo2bo3b2o
$2b2ob2o5b2o8bob5o$2bo2bo10b2o5b4o$obo2bobo7bobo8bo$2o4b2o3bo3b2o4bob
2obobo$10bobo9b2obo$11bo9b2obobobo3$2b3o6b2o4bo2bo2bobo2bo$11bobo2bob
o2bobob3o$obo3b2o5bo3bo2b3o5b2o$b3o9b2o3b2obo3b2o$2bo3bo10bo2b2ob3ob3o
$2o3b2obo9bo2bobo4b2o$obo2bo6b2ob2obob6ob4o$o2b2ob2o4b2ob4obo2b3o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 680 HEIGHT 660 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 32
|rowspan=5| 1 120 271
|rowspan=5| {{LV:Viewer|x = 32, y = 32, rule = B3/S23
obo2bob2obo9bo$2o3b2ob2obo6b3o8b2o$bo9bo5bo11bo$11b2o5bo6b2o4bo$3bo2b
2o4bo4b2o5bobo3b2o$2bo2bobo3bo9bo2bo$5obo5b3o6b3obo$2bo2bo3b3o2bo9bo4b
2o$3bo4bo2bo7b3obo4bobo$9b2o7bo2b2o5bo$2ob3o7b2o4bo6b2obo$2o2bo2bo4bob
o3b2ob2o4bobo$o6bo3bobo5bobo5bob2o$2o2bo2bobo2bo6bobo4b2obo$2bo4bo5b3o
2b2ob2o3bo2bo$3bo2bobo6bo3bobo5bob2o$5bo12bo2bo6bo$2bob3o3bo8b2o8bobo$
4bo5bo19b2o$3bo3bo2b2o$12bo10bo$12b3o7bobob2o2b2o$18bo3bobobo3b2o$16bo
6b2o2bo$12bo4b4o4b2obo$14bobo8bo2bo$14b2o5bo4b2o$2o2bo8b2o3bob2o6b3o$o
bobo7bo3bo4bobo4bo2bo$obo11bo2bo8b2o2bo$b2obo13bob2o3bo2b2o$3b2o13b4o
3b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 20 ]]
}}
|rowspan=5| <ref name="post167008"/>
|-
| 33
|-
| ...
|-
| 47
|-
| 48
|-
| 49
|rowspan=4| 1 237 975 907 532
|rowspan=4| {{LV:Viewer|x = 49, y = 49, rule = B3/S23
19b2o$b2ob2o12bobo2bo10b3o10b2o$bo3bo11bo2bobobo3b2obo2bo2bo7b2obo$bob
o4b2o7bobobo2bo8b2ob2o8bobo$8b2o8bo2bobo5b2o16bo$14b2o5b2o8b2o14b2o$2o
9bo2bo15b2o15bo$3o7bobobo27b2o$obo3b2o2bobo2b2o6b2o4bo6b2obobobo$obo3b
obobo2b2o2bo4bobo10bobob2o$2o7b2o4b2o4bobo11bo11b2o$3o8b4o6b2o4b2o4bob
o12bo$b2o8bo2bo12b2o4b2o11bo$38b2o6b2o$4b2ob2o14b2o5b2o6bobo6bo$obo2bo
bo4b2o9b2o5b2o3b2obobo5bo$2o3bobo4bo2b2o19bo2bo6b2o$bo4bo6b2obo19bo$9b
2o16b2o2bob2obobo$8bobo11b2o3bo3b2obo2bobo3b2ob2o$3bo5bo3b2o7bo5b3o3bo
3bo4b2obo$12bobo8bo7bobo14bo$2ob3o7bo8b2o2bo3bo3b3o4bo5b2o$2o2bo2bo8b
2o5bobobo3b3o2bo4b3o2bo$o6bo8b2o5bo2bobo4bo10bo2b2o$2o2bo2bobo14bobobo
9bo4bo4bo$2bo4bo5b2o10bo3b2o5b3o5b4o$3bo2bobo4b2o15bo4bo$5bo17bo5bo5b
2o9b2o$2bob3o3bo11bobo3bo17bo$4bo5bo5b2o5b2o3b2o9b2ob2o3bo$3bo3bo2b2o
4b2o21b2obo5bo$12bo31bo2b2o$12b3o10bo7bo9b2o$18bo5bobo5b3o$16bo6bobo6b
3o5b2o$12bo4b4o3bo16bo2bo$14bobo13b2o3b2o4bobobo$14b2o5bo8b2o3b2o2b2ob
obobo$13b2o3bob2o18bobo2bo$12bo3bo4bobo2bo13bo2b2o$14bo2bo7bobo11b2o$
18bob2o4bo$18b4o$2o2bo$obobo30b2o$obo19b3o10bo$b2obo18b3o10b3o$3b2o33b
o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 12 ]]
}}
|rowspan=4| <ref name="post200083"/>
|-
| 50
|-
| 51
|-
| 52
|-
| 53
|rowspan=5| 2 738 059 586 423 623 206
|rowspan=5| {{LV:Viewer|x = 53, y = 53, rule = B3/S23
4b6o2b4ob4ob2o25bob2o$6bo7b4obobo2bo10b3o12b3o$10bo6bobo2bo5bo5bo2bo
14bo$5b5o6bo3bobo4bob2obo4bo11b2obo$7b2o21bobo15bob3o$4bob2o24bobo16b
2o$7bo4b2o8bo24b3ob2o$15bobobo2b3o12b2o9bo$12b2obobobo5bo12bo8bo3bo$
22b2obo9b3o10bo$bo10bob3obo3bobo3b2o4bo$obo10bo2b2o10b2o4b4o$bobo9bo2b
2ob2o16bo$bo2bo3bo4bobo2bo5b2o6b3o$b2o5bo5bobobobo3b2o6bo2bo$bo5bo6bo
2bob2o12b2o$6bo14b2o14bo8b2obo$11b2obobob2obo14bobo6bo5b2o$17bo3b2o6bo
5bobo8b2ob2obo$13b2o2bo4b2o4bobo5bo8b3obob2o$16b3o3bob2o3bo16bo4b2o$
15b2o5bob2o18bobo2bo2bo$ob3o12b2o25b2obobo$ob4o11b2o27bo2bob2o$o5bo32b
o6bo2bo2bo$bobobo2b3o3b2o13bo7b3o11b2o$2bobob4o4b2o12bo2bo4bo7b2obo4bo
$3bo2bob2o18bo2bo4b2o10b2ob2o$3bo3b3obo9bobobo4bo21bo$4b3o2b2obo4b2o2b
obo2bo6b3o7b2obo3bo$10bobo4b2o4bobo7b3o7bob2o$11bob2o6bo19bobo$12bo2bo
5bobo3b2o11bobo2b2o$13b2o6bo4bobo12bo4bo$14b5o3bo3bo4b2o3b2o7bo$15b4o
6b2o5b5o8b2o$15bobo15b3o4bob2obo$14bob2obo14bo5b2obo2bo$14bo3bobo22bob
2o$14bo2bo2b2o18b2obobo4bobo$15b2obob2o18bobo2bo5bo$17bo2b2o4b2o2bo10b
o3b2o3bobo$18bo10b2o20b2o$19b3o4bo2bo19bo2bo$obo2b2o3bo13b3o2bo21b2o$b
2o2bo4b2obo12bo2bo3b2o12b3o2bo$2bo2bob2o3b2o10bob2ob2o2b2o17bo$o5bo4bo
bo8b4obo21bo$b3obo5bob2o4bo2bo4b4o$bob2obo3bo3bo2bo3bo4bo2bo3bo$2o2bo
3b2o3bo5bo5bo4b3o$4b2o2bob2o6bo2b3o5b2o2bo$5b2o2b5o2b5obo2b7o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 12 ]]
}}
|rowspan=5| <ref name="post169209"/>
|-
| 54
|-
| ...
|-
| 58
|-
| 59
|-
| 60
| 2.7324 × 10{{sup|27284}}
| {{LV:Viewer|x = 60, y = 60, rule = B3/S23
11b6o2b4ob4ob2o25bob2o$13bo7b4obobo2bo10b3o12b3o$17bo6bobo2bo5bo5bo2bo
14bo$12b5o6bo3bobo4bob2obo4bo11b2obo$14b2o21bobo15bob3o$11bob2o24bobo
16b2o$5bo8bo14bo24b3ob2o$5b3o21b3o12b2o9bo$8bo23bo12bo8bo3bo$7b2o3bo
16b2obo9b3o10bo$12bobo14bobo3b2o4bo$11bobo21b2o4b4o$6bobo4bo30bo$7b2o
22b2o6b3o$7bo23b2o6bo2bo$15b2o3b2o2b2o14b2o$15b2o2bo2bo2bo18bo8b2obo$
3b2ob2o11bob2obo18bobo6bo5b2o$3b3o2bo3bo7bo3b2o10bo5bobo8b2ob2obo$2bo
4b2o2bobob2obobob2o6b2o3bobo5bo8b3obob2o$b3ob3o3bobobob2ob2obo6bobo3bo
16bo4b2o$b2obob2o4bo18b2o18bobo2bo2bo$bo49b2obobo$bo2b3obo44bo2bob2o$b
ob2o41bo6bo2bo2bo$21b2o13bo7b3o11b2o$4bo16b2o12bo2bo4bo7b2obo4bo$3bo
31bo2bo4b2o10b2ob2o$31b2o4bo21bo$2ob3o18b2o4bobo17b2obo3bo$2o2bo2bo16b
2o4b2o18bob2o$o6bo6b2o32bobo$2o2bo2bobo5bo11b2o5b2o11bobo2b2o$2bo4bo7b
obo8bobo4bobo12bo4bo$3bo2bobo7b2o3bo4b2o5bo4b2o3b2o7bo$5bo14bobo9b2o4b
2o3b2o7b2o$2bob3o3bo10bo25bob2obo$4bo5bo7bo10b2o9b3o4b2obo2bo$3bo3bo2b
2o5bobo8bobo9b3o7bob2o$12bo5bo4b2o3bo12bo5b2obobo4bobo$12b3o8b2o2b2o4b
2o12bobo2bo5bo$18bo14bo14bo3b2o3bobo$16bo18bo22b2o$12bo4b4o7b2o4b2o20b
o2bo$14bobo11b2o3bo24b2o$14b2o5bo4b2o6bobobob2o12b3o2bo$13b2o3bob2o4b
2o3bo3b2obobo3bo14bo$12bo3bo4bobo7bo5b3o2bo13bo$14bo2bo11b3o5bo2b4o$
18bob2o2b2obo3bobobob2ob2obo$18b4o5bo6b2o3bo$24b3o2b4ob2o3b3obo$24b2o
3b2o7bo3bo$18b2o4bobo2bobo3b2o3bob2o$22b2o9b2ob2o2bo3bo$18b3o4b2obobob
3o2bo2b2o2bo$16bob4ob3o4b2o4bob2obo$14b2o4bo2b2o2b3o2bo3b2o2bo2bo$15bo
2b2ob3obo3bobob3o2b2ob2o$18b2obob3ob8obob2obobo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 780 HEIGHT 780 ZOOM 12 ]]
}}
| <ref name="post169196"/>
|}

== References ==
<references>
<ref name="post164797">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 164797
|author = Pyry Virtanen
|date = August 9, 2023
}}</ref>
<ref name="post167008">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 167008
|author = Tim Coe
|date = September 14, 2023
}}</ref>
<ref name="post168226">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 168226
|author = Dean Hickerson
|date = October 1, 2023
}}</ref>
<ref name="post168418">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 168418
|author = b3s23love
|date = October 3, 2023
}}</ref>
<ref name="post169048">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 169048
|author = Pyry Virtanen
|date = October 13, 2023
}}</ref>
<ref name="post169196">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 169196
|author = Tim Coe
|date = October 16, 2023
}}</ref>
<ref name="post169209">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 169209
|author = b3s23love
|date = October 16, 2023
}}</ref>
<ref name="post200083">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 200083
|author = moebius
|date = December 18, 2024
}}</ref>
</references>

Engineered diehard

2025-01-07T15:49:58Z

C7X: Whoops, b3s23love's reduction wasn't exactly equivalent. Sorry

{{stub}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|pname = diehard30273
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 ZOOM 14 ]]
|position = center
|caption = 30,273-tick diehard with bounding box {{times|32|32}} by Hickerson<ref name="post143921" />
}}
|}
{{main|Die hard#"Die hard" as a general term}}
Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes. On March 1, [[Dean Hickerson]] shared a 9044-tick {{times|32|32}} diehard in a private email to [[Dave Greene]]. After a complex series of interactions between an active reaction and various still lifes, a single [[lightweight spaceship]] is produced which eventually catches up to and collides with [[30P5H2V0]], producing a single [[loaf]]. Finally, an even slower [[25P3H1V0.1]] eventually collides with the loaf, destroying both of them.<ref name="post143573" /> On March 6, more optimized versions using different combinations of spaceships (including the especially slow [[copperhead]]) were shared, including a 14,010-tick diehard at {{times|32|32}} and an 18,477-tick diehard at {{times|36|36}}.<ref name="post143574" />

Although Hickerson's results were not initially posted publicly, a forum thread was coincidentally started a few weeks later dedicated to diehards, including engineered ones.<ref name="post143559" /> On March 31, [[Pavel Grankovskiy]] posted a 50,716-tick diehard in which a [[Simkin glider gun]] and [[pulse divider|pulse-dividing]] glider reflectors are used to slowly eat through a series of [[tub]]s. Although significantly larger than Hickerson's constructions at {{times|90|86}}, Grankovskiy's 50,716-tick diehard does not use the "spaceship-chasing" technique, meaning that throughout its evolution, the pattern only slightly exceeds its initial bounds. Using spaceship-chasing, however, the pattern's lifespan can be increased by an order of magnitude to 518,476 ticks without further increasing the bounding box.<ref name="post143605" /> [[Jiahao Yu]] optimized the bounding box of both of these patterns to {{times|87|86}},<ref name="post143624" /> as shown below.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = diehard50716
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 50,716-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = diehard518476
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 518,476-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery bottom}}

==Sawtooth-based designs==
Using a [[sawtooth]] allows for the creation of extremely long-lasting diehards. On April 7, 2022, Pavel Grankovskiy successfully constructed a diehard using a sawtooth an {{c|Sawtooths with expansion factor 121|expansion factor of 121}}. The pattern fits within a bounding box of {{times|99|101}} (just barely meeting the 10,000-cell restriction specified in the original post<ref name="post143559" />) and lasts approximately {{times|2.280624|10{{sup|870}}}} generations.<ref name="post143908" /> Further optimizations, with the help of [[toroidalet]],<ref name="post143914" /> Dean Hickerson,<ref name="post143920" /> [[EvinZL]],<ref name="post143997" /> [[Rocknlol]],<ref name="post144020" /> and [[Adam P. Goucher]]<ref name="post144030" /> increased its lifespan to {{times|~1.33616|10{{sup|1443}}}} ticks<ref name="post144027" /> and decreased its bounding box to {{times|94|98}}.<ref name="post144045" />

{{EmbedViewer
|pname = diehard1e1443
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 700 ZOOM 6 ]]
|position = center
|caption = {{times|94|98}} exponential diehard by Grankovskiy et al.
|style = width:300px;
}}

On April 9, Grankovskiy posted a concept for a pattern whose lifespan is measured via [[tetration]], the next hyperoperator after exponentiation. Originally posted in the form of a methuselah,<ref name="post144034" /> the diehard version was completed on April 11.<ref name="post144077" /> With optimization by [[Tanner Jacobi]]<ref name="post144087" /> and toroidalet,<ref name="post144162" /><ref name="post149066" /> its lifespan is somewhere between 1510 and 1610 ticks.<ref>{{Cite web|url=https://btm.qva.mybluehost.me/telling-the-tale-of-two-tetrations/|author=Brett Berger|title=Telling the tale of two tetrations|work=a blog by biggiemac42|date=April 17, 2022|accessdate=April 17, 2022}}</ref>

{{EmbedViewer
|pname = diehardtetration
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|111|90}} tetrational diehard by Grankovskiy et al.
|style = width:300px;
}}

On July 9, 2023, [[EvinZL]] proposed adding loaf-making fuse to increase the lifespan of the methuselah by extending power tower length,<ref name="post163493" /> based on the original idea of [[Tanner Jacobi]].<ref name="post148684" /> In a flurry of activity that followed after, [[toroidalet]], [[Adam P. Goucher]], [[Pavel Grankovskiy]] and [[EvinZL]] pushed the number of loaves from 15<ref name="tetrational_15_loaves" /> to approximately {{times|3.52|10{{sup|48}}}}<ref name="tetrational_1e48" />, with the latter improvement based on idea by [[Adam P. Goucher]] to use gliders from exponential part of diehard to ignite the fuse.<ref name="tetrational_exp_idea" /> This was subsequently improved to {{times|1.1|10{{sup|1046}}}}<ref name="tetrational_1e1046" /><ref name="tetrational_exp_cp4space" />.

{{EmbedViewer
|pname = diehardtetration1046
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|109|91}} tetrational diehard with a lifespan exceeding (101046)10.
|style = width:300px;
}}

On December 23, 2024, [[moebius]] posted a {{times|49|49}} sawtooth-based diehard with lifetime 1237975907532, reducing the size of the sawtooth base.<ref name="post200083" />

==Double-tetrational designs==
On 15th September 2023, [[Tim Coe]] and b3s23love increased the height of the tetrational tower from {{times|1.1|10{{sup|1046}}}} to 121{{sup|{{times|8.46|10{{sup|1059}}}}}}. The following day, Tim Coe further improved this height to 121{{sup|121{{sup|121{{sup|121{{sup|498}}}}}}}}, so the height of the tetrational tower is itself a tetrational tower. This was subsequently further improved by Tim Coe, toroidalet, EvinZL, and b3s23love, culminating in a height of 121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|1356648129958673823266622201465466300}}}}}}}}}}}}}}}}}} as of the 28th September 2023. The overall lifespan of the diehard exceeds {{sup|{{sup|11}}11}}11, or 11^^^3 in Knuth's up-arrow notation. More recent designs have further improved lifespans, with the current record holder taking 17^^^3 generations to die out entirely.

{{EmbedViewer
|pname = diehardtetration17uuu3
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|116|86}} tetrational diehard with a lifespan exceeding 17↑↑↑3.
|style = width:300px;
}}

==Timetable==
In many cases, several incremental record-breaking improvements were made inside 24 hours. In the following table, the record-breaking pattern for each day is listed (with each day beginning and ending at UTC 0:00).<ref name="message1156939723001049189" />

{| class="wikitable"
! Date
! Lifespan
! Bounding box size
! Bounding box cells
! Contributor(s)
|-
!2022-02-21
|2474
|32×32
|1024
|Charity Engine
|-
!2022-03-01
|9044
|32×32
|1024
|Dean Hickerson
|-
!2022-03-06
|14010
|32×32
|1024
|Dean Hickerson
|-
!2022-03-31
|518476
|90×86
|7740
|Pavel Grankovskiy
|-
!2022-04-01
|518476
|87×86
|7482
|Jiahao Yu
|-
!2022-04-07
|2.28 × 10^870
|99×101
|9999
|Pavel Grankovskiy
|-
!2022-04-09
|1.77 × 10^1295
|94x96
|9024
|Pavel Grankovskiy, toroidalet, Rocknlol
|-
!2022-04-10
|1.476 × 10^1595
|94×99
|9306
|Pavel Grankovskiy, Dean Hickerson
|-
!2022-04-11
|11 ^^ 10
|105×95
|9975
|Pavel Grankovskiy
|-
!2022-04-13
|11 ^^ 11
|108×92
|9936
|toroidalet, Pavel Grankovskiy
|-
!2022-04-14
|11 ^^ 13
|109×91
|9919
|Pavel Grankovskiy, toroidalet, Tanner Jacobi
|-
|
|-
!2023-07-17
|121 ^^ 15
|110×90
|9900
|toroidalet, Pavgran
|-
!2023-07-18
|121 ^^ (4.98 × 10^27)
|111×90
|9990
|Pavel Grankovskiy, toroidalet, EvinZL, Adam P. Goucher
|-
!2023-07-19
|121 ^^ (5.94 × 10^54)
|109×91
|9919
|Pavel Grankovskiy, May13, toroidalet, EvinZL, Adam P. Goucher
|-
!2023-07-20
|121 ^^ (1.67 × 10^903)
|109×91
|9919
|May13, EvinZL
|-
!2023-07-23
|121 ^^ (1.10 × 10^1046)
|109×91
|9919
|Adam P. Goucher
|-
!2023-09-15
|121 ^^ (121 ^ (8.46 × 10^1059))
|108×91
|9828
|Tim Coe, b3s23love
|-
!2023-09-16
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 498)
|109×91
|9919
|Tim Coe
|-
!2023-09-19
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ (9.74 × 10^51))
|109×91
|9919
|b3s23love, toroidalet, EvinZL
|-
!2023-09-21
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 60143)
|109×91
|9919
|EvinZL, Tim Coe
|-
!2023-09-22
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 70433)
|112×89
|9968
|b3s23love, toroidalet, EvinZL
|-
!2023-09-24
|9 ^^^ 3
|112×89
|9968
|Tim Coe
|-
!2023-09-28
|11 ^^^ 3
|112×89
|9968
|toroidalet
|-
!2023-10-05
|17 ^^^ 3
|116×86
|9976
|Tim Coe, EvinZL, [https://conwaylife.com/forums/viewtopic.php?p=168589#p168589 Adam P. Goucher]
|-
!2023-10-05
|17 ^^^ 3 +
|116×86
|9976
|[https://conwaylife.com/forums/viewtopic.php?p=169264#p169264 toroidalet]
|}

==References==
<references>
<ref name="post143573">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143573
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143574">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143574
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143559">{{LinkForumThread
|format = ref
|title = (Engineered) diehards
|p = 143559
|author = squareroot12621
|date = March 30, 2022
}}</ref>
<ref name="post143605">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143605
|author = Pavel Grankovskiy
|date = March 31, 2022
}}</ref>
<ref name="post143624">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143624
|author = Jiahao Yu
|date = March 31, 2022
}}</ref>
<ref name="post143921">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143921
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143908">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143908
|author = Pavel Grankovskiy
|date = April 7, 2022
}}</ref>
<ref name="post143914">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143914
|author = toroidalet
|date = April 7, 2022
}}</ref>
<ref name="post143920">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143920
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143997">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143997
|author = EvinZL
|date = April 9, 2022
}}</ref>
<ref name="post144020">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144020
|author = Rocknlol
|date = April 10, 2022
}}</ref>
<ref name="post144030">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144030
|author = Adam P. Goucher
|date = April 10, 2022
}}</ref>
<ref name="post144027">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144027
|author = Dean Hickerson
|date = April 10, 2022
}}</ref>
<ref name="post144045">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144045
|author = toroidalet
|date = April 10, 2022
}}</ref>
<ref name="post144034">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144034
|author = Pavel Grankovskiy
|date = April 9, 2022
}}</ref>
<ref name="post144077">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144077
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144087">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144087
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144162">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144162
|author = toroidalet
|date = April 13, 2022
}}</ref>
<ref name="post149066">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 149066
|author = toroidalet
|date = August 2, 2022
}}</ref>
<ref name="post163493">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163493
|author = EvinZL
|date = July 9, 2023
}}</ref>
<ref name="post148684">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 148684
|author = Tanner Jacobi
|date = July 25, 2022
}}</ref>
<ref name="post200083">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 200083
|author = moebius
|date = December 18, 2024
}}</ref>
<ref name="tetrational_15_loaves">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163828
|author = toroidalet
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e48">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163888
|author = Adam P. Goucher
|date = July 19, 2023
}}</ref>
<ref name="tetrational_exp_idea">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163848
|author = Adam P. Goucher
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e1046">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 164085
|author = Adam P. Goucher
|date = July 23, 2023
}}</ref>
<ref name="tetrational_exp_cp4space">{{cite web|url=https://cp4space.hatsya.com/2023/07/23/miscellaneous-discoveries/|title=Miscellaneous discoveries|work=Complex Projective 4-Space|accessdate=May 23, 2023}}</ref>
<ref name="message1156939723001049189">{{CiteDiscord
|author = Adam P. Goucher
|date = September 28, 2023
|channel = cgol
|id = 1156939723001049189
}}</ref>
</references>

==External links==
* {{LinkForumThread|title=Re: (Engineered) diehards|p=144151|author=Pavel Grankovskiy|date=April 12, 2022}} (analysis of the tetrational diehard's total runtime)

[[Category:Methuselahs]]
[[Category:Gliderless methuselahs]]

User:Galoomba/Longest diehards by bounding box

2025-01-07T15:44:46Z

C7X: Update

This table lists the longest-lasting known [[diehard]]s fitting in a n×n bounding box.

{| class="sortable wikitable"
|-
! n
! Lifetime
! Pattern
! Link
|-
| 1
|rowspan=2| 1
|rowspan=2| {{LV:Viewer|x = 1, y = 1, rule = B3/S23
o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 ZOOM 64 ]]}}
|rowspan=2|
|-
| 2
|-
| 3
| 9
| {{LV:Viewer|x = 3, y = 3, rule = B3/S23
obo$3o$o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 4
| 88
| {{LV:Viewer|x = 4, y = 4, rule = B3/S23
4o$bobo$2obo$4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 400 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 5
| 259
| {{LV:Viewer|x = 5, y = 5, rule = B3/S23
2o2bo$o2b2o$2o2bo$2bo$b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 64 ]]
}}
| <ref name="post168226"/>
|-
| 6
|rowspan=2| 798
|rowspan=2| {{LV:Viewer|x = 6, y = 6, rule = B3/S23
o2b3o$5bo$obobo$2bob2o$2obo$3ob2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 60 ]]
}}
|rowspan=2| <ref name="post168418"/>
|-
| 7
|-
| 8
| 1 002
| {{LV:Viewer|x = 8, y = 7, rule = B3/S23
6bo$o5bo$4ob2o$bo4bo$2b2obobo$2o4bo$3ob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 52 ]]
}}
| <ref name="post164797"/>
|-
| 9
| 1 069
| {{LV:Viewer|x = 9, y = 8, rule = B3/S23
o2bobob2o$ob2o$o2bobob2o$5bo2bo$6bo$2b2o2bo$2b4ob2o$4b3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 48 ]]
}}
| <ref name="post164797"/>
|-
| 10
| 1 118
| {{LV:Viewer|x = 10, y = 9, rule = B3/S23
o$o$o4bo$4bobo$3bob2o$4obo3bo$5bo3bo$2o6b2o$bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 48 ]]
}}
| <ref name="post169048"/>
|-
| 11
| 1 119
| {{LV:Viewer|x = 11, y = 8, rule = B3/S23
3o$5b2o$7bo$o5bo$bob4o3bo$2bobo5bo$b2o2bo3b2o$2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 44 ]]
}}
| <ref name="post164797"/>
|-
| 12
|rowspan=4| 1 143
|rowspan=4| {{LV:Viewer|x = 12, y = 9, rule = B3/S23
5bobo$2bo3b4o$2obo5bobo$2bo3bo3b2o$obob2o2bo2bo$b3o4bo$2o4b2o2bo$3b3o$
5bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 40 ]]
}}
|rowspan=4| <ref name="post169048"/>
|-
| 13
|-
| 14
|-
| 15
|-
| 16
|rowspan=2| 1 456
|rowspan=2| {{LV:Viewer|x = 16, y = 16, rule = B3/S23
4o2bo5bo$3b3o5b2o$8b2o4bo$o2b3o2bo3bo2bo$2o2bo6b3o$o3bobo6bo$bo2b2o9b
o$b2ob2o3bobo3bo$3obo4b3o3bo$8b2o3b2o$12bob2o$10b4o$2b2o4bobob4o$2bo6b
o3b3o$3bo3b2obo3bo$2b2o4b3ob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 28 ]]
}}
|rowspan=2| <ref name="post168226"/>
|-
| 17
|-
| 18
| 2 094
| {{LV:Viewer|x = 18, y = 18, rule = B3/S23
2bo4bobo$2b2o2bob2o$3o2bo2bo5bo$2b2o3bo5bobo$2o2b3ob3o4b2o$bob2o2bobo
5bo$bobo5bo4bobo$2ob3o2bo7bo$8b2o7bo$9bo5bobo$15bobo$13b4o$8b2o2bobo$
5bo2bo3bobo$4bobobo6bo$3bobobo6b2o$2bo2bobobo3bobo$3b2o3b2o4bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 19
| 2 272
| {{LV:Viewer|x = 19, y = 19, rule = B3/S23
o4b2o7bobobo$o5bo9b2o$b2o2bo8b2obo$2bo2b2o$14bo$o2bo10b2obo$o8bobo2bo
b2o$4o5b2o5bo$2o8bo4bobo$16bo$2bob2o4b2o5bo$2bobobo2bobo3bobo$6bo2bo4b
o$5b2ob2o4bobo$3bo2bo$3b2obo8bobo$4bob2ob2o4bo$4bo2bob2o4bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 20
| 2 287
| {{LV:Viewer|x = 20, y = 19, rule = B3/S23
o4b2o8bobobo$o5bo10b2o$b2o2bo9b2obo$2bo2b2o$15bo$o2bo6bo4b2obo$o9bobo
2bob2o$4o6b2o5bo$2o14bobo$17bo$2bob2o4b2o6bo$2bobobo2bobo4bobo$6bo2bo
5bo$5b2ob2o5bobo$3bo2bo$3b2obo9bobo$4bob2ob2o5bo$4bo2bob2o5bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
|
|-
| 21
| 2 308
| {{LV:Viewer|x = 21, y = 19, rule = B3/S23
o4b2o9bobobo$o5bo11b2o$b2o2bo10b2obo$2bo2b2o$11bobo2bo$o2bo7b2o3b2obo$
o11bo3bob2o$4o14bo$2o15bobo$18bo$2bob2o4b2o7bo$2bobobo2bobo5bobo$6bo2b
o6bo$5b2ob2o6bobo$3bo2bo$3b2obo10bobo$4bob2ob2o6bo$4bo2bob2o6bo$5b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 500 ZOOM 24 ]]
}}
|
|-
| 22
| 6 579
| {{LV:Viewer|x = 22, y = 21, rule = B3/S23
7bo$8bo2bo$8bobob2o$4b2o5b2ob2o$4b2o5b2ob2o$8bobob2o4bo$bo6bo2bo5bobo
$2bo4bo9bobo$3o16bo$19b2o$18bobo$2o4b2o3b2o$obo2bobo3bo3bo3b3o$2bo2bo
6b4o3bobo$2b2ob2o11bobo$5bo2bo3b4o4b2o$5bob2o3bo2bo$b2ob2obo12bo$b2ob
o2bo10bobo$5b2o11bobo$19bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 540 ZOOM 24 ]]
}}
| <ref name="post168226"/>
|-
| 23
| 6 803
| {{LV:Viewer|x = 22, y = 23, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo4bo$11b2o4bobo$bo5b4obo6b2o$
ob4o3b3o7bo$4bo5bobo5bobo$16bo3bo$14b2o5bo$15b2o2bobo$2o16bo2bo$obo$2b
o16b3o$bo18b2o$b2o4b2o4b2o4bo$7bo3bo2bo5b2o$10bo7bobo$b2o6b3obo5bo$2b
o2b2o3b2o$bo11bo$o3bo2b2ob3o$2o5b4o2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 520 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 24
| 6 998
| {{LV:Viewer|x = 24, y = 24, rule = B3/S23
3b3ob2o$5b2o2b2o$2o4bo4bo$2o4bo4bo$5b2o2b2o9bo$3b3ob2o6b2o2bobo$14b3o
4b2o$21bo$17bo2bobo$18bo3bo$16b2o5bo$21bobo$2o18bo2bo$obo$2bo18b3o$bo
20b2o$b2o4b2o4b2o6bo$7bo3bo2bo7b2o$10bo9bobo$b2o6b3obo7bo$2bo2b2o3b2o
$bo11bo$o3bo2b2ob3o$2o5b4o2bo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 530 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 25
| 7 483
| {{LV:Viewer|x = 25, y = 25, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo7bo$11b2o7bobo$bo5b4obo7bobo
$ob4o3b3o10bo$4bo5bobo9b2o$21bobo2$22b3o$obo19bobo$2o3bo15bobo$5o18b2o
$obobob2o$3bob2o16bo$o2b2o8bo7bobo$bo4bo6b3o5bobo$b2ob2o10bo5bo$obob2o
bo5b3obo$o2bo9bo3bo$3b3obo6b3o$o4b2o4b3o$3obobo3bo3b2obo$bo2bobo3b2o2b
ob2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 540 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 26
| 10 320
| {{LV:Viewer|x = 26, y = 26, rule = B3/S23
11bo2b2o$11b2o3bobo$9b2o4bo2bo$9bo5bo2bo$2bob2o3bob2o3bobo3bo$o4bo5bo
2b2o5bobo$obo6bo13b2o$5o18bo$2o3b2o15bobo$2o2bo19bo$4bo20bo$o3bo18bob
o$obobo17bo2bo$obo2b2o10bobo$bobobo11bobo3b3o$bobob2o8bob2o5b2o$bo14b
o2b2o2bo$13bob2o2bo4b2o$5b2o4bo6b2o2bobo$5b2o2b2o3bo4bo3bo$7bo3b2ob2o
2bo$7b2obo3b2o2b2o$9b3o7bo$9bo2bo2bo3bo$6b2ob2ob4o2bo$6b2obo2bo4b4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 560 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 27
| 10 420
| {{LV:Viewer|x = 27, y = 26, rule = B3/S23
10bo2b2o$10b2o3bobo$8b2o4bo2bo$3bo4bo5bo2bo$o2b2o3bob2o3bobo5bo$2bo7b
o2b2o7bobo$o7bo15b2o$obobo19bo$obobo18bobo$3bo21bo$2obobo20bo$bob2o19b
obo$23bo2bo$18bobo$2b4o12bobo3b3o$4bo11bob2o5b2o$17bo2b2o2bo$14bob2o2b
o4b2o$6b2o4bo6b2o2bobo$6b2o2b2o3bo4bo3bo$8bo3b2ob2o2bo$8b2obo3b2o2b2o
$10b3o7bo$10bo2bo2bo3bo$7b2ob2ob4o2bo$7b2obo2bo4b4o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 HEIGHT 560 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 28
| 16 560
| {{LV:Viewer|x = 28, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o10bo$o13b5o$11bob
o5bo$12bob2o2bo$16b2o$3o3bo4bo11b2o$o3b3o3b2obo7bobobobo$bo2b4o3bo2bo
9bo2bo$obo2b3o3bo2bo6bobobobo$5o7b2o9bo3bo$ob2obo18b2obo$22bobo$22b2o
bobo$18bobo2bo$b2o4b2o9b2o3bo$bobo2bobo11b3o2bo$3bo2bo15bo$3b2ob2o4b2o
$6bo2bo2b2o$6bob2o8b2o2b2o$2b2ob2obo10bo3bo2b2o$2b2obo2bo5b2o2bo3bo3b
2o$6b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 620 HEIGHT 620 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 29
| 16 570
| {{LV:Viewer|x = 29, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o11bo$o14b5o$12bobo
5bo$13bob2o2bo$17b2o$b3o3bo4bo11b2o$bo3b3o3b2obo7bobobobo$2bo2b4o3bo2b
o9bo2bo$bobo2b3o3bo2bo6bobobobo$b5o7b2o9bo3bo$bob2obo18b2obo$23bobo$
23b2obobo$19bobo2bo$2b2o4b2o9b2o3bo$2bobo2bobo11b3o2bo$4bo2bo15bo$4b2o
b2o4b2o$7bo2bo2b2o$7bob2o8b2o2b2o$3b2ob2obo10bo3bo2b2o$3b2obo2bo5b2o2b
o3bo3b2o$7b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 640 HEIGHT 640 ZOOM 20 ]]
}}
|
|-
| 30
| 16 660
| {{LV:Viewer|x = 30, y = 28, rule = B3/S23
2bo2b2o$2b2o3bobo$2o4bo2bo$o5bo2bo$ob2o3bobo$2bo2b2o10bo$o13b5o$11bobo
5bo$12bob2o2bo$16b2o$3o3bo4bo13b2o$o3b3o3b2obo9bobobobo$bo2b4o3bo2bo
11bo2bo$obo2b3o3bo2bo8bobobobo$5o7b2o11bo3bo$ob2obo20b2obo$24bobo$24b
2obobo$20bobo2bo$b2o4b2o11b2o3bo$bobo2bobo13b3o2bo$3bo2bo17bo$3b2ob2o
4b2o$6bo2bo2b2o$6bob2o8b2o2b2o$2b2ob2obo10bo3bo2b2o$2b2obo2bo5b2o2bo3b
o3b2o$6b2o6b2o2b2o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 640 HEIGHT 640 ZOOM 20 ]]
}}
|
|-
| 31
| 31 013
| {{LV:Viewer|x = 31, y = 31, rule = B3/S23
2b3obob3o$6b2o3b3o$3obo2bo3bo$2b3o2b2o4bo$11b2o$bo5b4obo2bobo2b3o$ob4o
3b3o3bobob2o2bo$4bo5bobo3bo2b2obo$21bo3bo$15bo9b2obo$5b2o8b3o8bo2bo$b
2obo2bo7bo2bo6b2o3bo$b2ob2obo8b2o7b2o3bo$5bob2o7b2o8b2ob2o$5bo2bo3b2o
$2b2ob2o5b2o8bob5o$2bo2bo10b2o5b4o$obo2bobo7bobo8bo$2o4b2o3bo3b2o4bob
2obobo$10bobo9b2obo$11bo9b2obobobo3$2b3o6b2o4bo2bo2bobo2bo$11bobo2bob
o2bobob3o$obo3b2o5bo3bo2b3o5b2o$b3o9b2o3b2obo3b2o$2bo3bo10bo2b2ob3ob3o
$2o3b2obo9bo2bobo4b2o$obo2bo6b2ob2obob6ob4o$o2b2ob2o4b2ob4obo2b3o2b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 680 HEIGHT 660 ZOOM 20 ]]
}}
| <ref name="post168226"/>
|-
| 32
|rowspan=5| 1 120 271
|rowspan=5| {{LV:Viewer|x = 32, y = 32, rule = B3/S23
obo2bob2obo9bo$2o3b2ob2obo6b3o8b2o$bo9bo5bo11bo$11b2o5bo6b2o4bo$3bo2b
2o4bo4b2o5bobo3b2o$2bo2bobo3bo9bo2bo$5obo5b3o6b3obo$2bo2bo3b3o2bo9bo4b
2o$3bo4bo2bo7b3obo4bobo$9b2o7bo2b2o5bo$2ob3o7b2o4bo6b2obo$2o2bo2bo4bob
o3b2ob2o4bobo$o6bo3bobo5bobo5bob2o$2o2bo2bobo2bo6bobo4b2obo$2bo4bo5b3o
2b2ob2o3bo2bo$3bo2bobo6bo3bobo5bob2o$5bo12bo2bo6bo$2bob3o3bo8b2o8bobo$
4bo5bo19b2o$3bo3bo2b2o$12bo10bo$12b3o7bobob2o2b2o$18bo3bobobo3b2o$16bo
6b2o2bo$12bo4b4o4b2obo$14bobo8bo2bo$14b2o5bo4b2o$2o2bo8b2o3bob2o6b3o$o
bobo7bo3bo4bobo4bo2bo$obo11bo2bo8b2o2bo$b2obo13bob2o3bo2b2o$3b2o13b4o
3b2o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 20 ]]
}}
|rowspan=5| <ref name="post167008"/>
|-
| 33
|-
| ...
|-
| 45
|-
| 46
|-
| 47
|rowspan=5| 1 237 975 907 532
|rowspan=5| {{LV:Viewer|x = 47, y = 47, rule = B3/S23
3ob4obob3o4b3o2b2o8b3o3bo4bobo$2bo2bo3b2o6bo4bo4b2obo2bo2bo4b4obo$2b2o
b4o2bo4b2o4bo9b2ob2o2b2o3bobo$2bobo2bobo9bo2bobo3b2o13b3o$2bo2bo7b2o6b
2o7b2o7b2obo3bo$o2bo6bo2bo7bobo5b2o10b2obobo$o8bobobo9bo15b2o3bo$3o2b
2o2bobo2b2o3b2o7bo6b2o2b3o2b3o$2o3bobobo2b2o2bo5b2o10bobo2bo4b2o$obo5b
2o4b2o3b2o13bo4bo4bo$obo7b4o7b2o3b2o4bobo10b2o$10bo2bo12b2o4b2o9b2o$
37b2o4bo$o3bobo15b2o5b2o6bobo3bob2o$2ob2ob2o3b2o9b2o5b2o3b2obobo6bo$o
3bobobo2bo2b2o19bo2bo5bobo$3ob2o2bo3b2obo19bo$3o4bo18b2o2bob2obobo$5b
2o14b2o3bo3b2obo2bobo2bobobo$2o3bo2bo3b2o7bo5b3o3bo3bo4bo3bo$4o3bo3bob
o8bo7bobo7bob2o2bo$3o2bob2o3bo8b2o2bo3bo3b3o9b2o$o2bob3obo5b2o5bobobo
3b3o2bo4bo$2o2b4o7b2o5bo2bobo4bo8b2obobo$o4bo3bo13bobobo12bo3bo$2obo3b
2o3b2o10bo3b2o5bob3o5b2o$obo2bobobo2b2o15bo5bob2o3b2obo$6bo15bo5bo5bo
4bobob4o$2o2b2o3bo11bobo3bo8b3o2b3o$2b2obo3bobobo8b2o3b2o8b2obo2bobo$
2bob2o2bob2ob4obo17bo4bob2obo$8b2o4b2o2bo19b2ob2obobo$9bo9b2o3b2o6bo6b
2o4b2o$bobobo3bob2o4b2obo3bo6b3o4bo3bo$bob2obo4bo2b2o2bo2bobobo5b3o6bo
bo2bo$2b3o6b4o2bo3bo3bo12b4ob2obo$5bo7bo2b2ob2o8b2o3b2o4bobo2bo$b6o4bo
6bob2o7b2o3b2o2b2ob2o2bo$bo4b2o4bo2bob5o17bo3b2o$2o4bobo2bobobo9bo13bo
bo3b2o$ob3o6bobo5b2o3bobo11b2o5bo$3b3ob2o7bo2b2o4bo13bob2obo$obo12bo5b
o17bo3b4o$2o2b2obo3bobob3obo13bo4bo2b2obo$obo4bo3bo2bobobo15bobo$2o2b
4o13b3o11bo$ob3obo15b3o9bob3o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 12 ]]
}}
|rowspan=5| <ref name="post200295"/>
|-
| 48
|-
| ...
|-
| 51
|-
| 52
|-
| 53
|rowspan=5| 2 738 059 586 423 623 206
|rowspan=5| {{LV:Viewer|x = 53, y = 53, rule = B3/S23
4b6o2b4ob4ob2o25bob2o$6bo7b4obobo2bo10b3o12b3o$10bo6bobo2bo5bo5bo2bo
14bo$5b5o6bo3bobo4bob2obo4bo11b2obo$7b2o21bobo15bob3o$4bob2o24bobo16b
2o$7bo4b2o8bo24b3ob2o$15bobobo2b3o12b2o9bo$12b2obobobo5bo12bo8bo3bo$
22b2obo9b3o10bo$bo10bob3obo3bobo3b2o4bo$obo10bo2b2o10b2o4b4o$bobo9bo2b
2ob2o16bo$bo2bo3bo4bobo2bo5b2o6b3o$b2o5bo5bobobobo3b2o6bo2bo$bo5bo6bo
2bob2o12b2o$6bo14b2o14bo8b2obo$11b2obobob2obo14bobo6bo5b2o$17bo3b2o6bo
5bobo8b2ob2obo$13b2o2bo4b2o4bobo5bo8b3obob2o$16b3o3bob2o3bo16bo4b2o$
15b2o5bob2o18bobo2bo2bo$ob3o12b2o25b2obobo$ob4o11b2o27bo2bob2o$o5bo32b
o6bo2bo2bo$bobobo2b3o3b2o13bo7b3o11b2o$2bobob4o4b2o12bo2bo4bo7b2obo4bo
$3bo2bob2o18bo2bo4b2o10b2ob2o$3bo3b3obo9bobobo4bo21bo$4b3o2b2obo4b2o2b
obo2bo6b3o7b2obo3bo$10bobo4b2o4bobo7b3o7bob2o$11bob2o6bo19bobo$12bo2bo
5bobo3b2o11bobo2b2o$13b2o6bo4bobo12bo4bo$14b5o3bo3bo4b2o3b2o7bo$15b4o
6b2o5b5o8b2o$15bobo15b3o4bob2obo$14bob2obo14bo5b2obo2bo$14bo3bobo22bob
2o$14bo2bo2b2o18b2obobo4bobo$15b2obob2o18bobo2bo5bo$17bo2b2o4b2o2bo10b
o3b2o3bobo$18bo10b2o20b2o$19b3o4bo2bo19bo2bo$obo2b2o3bo13b3o2bo21b2o$b
2o2bo4b2obo12bo2bo3b2o12b3o2bo$2bo2bob2o3b2o10bob2ob2o2b2o17bo$o5bo4bo
bo8b4obo21bo$b3obo5bob2o4bo2bo4b4o$bob2obo3bo3bo2bo3bo4bo2bo3bo$2o2bo
3b2o3bo5bo5bo4b3o$4b2o2bob2o6bo2b3o5b2o2bo$5b2o2b5o2b5obo2b7o!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 720 HEIGHT 700 ZOOM 12 ]]
}}
|rowspan=5| <ref name="post169209"/>
|-
| 54
|-
| ...
|-
| 58
|-
| 59
|-
| 60
| 2.7324 × 10{{sup|27284}}
| {{LV:Viewer|x = 60, y = 60, rule = B3/S23
11b6o2b4ob4ob2o25bob2o$13bo7b4obobo2bo10b3o12b3o$17bo6bobo2bo5bo5bo2bo
14bo$12b5o6bo3bobo4bob2obo4bo11b2obo$14b2o21bobo15bob3o$11bob2o24bobo
16b2o$5bo8bo14bo24b3ob2o$5b3o21b3o12b2o9bo$8bo23bo12bo8bo3bo$7b2o3bo
16b2obo9b3o10bo$12bobo14bobo3b2o4bo$11bobo21b2o4b4o$6bobo4bo30bo$7b2o
22b2o6b3o$7bo23b2o6bo2bo$15b2o3b2o2b2o14b2o$15b2o2bo2bo2bo18bo8b2obo$
3b2ob2o11bob2obo18bobo6bo5b2o$3b3o2bo3bo7bo3b2o10bo5bobo8b2ob2obo$2bo
4b2o2bobob2obobob2o6b2o3bobo5bo8b3obob2o$b3ob3o3bobobob2ob2obo6bobo3bo
16bo4b2o$b2obob2o4bo18b2o18bobo2bo2bo$bo49b2obobo$bo2b3obo44bo2bob2o$b
ob2o41bo6bo2bo2bo$21b2o13bo7b3o11b2o$4bo16b2o12bo2bo4bo7b2obo4bo$3bo
31bo2bo4b2o10b2ob2o$31b2o4bo21bo$2ob3o18b2o4bobo17b2obo3bo$2o2bo2bo16b
2o4b2o18bob2o$o6bo6b2o32bobo$2o2bo2bobo5bo11b2o5b2o11bobo2b2o$2bo4bo7b
obo8bobo4bobo12bo4bo$3bo2bobo7b2o3bo4b2o5bo4b2o3b2o7bo$5bo14bobo9b2o4b
2o3b2o7b2o$2bob3o3bo10bo25bob2obo$4bo5bo7bo10b2o9b3o4b2obo2bo$3bo3bo2b
2o5bobo8bobo9b3o7bob2o$12bo5bo4b2o3bo12bo5b2obobo4bobo$12b3o8b2o2b2o4b
2o12bobo2bo5bo$18bo14bo14bo3b2o3bobo$16bo18bo22b2o$12bo4b4o7b2o4b2o20b
o2bo$14bobo11b2o3bo24b2o$14b2o5bo4b2o6bobobob2o12b3o2bo$13b2o3bob2o4b
2o3bo3b2obobo3bo14bo$12bo3bo4bobo7bo5b3o2bo13bo$14bo2bo11b3o5bo2b4o$
18bob2o2b2obo3bobobob2ob2obo$18b4o5bo6b2o3bo$24b3o2b4ob2o3b3obo$24b2o
3b2o7bo3bo$18b2o4bobo2bobo3b2o3bob2o$22b2o9b2ob2o2bo3bo$18b3o4b2obobob
3o2bo2b2o2bo$16bob4ob3o4b2o4bob2obo$14b2o4bo2b2o2b3o2bo3b2o2bo2bo$15bo
2b2ob3obo3bobob3o2b2ob2o$18b2obob3ob8obob2obobo!
[[ THUMBNAIL THEME 6 GRID GRIDMAJOR 0 THUMBSIZE 4 WIDTH 780 HEIGHT 780 ZOOM 12 ]]
}}
| <ref name="post169196"/>
|}

== References ==
<references>
<ref name="post164797">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 164797
|author = Pyry Virtanen
|date = August 9, 2023
}}</ref>
<ref name="post167008">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 167008
|author = Tim Coe
|date = September 14, 2023
}}</ref>
<ref name="post168226">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 168226
|author = Dean Hickerson
|date = October 1, 2023
}}</ref>
<ref name="post168418">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 168418
|author = b3s23love
|date = October 3, 2023
}}</ref>
<ref name="post169048">{{LinkForumThread
|format = ref
|title = Re: Thread for small diehards
|p = 169048
|author = Pyry Virtanen
|date = October 13, 2023
}}</ref>
<ref name="post169196">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 169196
|author = Tim Coe
|date = October 16, 2023
}}</ref>
<ref name="post169209">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 169209
|author = b3s23love
|date = October 16, 2023
}}</ref>
<ref name="post200295">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 200295
|author = b3s23love
|date = December 23, 2024
}}</ref>
</references>

Engineered diehard

2025-01-07T15:40:58Z

C7X: Add parentheses for readability, add new developments in decreasing bound box of sawtooth-based mechanism

{{stub}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|pname = diehard30273
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 ZOOM 14 ]]
|position = center
|caption = 30,273-tick diehard with bounding box {{times|32|32}} by Hickerson<ref name="post143921" />
}}
|}
{{main|Die hard#"Die hard" as a general term}}
Beginning in early 2022, there has been considerable interest in constructing artificial diehards within small bounding boxes. On March 1, [[Dean Hickerson]] shared a 9044-tick {{times|32|32}} diehard in a private email to [[Dave Greene]]. After a complex series of interactions between an active reaction and various still lifes, a single [[lightweight spaceship]] is produced which eventually catches up to and collides with [[30P5H2V0]], producing a single [[loaf]]. Finally, an even slower [[25P3H1V0.1]] eventually collides with the loaf, destroying both of them.<ref name="post143573" /> On March 6, more optimized versions using different combinations of spaceships (including the especially slow [[copperhead]]) were shared, including a 14,010-tick diehard at {{times|32|32}} and an 18,477-tick diehard at {{times|36|36}}.<ref name="post143574" />

Although Hickerson's results were not initially posted publicly, a forum thread was coincidentally started a few weeks later dedicated to diehards, including engineered ones.<ref name="post143559" /> On March 31, [[Pavel Grankovskiy]] posted a 50,716-tick diehard in which a [[Simkin glider gun]] and [[pulse divider|pulse-dividing]] glider reflectors are used to slowly eat through a series of [[tub]]s. Although significantly larger than Hickerson's constructions at {{times|90|86}}, Grankovskiy's 50,716-tick diehard does not use the "spaceship-chasing" technique, meaning that throughout its evolution, the pattern only slightly exceeds its initial bounds. Using spaceship-chasing, however, the pattern's lifespan can be increased by an order of magnitude to 518,476 ticks without further increasing the bounding box.<ref name="post143605" /> [[Jiahao Yu]] optimized the bounding box of both of these patterns to {{times|87|86}},<ref name="post143624" /> as shown below.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = diehard50716
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 50,716-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = diehard518476
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 640 WIDTH 640 ZOOM 6 ]]
|position = center
|caption = 518,476-tick diehard with bounding box {{times|87|86}} by Grankovskiy and Yu
|style = width:300px;
}}}}
{{gallery bottom}}

==Sawtooth-based designs==
Using a [[sawtooth]] allows for the creation of extremely long-lasting diehards. On April 7, 2022, Pavel Grankovskiy successfully constructed a diehard using a sawtooth an {{c|Sawtooths with expansion factor 121|expansion factor of 121}}. The pattern fits within a bounding box of {{times|99|101}} (just barely meeting the 10,000-cell restriction specified in the original post<ref name="post143559" />) and lasts approximately {{times|2.280624|10{{sup|870}}}} generations.<ref name="post143908" /> Further optimizations, with the help of [[toroidalet]],<ref name="post143914" /> Dean Hickerson,<ref name="post143920" /> [[EvinZL]],<ref name="post143997" /> [[Rocknlol]],<ref name="post144020" /> and [[Adam P. Goucher]]<ref name="post144030" /> increased its lifespan to {{times|~1.33616|10{{sup|1443}}}} ticks<ref name="post144027" /> and decreased its bounding box to {{times|94|98}}.<ref name="post144045" />

{{EmbedViewer
|pname = diehard1e1443
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 700 ZOOM 6 ]]
|position = center
|caption = {{times|94|98}} exponential diehard by Grankovskiy et al.
|style = width:300px;
}}

On April 9, Grankovskiy posted a concept for a pattern whose lifespan is measured via [[tetration]], the next hyperoperator after exponentiation. Originally posted in the form of a methuselah,<ref name="post144034" /> the diehard version was completed on April 11.<ref name="post144077" /> With optimization by [[Tanner Jacobi]]<ref name="post144087" /> and toroidalet,<ref name="post144162" /><ref name="post149066" /> its lifespan is somewhere between 1510 and 1610 ticks.<ref>{{Cite web|url=https://btm.qva.mybluehost.me/telling-the-tale-of-two-tetrations/|author=Brett Berger|title=Telling the tale of two tetrations|work=a blog by biggiemac42|date=April 17, 2022|accessdate=April 17, 2022}}</ref>

{{EmbedViewer
|pname = diehardtetration
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|111|90}} tetrational diehard by Grankovskiy et al.
|style = width:300px;
}}

On July 9, 2023, [[EvinZL]] proposed adding loaf-making fuse to increase the lifespan of the methuselah by extending power tower length,<ref name="post163493" /> based on the original idea of [[Tanner Jacobi]].<ref name="post148684" /> In a flurry of activity that followed after, [[toroidalet]], [[Adam P. Goucher]], [[Pavel Grankovskiy]] and [[EvinZL]] pushed the number of loaves from 15<ref name="tetrational_15_loaves" /> to approximately {{times|3.52|10{{sup|48}}}}<ref name="tetrational_1e48" />, with the latter improvement based on idea by [[Adam P. Goucher]] to use gliders from exponential part of diehard to ignite the fuse.<ref name="tetrational_exp_idea" /> This was subsequently improved to {{times|1.1|10{{sup|1046}}}}<ref name="tetrational_1e1046" /><ref name="tetrational_exp_cp4space" />.

{{EmbedViewer
|pname = diehardtetration1046
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|109|91}} tetrational diehard with a lifespan exceeding (101046)10.
|style = width:300px;
}}

On December 23, 2024, [[b3s23love]] posted a {{times|47|47}} sawtooth-based diehard with lifetime 1237975907532, reducing the size of the sawtooth base.<ref name="post200295" />

==Double-tetrational designs==
On 15th September 2023, [[Tim Coe]] and b3s23love increased the height of the tetrational tower from {{times|1.1|10{{sup|1046}}}} to 121{{sup|{{times|8.46|10{{sup|1059}}}}}}. The following day, Tim Coe further improved this height to 121{{sup|121{{sup|121{{sup|121{{sup|498}}}}}}}}, so the height of the tetrational tower is itself a tetrational tower. This was subsequently further improved by Tim Coe, toroidalet, EvinZL, and b3s23love, culminating in a height of 121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|121{{sup|1356648129958673823266622201465466300}}}}}}}}}}}}}}}}}} as of the 28th September 2023. The overall lifespan of the diehard exceeds {{sup|{{sup|11}}11}}11, or 11^^^3 in Knuth's up-arrow notation. More recent designs have further improved lifespans, with the current record holder taking 17^^^3 generations to die out entirely.

{{EmbedViewer
|pname = diehardtetration17uuu3
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 670 WIDTH 760 ZOOM 6 ]]
|position = center
|caption = {{times|116|86}} tetrational diehard with a lifespan exceeding 17↑↑↑3.
|style = width:300px;
}}

==Timetable==
In many cases, several incremental record-breaking improvements were made inside 24 hours. In the following table, the record-breaking pattern for each day is listed (with each day beginning and ending at UTC 0:00).<ref name="message1156939723001049189" />

{| class="wikitable"
! Date
! Lifespan
! Bounding box size
! Bounding box cells
! Contributor(s)
|-
!2022-02-21
|2474
|32×32
|1024
|Charity Engine
|-
!2022-03-01
|9044
|32×32
|1024
|Dean Hickerson
|-
!2022-03-06
|14010
|32×32
|1024
|Dean Hickerson
|-
!2022-03-31
|518476
|90×86
|7740
|Pavel Grankovskiy
|-
!2022-04-01
|518476
|87×86
|7482
|Jiahao Yu
|-
!2022-04-07
|2.28 × 10^870
|99×101
|9999
|Pavel Grankovskiy
|-
!2022-04-09
|1.77 × 10^1295
|94x96
|9024
|Pavel Grankovskiy, toroidalet, Rocknlol
|-
!2022-04-10
|1.476 × 10^1595
|94×99
|9306
|Pavel Grankovskiy, Dean Hickerson
|-
!2022-04-11
|11 ^^ 10
|105×95
|9975
|Pavel Grankovskiy
|-
!2022-04-13
|11 ^^ 11
|108×92
|9936
|toroidalet, Pavel Grankovskiy
|-
!2022-04-14
|11 ^^ 13
|109×91
|9919
|Pavel Grankovskiy, toroidalet, Tanner Jacobi
|-
|
|-
!2023-07-17
|121 ^^ 15
|110×90
|9900
|toroidalet, Pavgran
|-
!2023-07-18
|121 ^^ (4.98 × 10^27)
|111×90
|9990
|Pavel Grankovskiy, toroidalet, EvinZL, Adam P. Goucher
|-
!2023-07-19
|121 ^^ (5.94 × 10^54)
|109×91
|9919
|Pavel Grankovskiy, May13, toroidalet, EvinZL, Adam P. Goucher
|-
!2023-07-20
|121 ^^ (1.67 × 10^903)
|109×91
|9919
|May13, EvinZL
|-
!2023-07-23
|121 ^^ (1.10 × 10^1046)
|109×91
|9919
|Adam P. Goucher
|-
!2023-09-15
|121 ^^ (121 ^ (8.46 × 10^1059))
|108×91
|9828
|Tim Coe, b3s23love
|-
!2023-09-16
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 498)
|109×91
|9919
|Tim Coe
|-
!2023-09-19
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ (9.74 × 10^51))
|109×91
|9919
|b3s23love, toroidalet, EvinZL
|-
!2023-09-21
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 60143)
|109×91
|9919
|EvinZL, Tim Coe
|-
!2023-09-22
|121 ^^ (121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 121 ^ 70433)
|112×89
|9968
|b3s23love, toroidalet, EvinZL
|-
!2023-09-24
|9 ^^^ 3
|112×89
|9968
|Tim Coe
|-
!2023-09-28
|11 ^^^ 3
|112×89
|9968
|toroidalet
|-
!2023-10-05
|17 ^^^ 3
|116×86
|9976
|Tim Coe, EvinZL, [https://conwaylife.com/forums/viewtopic.php?p=168589#p168589 Adam P. Goucher]
|-
!2023-10-05
|17 ^^^ 3 +
|116×86
|9976
|[https://conwaylife.com/forums/viewtopic.php?p=169264#p169264 toroidalet]
|}

==References==
<references>
<ref name="post143573">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143573
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143574">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143574
|author = Dave Greene
|date = March 31, 2022
}}</ref>
<ref name="post143559">{{LinkForumThread
|format = ref
|title = (Engineered) diehards
|p = 143559
|author = squareroot12621
|date = March 30, 2022
}}</ref>
<ref name="post143605">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143605
|author = Pavel Grankovskiy
|date = March 31, 2022
}}</ref>
<ref name="post143624">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143624
|author = Jiahao Yu
|date = March 31, 2022
}}</ref>
<ref name="post143921">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143921
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143908">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143908
|author = Pavel Grankovskiy
|date = April 7, 2022
}}</ref>
<ref name="post143914">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143914
|author = toroidalet
|date = April 7, 2022
}}</ref>
<ref name="post143920">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143920
|author = Dean Hickerson
|date = April 7, 2022
}}</ref>
<ref name="post143997">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 143997
|author = EvinZL
|date = April 9, 2022
}}</ref>
<ref name="post144020">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144020
|author = Rocknlol
|date = April 10, 2022
}}</ref>
<ref name="post144030">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144030
|author = Adam P. Goucher
|date = April 10, 2022
}}</ref>
<ref name="post144027">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144027
|author = Dean Hickerson
|date = April 10, 2022
}}</ref>
<ref name="post144045">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144045
|author = toroidalet
|date = April 10, 2022
}}</ref>
<ref name="post144034">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144034
|author = Pavel Grankovskiy
|date = April 9, 2022
}}</ref>
<ref name="post144077">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144077
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144087">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144087
|author = Pavel Grankovskiy
|date = April 11, 2022
}}</ref>
<ref name="post144162">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 144162
|author = toroidalet
|date = April 13, 2022
}}</ref>
<ref name="post149066">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 149066
|author = toroidalet
|date = August 2, 2022
}}</ref>
<ref name="post163493">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163493
|author = EvinZL
|date = July 9, 2023
}}</ref>
<ref name="post148684">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 148684
|author = Tanner Jacobi
|date = July 25, 2022
}}</ref>
<ref name="post200295">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 200295
|author = b3s23love
|date = December 23, 2024
}}</ref>
<ref name="tetrational_15_loaves">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163828
|author = toroidalet
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e48">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163888
|author = Adam P. Goucher
|date = July 19, 2023
}}</ref>
<ref name="tetrational_exp_idea">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 163848
|author = Adam P. Goucher
|date = July 18, 2023
}}</ref>
<ref name="tetrational_1e1046">{{LinkForumThread
|format = ref
|title = Re: (Engineered) diehards
|p = 164085
|author = Adam P. Goucher
|date = July 23, 2023
}}</ref>
<ref name="tetrational_exp_cp4space">{{cite web|url=https://cp4space.hatsya.com/2023/07/23/miscellaneous-discoveries/|title=Miscellaneous discoveries|work=Complex Projective 4-Space|accessdate=May 23, 2023}}</ref>
<ref name="message1156939723001049189">{{CiteDiscord
|author = Adam P. Goucher
|date = September 28, 2023
|channel = cgol
|id = 1156939723001049189
}}</ref>
</references>

==External links==
* {{LinkForumThread|title=Re: (Engineered) diehards|p=144151|author=Pavel Grankovskiy|date=April 12, 2022}} (analysis of the tetrational diehard's total runtime)

[[Category:Methuselahs]]
[[Category:Gliderless methuselahs]]

Lifeline Volume 8

2024-09-18T06:55:16Z

C7X: Typos are preserved, but this typo is not present in the scan /* Page 6 */

__NOTOC__{{LifeLine|vol=8|date=December 1972}}

====Page 1====
''View [[:File:Lifeline vol 8.png|scan of this page]]''

[[Conway's Game of Life|Life]] is enjoying a revival of activity as evidenced by recent reader response containing many amazing new discoveries. Specific among these are included a basically new type of [[puffer train]] which can be used to generate all kinds of objects including [[glider|gliders]](!), some exotic collisions involving only gliders and [[block]]s which may be used to assemble new types of [[spaceship]] [[gun]]s as well as build the logical circuitry for a Life computer, and many exciting [[oscillator]]s including a [[predecessor]] for the [[tumbler]]! Some of this material is contained herein; however, additional time will be required in order to present all the findings in such a way so that they will compliment and reinforce work previously reported.

{| class="wikitable" style="margin-left: auto; margin-right: auto;"
! style="text-align:left" |[[Buckingham's combine|'Buckinghams Combine']] revisited . . .
|-
|{{LV:Viewer|{{LifeViewer config/lifeline|zoom=24|width=70|height=30}}
#C [[ THUMBSIZE 3 ]]
#C [[ LABEL -1.5 0 8 "a" ]]
#C [[ LABEL 21.5 0 8 "b" ]]
#C [[ LABEL 34 0 8 "c" ]]
#C [[ LABEL 50 0 8 "d" ]]
#C [[ LABEL 0 15 8 "e" ]]
#C [[ LABEL 17 15 8 "f" ]]
#C [[ LABEL 34 15 8 "g" ]]
#C [[ LABEL 48 15 8 "h" ]]
#C Note that pattern g fails (see Lifeline #9 page 3 for correction)
2o16b2o3b2o4b2o9bo16bo$bo16bo5bo4bo9bobo13b5o$bobo12bobo5bob2obo8bobob
o11bo5bo$2b2o12b2o7bo2bo9bo3bo8bo2bo2b3obo$7bo4bo13bo9b2o2bo2b2o5bobob
obo4bo2bo$5b2ob4ob2o13bo6bo4bo4bo5bo2bo4bobobobo$7bo4bo11b2o8bobob2ob
2obobo7bob3o2bo2bo$2b2o12b2o10b2o5bo4bo4bo9bo5bo$bobo12bobo6bo10b2o2bo
2b2o11b5o$bo16bo8bo10bo3bo15bo$2o16b2o5bo2bo9bobobo$7bo16bob2obo9bobo$
6bobo15bo4bo10bo$7bo15b2o4b2o2$5b5o31b2o8b2o8b2o$4bo5bob2o6b2o5b2o13bo
8bobo6bobo$3bob2o3bob2o6bo7bo10b3o11bo6bo$3bobo2bobo6b2obo7bob2o6bo3b
3o6bob2o4b2obo$2obo3b2obo6b2obob5obob2o5bo3bo2bo4b3o2bo4bo2b3o$2obo5bo
11bo2bo2bo9bobobobo4bo3bo8bo3bo$4b5o13b5o8b2o4bob2o4b3o2bo4bo2b3o$34bo
2b4o10bob2o4b2obo$6bo17bo9b2o17bo6bo$5bobo15bobo13b2o10bobo6bobo$6bo
17bo14b2o10b2o8b2o!
|[[File:Lifeline vol08 101.png]]
}}
|}

This profusion of material sent in as well as the torrent of reader replys from [[Martin Gardner]]'s recent plug in Scientific American have really affected my plans to issue LIFELINE. However, with Number Eight now published and mailed, we are again back on schedule and I will resume the regular quarterly publication with Number Nine in March 1973. On the last page of this issue you will find a LIFESAVER form required for renewal of your LIFELINE subscription.

====Page 2====
''View [[:File:Lifeline vol 8 p2.jpg|scan of this page]]''

{| class="wikitable"
|+ style="text-align:left" | Class E, Evolutionaries, Exercises, Events, Et cetera . . .
|<div style="float:right">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=64|width=10|height=5}}
#C [[ THUMBSIZE 4 ]]
2o2bo$2obobo$4b2o!
|[[File:Lifeline vol08 201.png]]
}}</div>
[[Paul Schick]] of Madison, Wi. notes the following interaction involving a [[block]] and a [[boat]] which in eight generations form a [[block]] and a [[beehive]]. The [[block]] and [[beehive]] in turn interacts as described on page five of [[Lifeline Volume 3|LIFELINE Number Three]] to form another [[block]] and [[beehive]]. (EN: also see [[Lifeline Volume 6#Page 2|No.6,p.2]])
|}

{| class="wikitable"
|+ style="text-align:left" | Class I, Still Lifes and Stable Forms . . .
! style="text-align:left" | LIFEXPLAINATIONS by [[Paul Dietz]] of Ellicott City, Md.
|-
|<div style="float:right">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=24|width=50|height=20}}
#C [[ THUMBSIZE 3 ]]
#C [[ GRIDMAJOR 10 ]]
#C [[ X 2 ]]
#C [[ ARROW 4.5 7.5 4.5 11 6 ]]
#C [[ ARROW 14.5 7.5 14.5 11 6 ]]
#C [[ ARROW 24.5 7.5 24.5 11 6 ]]
#C [[ ARROW 34.5 7.5 34.5 11 6 ]]
#C [[ ARROW 44.5 7.5 44.5 11 6 ]]
#C [[ COLOR POLY White ]]
#C [[ POLYALPHA 0.5 ]]
#C [[ POLYT 0 0 0 ]]
#C [[ POLYFILL {{PolyCell|x=6|y=3}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=16|y=3}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=16|y=6}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=26|y=3}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=23|y=6}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=36|y=3}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=36|y=6}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=33|y=6}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=46|y=3}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=46|y=6}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=43|y=6}} 64 ]]
#C [[ POLYFILL {{PolyCell|x=43|y=3}} 64 ]]
3$6bo9bo9bo9bo6bo2bo$4b2o8b2o8b2o8b2o8b2o$4b2o8b2o8b2o8b2o8b2o$16bo6bo
9bo2bo6bo2bo7$5bo9bo9bo9bo8b2o$4bobo7bobo7bobo7bobo6bo2bo$4b2o8bobo6bo
bo7bo2bo6bo2bo$15bo8bo9b2o8b2o!
|[[File:Lifeline vol08 202.png]]
}}</div>
I have noticed a surprising phenomenon in Life regarding the [[block|smallest and most compact stable object]]. In all cases where a single bit is placed on one or more corners of a [[block]], a new stable configuration is formed the next generation. Also to be noted is the fact that the size of the resulting object in all cases is equal to four (the size of the block) plus the total number of bits placed on the corners. These are shown at the right.

EN: this generality also applies in at least three instances involving bit-pairs thereby adding credibility to Dietz's Lifexplaination. Can you identify these?
|-
! style="text-align:left" | Ten-bit Still Lifes by [[Everett Boyer|V. Everett Boyer]] of San Diego, Ca.
|-
|<div style="float:right">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=64|width=14|height=7}}
#C [[ THUMBSIZE 4 ]]
b2o6bobo$o2bo4bob2o$obobo3bo$bobo5b3o$2bo8bo!
|[[File:Lifeline vol08 203.png]]
}}</div>
There are at least 25 [[:Category:Strict still lifes with 10 cells|stable objects of size ten]], but these two are especially easy to miss. Will those who committed themselves to only 24 check their lists!

EN: I have checked my list and it still contains only 24 objects!
|}

{| class="wikitable"
|+ style="text-align:left" | Class II, Oscillators . . .
|-
| colspan=3 |The eight objects shown on the [[#Page 1|cover page]] of LIFELINE Number Eight were discovered and sent in by [[David Buckingham]], [[Mark Niemiec]], and [[Peter Raynham]] of Sarnia, Ontario, Canada. These were chosen by the writer from those sent in by this ingenious prolific group who have now reported over fifty new oscillators of periods greater than two! Since each of the obejcts shown on the cover are easy to track, I will leave for the reader the enjoyment of determining their periods which incidentally are all different. Like the collection presented on the cover of [[Lifeline Volume 5|LIFELINE Number Five]] this arrangement as shown will reappear again only after 2,520 generations. Details, credits etc. next issue.
|-
| style="border:none;vertical-align:top" | [[Paul Schick|Schick]] has submitted an arrangement of two simple objects which when properly bounded, on a small finite surface will evolve into a [[tumbler]]! Shown here is a row of sixteen bits with one bit removed.(cont. on [[#Page 5|page 5]])
| style="border:none;text-align:right;width:250px" | {{LV:Viewer|{{LifeViewer config/lifeline|zoom=48|width=20|height=11}}
#C [[ THUMBSIZE 4 ]]
#C [[ X 0 ]]
<nowiki>
x = 20, y = 11, rule = B3/S23:P20,11
5$b5ob10o!
</nowiki>
|[[File:Lifeline vol08 204.png]]
}}
| style="border:none" |11×20 finite surface     &ldsh;
|}

====Page 3====
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{| class="wikitable"
|+ style="text-align:left" | Reader Article . . .
|-
! Progress on the "Life Codex"

by [[Hugh W. Thompson]]
|-
|[[Bob Wainwright]] has mentioned my work on my "Life Codex" several times in LIFELINE. Now that its format and ultimate scope have firmed up, I think it is appropriate for me to step to stage center and describe the thing in detail.

The Codex itself simply contains pictures of the "Life" objects, from three cells on up, arranged by number of cells, with a sequence number assigned to each object. A sample page is shown (see page 5 ). The complete "Life Codex Number" (LC#) of an object is the number of cells, followed by the sequence number in parentheses. Thus our old friends "[[R-pentomino|r]]" and "[[Pi-heptomino|π]]" have the prosaic designations of 5(9) and 7(101), respectively; the "[[beehive]]" is 6(485). The Codex divides logically, but not physically, into two segments: a "fixed" portion and a "random" portion. The fixed portion consists of objects to which I have assigned sequence numbers, in a more or less logical manner, before their histories were known. It includes all possible objects from 3 to 6 cells, the 3031 7-cell "[[polyplet|tangoes]]", the 369 [[octomino]]es plus a few other 8-cell tangoes, the 1285 [[nonomino]]es, about 100 [[decomino]]es, the straight [[n-omino]]es (n-rows) for n = 11 thru 22, and all simple objects discussed in SCIENTIFIC AMERICAN and LIFELINE, a total of roughly 12,700 objects. (By "simple" objects I specifically exclude such esoterics as [[glider gun]]s, [[billiard table|billiard-table]] configurations, [[fuse]]s, [[agar]]s, etc.) The random portion consists of objects which occur as descendants of the "fixed" objects, those sent to me by other contributors, directly or thru [[Bob Wainwright|Bob]], any which show up in future issues of LIFELINE, and any others which look interesting. These are sequenced on a first-come-first-served basis. This random portion, of course, is growing by leaps and bounds as I add more life histories, so that the total Codex consists of nearly 23,000 objects to date (Jan. 10th), and will likely be well over 30,000 by the time the Codex is "finished".

(A note about the word "tango" which I used above. This is a term coined by [[Curt Gibson]] to denote a kingwise-connected object, probably derived from the word "tangent". I would like to see it become common usage, since it is short, colorful and convenient. Gibson's word for a spatially-connected object, "incontinuo", is less pithy but could also be useful.)

The Codex has four companion volumes. The first, the Life History and Cross-Reference, lists each object by LC#, followed by the LC#'s of its successive generations until one of three things happens: (1) an object occurs (or a pattern) whose history has already been recorded; (2) a stable object or pattern occurs in 50 generations or less; (3) at least 20 generations have been recorded for a [[methuselah]] (51 gens. or more). Option (2) includes objects which die, since an empty universe is about as stable as you can get. Then follows an indication of the eventual terminus – stable object or pattern, death, or methuselah constellation – and the LC# of the first ancestor of the
|}

====Page 4====
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{| class="wikitable"
|object (if any). The second, the Terminus Cross-Reference, lists, for each stable object, pattern or [[methuselah]] constellation,all objects whose terminus is the given object or pattern. The stable objects and "short-life" patterns are arranged by [[Bob Wainwright|Bob]]'s original classification scheme, with a separate book (Class V-A) for objects that die. [[Methuselah]] constellations are arranged by the LC# of the "primary" (usually the first object, i.e. lowest LC#, to result in the given constellation). Listed for each object with a given terminus are the LC#, number of generations, first (lowest LC#) father, if any, and son. Listed also for methusaleh "secondaries" are the first ancestor and the generation numbers of the secondary and primary, respectively, which are identical. The third book is the [[Methuselah]] extract, giving, on a separate page for each primary, a picture of the primary, a picture, if available, of the final constellation, the number of generations, and such other demographic data as the maximum and final populations and the class of the final constellation (static, periodic, dead, or containing gliders). The fourth "book" is a codex of the "short-life" patterns which have occurred as termini of Life objects. These are pictured on 4x6 index cards, with descriptive notes as needed. The LC# for these consists of the total number of cells, followed by the letter P, followed by a sequence number which is merely the order in which the pattern was encountered in the History. "[[Traffic light]]s", for example, is 12P1.

As of this writing, the Life History and the other subsidiary volumes are complete thru about the first third of the nonominoes, leaving perhaps 1300 objects in the Codex whose history is unknown.

What is the use of all this compilation? Well, what was the "use" of climbing Mount Everest, or tabulating the first million prime numbers? apart from keeping me amused, and leading to the discovery of many objects with remarkable, and even esthetically pleasing, life histories, the Codex and its satellite volumes have already seen some use as a quesiton-answerer. A correspondent will write in with an object whose history is unknown to him, and after a look at the Life History, I can reply "Your object becomes a [[beehive]] in 35 moves", or whatever. Eventually I expect the Codex, etc., to become a compendium of all known simple objects, with their life histories. Eventually also, I expect my task to consist primarily of logging in the results obtained by others. Accordingly I am taking the fearful risk of listing my address with this article. If you have an object you wish to add to the Codex (or to find out if it's already there), send it on. Also, I reproduced this particular page of the Codex for a reason – except for 10(1), which becomes the [[pentadecathlon]], all of these decominoes are "unknown" to me, anyway. If you want to track a few histories and lay them on me, feel free.

EN: see Lifequote on [[#Page 7|page seven]]!
|}

====Page 5====
''View [[:File:Lifeline vol 8 p5.jpg|scan of this page]]''

{| class="wikitable"
| colspan=3 style="text-align:center" | Sample "Life Codex" page

[[File:Lifeline vol08 501.png]]
|-
| style="border:none;vertical-align:top;" | (cont. from [[#Page 2|page 2]])

The five-bit row is the familiar [[traffic light|traffic lite]] precursor and the ten-bit row the familiar pentadecathlon predecessor. Together as shown within the 11 by 20 bounded area they evolve in 29 generations into two [[blinker]]s and a [[tumbler]]! During the process, the north, south, and west border must by 'inducted'. If four mirror pairs of these rectangles are laid side by side (120 bits in all), they will evolve into 4 [[block]]s, 12 [[blinker]]s, and 2 [[tumbler]]s. EN: the [[T-tetromino]] is proving to be a virile ingredient for [[oscillator]]s ([[traffic light|t.lite]], [[pulsar]], [[tumbler]], and [[pentadecathlon]]) . . . any others?
| style="border:none;text-align:right;width:250px" | {{LV:Viewer|{{LifeViewer config/lifeline|zoom=32|width=41|height=47}}
#C [[ THUMBSIZE 4 ]]
5$3b10ob5o3b5ob10o12$3b10ob5o3b5ob10o12$3b10ob5o3b5ob10o12$3b10ob5o3b
5ob10o!
|[[File:Lifeline vol08 502.png]]
}}
| style="border:none" |47×41 unbounded area   &ldsh;
|}

{| class="wikitable"
|+ style="text-align:left" | Reader Briefs . . .
|<div style="float:left">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=64|width=9|height=5}}
#C [[ THUMBSIZE 4 ]]
o3bo$5o$o!
|[[File:Lifeline vol08 503.png]]
}}</div>
<div style="float:right">{{LV:Viewer|{{LifeViewer config/lifeline|zoom=64|width=9|height=6}}
#C [[ THUMBSIZE 4 ]]
3o$2bo$2bo2bo$4bobo!
|[[File:Lifeline vol08 504.png]]
}}</div>
[[Don Woods]] of Princeton, N.J. who first suggested measuring age to initial size (see [[Lifeline Volume 1#Page 6|No.1,p.6]]) has allowed for tracking just about all previously defined ratios and statistics in his general purpose program. One more that I would add is the 'procrastination quotient' as suggested by [[Everett Boyer|Boyer]]. Boyer defines this measure as the age divided by the product of the initial and final populations where the initial configuration must be a single object (see [[Lifeline Volume 2#Page 12|No.2,p.12]]). For all three-bit objects this value is maximum for the [[Pre-block|block predecessor]] (PQ = 1/3x4 = 0.083) since all other patterns die. For all four-bit objects this measure is maximum for the familiar [[T-tetromino]] grandfather (PQ = 0.229). A five-bit [[R-pentomino]] grandfather has a value of 1.905. The familiar [[procrastinator]] (see [[Lifeline Volume 4#Page 4|No.4,p.4]]) holds the record for all seven-bit objects with a value of 1.810. [[Hugh Thompson|Thompson]] reports the eight-bit object above left which is active for 78 generations before stabilizing into a single blinker (PQ = 78/8x3 = 3.250). Another eight-bit pattern reported by Thompson however runs for 189 generations before forming a [[beehive]]. This sets the current record for all objects with a procrastination quotient of 3.937.
|}

====Page 6====
''View [[:File:Lifeline vol 8 p6.jpg|scan of this page]]''

{| class="wikitable" style="text-align:left"
|+ style="text-align:left" |Lifearticle . . .
|-
| colspan=2 |<pre> ooooooooooooooooooooooooooooo oooo Systems
ooooooooooooooooooooooooooooooooo oooo Dimensions
ooooooooooooooooooooooooooooooooooooooo Limited
oooo oooooooo
oooooooooooooooo oooo ooooooo
oooooooooooooooo oooo ooooooo SYSTEMLETTER
ooooooooooooooooooo ooooooo
ooooooo ooooooooo
ooooooooooooooooooooooooooooooooooo ooooooooooooooooo Fall 1972
ooooooooooooooooo oooooooooooooooo oooooooooooooooo
oooooooooooooooo oooooooooooooo oooooooooooooo
page 5</pre>
|-
| rowspan=3 |'''THE GAME OF LIFE'''

"the Game Of Life" (Scientific American, <s>November</s> October
1970) can be basically described as a set of rules which
determine the growth pattern of any given cell structure.
Hence, a particular cell structure may grow and multiply
with succeeding generations and another structure may
in fact die after several generations. The algorithms for
cell propogation have been applied to some serious
research projects dealing with human cell structure, but
they have also been used for recreational programming.

The Iverson Computer Science Club (group of high
school students which meets at SDL, Ottawa, Saturday
mornings) have applied the Game of Life to a cell structure
which approximates the SDL Logo. After 75
generations the logo has grown to (and stabilized at) the
cell structure pictured below.

<center>{{LV:Viewer|{{LifeViewer config/lifeline|zoom=24|width=73|height=36}}
#C [[ THUMBSIZE 3 ]]
#C [[ STARTFROM 75 ]]
#C [[ X 5.5 Y -2 ]]
#C [[ ZOOM 5 ]]
3b29o3b4o$b33ob4o$39o$4o27b8o$16o2b4o10b7o$b16ob4o10b7o$3b19o10b7o$15b
7o9b9o$35ob17o$17ob16o3b16o$16o2b14o7b14o!
|[[File:Lifeline_vol08_601.png]]
}}</center>

Since the logo symbolically represents SDL as a company
it's interesting to speculate what this new structure
might represent. If you have any ideas we would like to
hear from you.

If you would like a free copy of the program and instructions
on how to apply it to your corporate symbol
please contact Dot Romhild, Secretary, Customer Service
and Education, Ottawa. Your Board of Directors
might be interested in a look into the future.
! style="text-align:left" |
Excursions Into the Universe
of [[OCA:3-4 Life|'3-4' Life]] . . .
|-
|
The following period two
oscillators all operate by
having four '[[rotor|active bits]]'
vibrating around respectively
three, six, and nine [[stator|stable
bits]].
|-
|
III by Tom Webster
of La Mesa, Ca.

<center>{{LV:Viewer|{{LifeViewer config/lifeline|zoom=30|width=20|height=10}}
#C [[ THUMBSIZE 3 ]]
#C [[ GRIDMAJOR 10 ]]
#C [[ AGESTATES 1 ]]
#C [[ COLOR BACKGROUND White ]]
#C [[ COLOR ALIVE Black ]]
#C [[ COLOR ALIVERAMP Gray ]]
#C [[ STARTFROM 2 ]]
<nowiki>
x = 20, y = 10, rule = B34/S34
3$5bo8bo$3bobo9b2o$4b3o6b3o$4bo10bo!
</nowiki>
|[[File:Lifeline_vol08_602.png]]
}}</center>

VI by Anonymous
of L.A., Ca.

<center>{{LV:Viewer|{{LifeViewer config/lifeline|zoom=30|width=20|height=10}}
#C [[ THUMBSIZE 3 ]]
#C [[ GRIDMAJOR 10 ]]
#C [[ AGESTATES 1 ]]
#C [[ COLOR BACKGROUND White ]]
#C [[ COLOR ALIVE Black ]]
#C [[ COLOR ALIVERAMP Gray ]]
#C [[ STARTFROM 2 ]]
<nowiki>
x = 20, y = 10, rule = B34/S34
3$4b2o8b2o$2b2obo8bob2o$3bob2o6b2obo$3b2o10b2o!
</nowiki>
|[[File:Lifeline_vol08_603.png]]
}}</center>

IX ('cluster')
by [[David Buckingham|Buckingham]]

<center>{{LV:Viewer|{{LifeViewer config/lifeline|zoom=30|width=20|height=10}}
#C [[ THUMBSIZE 3 ]]
#C [[ GRIDMAJOR 10 ]]
#C [[ AGESTATES 1 ]]
#C [[ COLOR BACKGROUND White ]]
#C [[ COLOR ALIVE Black ]]
#C [[ COLOR ALIVERAMP Gray ]]
#C [[ STARTFROM 2 ]]
#C [[ Y 1 ]]
<nowiki>
x = 20, y = 10, rule = B34/S34
3$4b2o8b2o$2b2obo8bob2o$2bobobo6bobobo$3bob2o6b2obo$3b2o10b2o!
</nowiki>
|[[File:Lifeline_vol08_604.png]]
}}</center>
|}

====Page 7====
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{| class="wikitable" style="text-align:left"
|+ style="text-align:left" |Reader Reply . . .
|-
|'''Reregarding the '[[Titanic toroidal traveler|Titanic Troidial Traveler]]' by David Buckingham'''

In Lifelines [[Lifeline Volume 4|4]] & [[Lifeline Volume 7|7]] the second 'Titanic Troidial Traveler was
mentioned but was not given a proven census or period. The
debris however, even though never becoming periodic, quickly
develops into a [[pentadecathlon]] [[agar]], which can exist on a
6 x N torus.

It has been noted by David Buckingham and Mark Niemiec that a
pentadec/2 expands indefinitely with a speed of almost C/5 in
both directions. This idea can also be increased to create another
class of oscillating agars. Thus, the exhaust of the
TT II can never achieve a stable period. This idea is based
on the following ideas: first of all the TT II creates TL's
at the end which move in the direction opposite to the wick
and they themselves are spaceships. After working with the
pentadecathlon agars I have found that the only possible
products in the field are [[bi-block|twin blocks]] [[File:Lifeline_vol08_701.png]], beehives, blinkers,
and traffic lights and predicessors thereto. If the stable
debris is hit with a traffic light,or some form thereof, it
will eventually form a traffic light or die and therefore
will not form a stable centre. If the stable centre does not
form and the 2 part s of the wick move further and further
apart then more and more different debris forms.

A simple example which comes to mind is this: since the inside
(between the wick and the outer traffic light) will never
stabilize, it will behave as an infinitely expanding pentadecathlon
agar or the inside will die out. Therefore the wick
and traffic light will create traffic lights that move towards
each other causing a mutual annihalation which will
take an increasing number of generations to cause since the
wick and the outer traffic light will constantly move further
apart. I think that this concludes a proof that the second
TTT has no finite period but possibly someone might figure
out an exponential period for it.
|}

{| class="wikitable" style="text-align:left"
|+ style="text-align:left;" |Lifequote submitted by Mark Linimon of Houston, Tx:
|-
|'Life is one long process of getting tired.'

<div style='text-align: right;'>. . . Samuel Butler</div>
|}

'''LIFE SAVER'''

{| style="text-align:center"
| style="padding-right: 1em;" |LIFELINE back issue and subscription rates:
| style="padding-left: 1em;padding-right: 1em;" | U.S. & Canada
| style="padding-left: 1em;padding-right: 1em;" | Foreign
|-
| style="padding-left: 2em;padding-right: 1em;text-align:left" |1971 (Nos. 1-4) 70 pages total, per set
| $10 || $15
|-
| style="padding-left: 2em;padding-right: 1em;text-align:left" |1972 (Nos. 5-8) 32 pages total, per set
| $4 || $6
|-
| style="padding-left: 2em;padding-right: 1em;text-align:left" |1973 (Nos. 9-12) new subscription
| $2 || $3
|}

====Page 8====
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{| class="wikitable" style="text-align:left"
|+ style="text-align:left" |Reader Reply . . .
|-
! colspan=8 |Regarding Those 'Titanic Toroidal Travelers' by [[Bill Gosper|R. Wm. Gosper, Jr.]]
|-
| colspan=8 |
The smoke puff emitted by A (see diagram below) before it becomes a
spaceship is itself a puffer train equivalent to several B with
different ages and displacements. Following one of these, calling
C generation zero, we find a complex, nonperiodic puffer expanding
in both directions at 7C/40 which consists of merely two C's whenever
generation = 200x2exp.n. Two of those out of phase with each
other will repeatedly react, causing their wave fronts to occasionally
lurch forward at 9C/46, apparently at ever decreasing frequency.

D moves at C/2, sends the same pattern in the opposite direction,
and fills the intervening space with C's of various ages (mind
boggling complexity).
|- style="vertical-align: top"
| style="border:none" |A
| style="border:none" |{{LV:viewer|{{LifeViewer config/lifeline|zoom=64|width=10|height=6}}
#C [[ THUMBSIZE 4 ]]
#C [[ X 0 ]]
<nowiki>
x = 6, y = 2, rule = B3/S23:T6,0
6o$3o!
</nowiki>
|[[Image:Lifeline_vol08_801.png]]
}}
| style="border:none" |B
| style="border:none" |{{LV:viewer|{{LifeViewer config/lifeline|zoom=64|width=10|height=6}}
#C [[ THUMBSIZE 4 ]]
#C [[ X 0 ]]
<nowiki>
x = 6, y = 2, rule = B3/S23:T6,0
3o$bo!
</nowiki>
|[[Image:Lifeline_vol08_802.png]]
}}
| style="border:none" |C
| style="border:none" |{{LV:viewer|{{LifeViewer config/lifeline|zoom=64|width=10|height=7}}
#C [[ THUMBSIZE 4 ]]
#C [[ X 0 ]]
<nowiki>
x = 6, y = 3, rule = B3/S23:T6,0
3o$obo$3o!
</nowiki>
|[[Image:Lifeline_vol08_803.png]]
}}
| style="border:none" |D
| style="border:none" |{{LV:viewer|{{LifeViewer config/lifeline|zoom=64|width=16|height=7}}
#C [[ THUMBSIZE 4 ]]
#C [[ X 0 ]]
<nowiki>
x = 12, y = 3, rule = B3/S23:T12,0
3o3b3o$o2bobo2bo$o7bo!
</nowiki>
|[[Image:Lifeline_vol08_804.png]]
}}
|}

Lifecomic by Harry J. Riley of Trenton, N.J.

[[Image:Lifeline_vol08_805.png|600px|take me to your leader!]]

{| class="wikitable" style="text-align:left"
|+ style="text-align:left" |Lifequote:
|-
|'One way to get the most out of Life is to look upon it as an adventure'.

<div style='text-align: right;'>. . . William Feather</div>
|}

'''COMING EVENTS:'''

* some amazing pi-heptomino reactions
* a host of clock predecessors
* a new period thirty shuttle device
* a period nine billiard tab le construction
* 'healthy patterns' that eradicate foreign implanted bits
* a brand new series of 12n period puffer trains!
* [[Lifeline Volume 9|LIFELINE Number Nine]] will be issued on schedule in March

Yes, I would like to continue receiving LIFELINE. I am subscribing
for my 1973 subscription as a:

: ▢Regular member (now encloing payment)
: ▢Participating member (will contribute to newsletter)

My correct mailing address is: 
Name:_________________________________________________________________ 
Address:______________________________________________________________ 
City:_______________________________State:_______________Zip:_________

==Page Scans==
<gallery>
Image:Lifeline_vol_8.png|Page 1
Image:Lifeline_vol_8_p2.jpg|Page 2
Image:Lifeline_vol_8_p3.jpg|Page 3
Image:Lifeline_vol_8_p4.jpg|Page 4
Image:Lifeline_vol_8_p5.jpg|Page 5
Image:Lifeline_vol_8_p6.jpg|Page 6
Image:Lifeline_vol_8_p7.jpg|Page 7
Image:Lifeline_vol_8_p8.jpg|Page 8
</gallery>

IceNine

2024-05-05T20:19:46Z

C7X: /* Notes */

{{Glossary}}{{about|a hypothetical unstoppable quadratic growth pattern|a Life-like rule|OCA:Iceballs}}
'''IceNine'''{{refn|group=note|The name is a reference to the [https://en.wikipedia.org/wiki/Ice-nine chemical of the same name] in the novel ''[https://en.wikipedia.org/wiki/Cat's_Cradle Cat's Cradle]'' by [https://en.wikipedia.org/wiki/Kurt_Vonnegut Kurt Vonnegut], with similar properties to the hypothetical pattern. It is not related to [https://en.wikipedia.org/wiki/Ice_IX Ice IX], a metastable form of solid water.}} is [[Dave Greene]]'s name for a hypothetical unstoppable [[quadratic growth]] pattern that expands outward through random [[ash]] at [[speed]] c/137, described as follows in a tongue-in-cheek post in February {{year|2008}}:

{{Cquote|Aha! You and your intuition have clearly not been exposed to the IceNine Agar, found recently with an alternate-universe oscilloscope:

<pre>#C IceNine seed -- currently this is the smallest sample
#C for which no external conditions have yet been found
#C that prevent long-term quadratic growth
x = 2718, y = 4669, rule = B3/S23
<<<Server notice from fermat.yahoo.com:
11.9MB nonstandard text removed from message
Please notify sender of potential virus threat>>></pre>

Every sufficiently large and ancient B3/S23 universe observed so far turns out to be full of this weird agar, which expands in all directions through random ash at c/137. IceNine seems to absorb blocks and blinkers particularly well, due to a complicated froth of sparks at its front lines -- not generated by glider collisions, but by a lucky accident of the agar's internal structure.

When the expanding front touches an active pattern that it can't immediately annihilate, the pattern "dies back" a short distance at near lightspeed, leaving behind a protective scattering of blocks; behind the blocks the front stabilizes and starts expanding again. Converging IceNine fronts usually cause small diebacks that stabilize as small defects in an apparent quasicrystalline structure.

And before you all ask, my alternate-universe oscilloscope was repossessed by the Outsiders the other day, so unfortunately I can't lend it out. But there didn't seem to be anything but IceNine out there anyway --}}

He went on to further characterize IceNine as follows:

{{Cquote|The IceNine I tried to describe doesn't have a memory per se, any more than a cell's DNA knows the position of every lipid molecule in its cell wall. It's an active, growing agar with lots of edge sparks that just happen to annihilate nearby gliders and still lifes unusually efficiently. Along with several other utterly improbable properties. Basically it's the spacefiller that wins the Survival of the Fittest Award in an infinite Life universe, and it's about as likely as the proverbial tornado in a junkyard building a jumbo jet.}}

It is generally agreed that a pattern exhibiting the characteristics of IceNine cannot exist in [[Conway's Game of Life]], but a formal proof remains elusive. However, mechanisms that a replicator could implement to clear random ash fields with a similar "dying back" process to the one described by Greene to act as a failsafe have been proposed and have been demonstrated to work with greater than 50% odds of success.<ref name="post136948" />

==Notes==
<references group="note" />

The coefficient <tt>1/137</tt> is likely a reference to the {{LinkWikipedia|Fine-structure_constant|name=fine-structure constant|nobullet=nobullet|nosuffix=nosuffix}}, a physical constant independent on the system of units in which it is measured. It was thought to be exactly <tt>1/137</tt>, but more accurate measurements have found its denominator to be more precisely <tt>137.035999206</tt>. (See {{OEIS|A005600}}.)</ref>

The dimensions <tt>x = 2718</tt> and <tt>y = 4669</tt> of the omitted [[RLE|RLE file]] are likely references to {{LinkWikipedia|Euler's_constant|name=Euler's constant|nobullet=nobullet|nosuffix=nosuffix}} and {{LinkWikipedia|Feigenbaum's_constant|name=Feigenbaum's constant|nobullet=nobullet|nosuffix=nosuffix}} respectively.

==References==
<references>
<ref name="post136948">{{LinkForumThread
|format = ref
|title = Re: Clearing Ash
|p = 136948
|author = mscibing
|date = October 23, 2021
}}</ref>
</references>

==External links==
* {{LinkForumThread|p=293|title=Re: Stable Life?|author=Adam P. Goucher|date=June 13, 2009}}

[[Category:Jokes]]

Mirage

2024-05-05T20:10:26Z

C7X:

{{Pattern
|name = Mirage
|pname = mirage
|c = 331
|bx = 68
|by = 46
|plaintext = true
|rle = true
|type = Spark
|viewerconfig = #C [[ THUMBSIZE 2 GPS 15 ]]
}}
'''Mirage''' (or '''Fata Morgana''') is a [[pure glider generator]] in which many sparse [[cell]]s quickly create 13 [[glider]]s. Eight of those gliders [[glider synthesis|construct]] a [[Gosper glider gun]] at [[generation]] 34, but the remaining five destroy the [[gun]] by generation 73.<ref>[[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifep.zip] pattern collection.</ref>

Similar patterns based on other glider syntheses can be constructed.<ref name="post12923" />

{|style="margin:auto;width:320px;"
|{{EmbedViewer
|pname = mirage2
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 15 ]]
|caption = A sparse variant of mirage constructed by [[wwei23]] in 2017
}}
|}

==References==
<references>
<ref name="post12923">{{LinkForumThread
|p = 12923
|format = ref
|title = Re: Pure Glider Generators
|author = Bob Shemyakin
|date = August 17, 2014
}}</ref>
</references>

[[Category:Sparks]]

Mirage

2024-05-05T20:09:36Z

C7X: Pattern dies at generation 73

{{Pattern
|name = Mirage
|pname = mirage
|c = 331
|bx = 68
|by = 46
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 2 GPS 15 ]]
}}
'''Mirage''' (or '''Fata Morgana''') is a [[pure glider generator]] in which many sparse [[cell]]s quickly create 13 [[glider]]s. Eight of those gliders [[glider synthesis|construct]] a [[Gosper glider gun]] at [[generation]] 34, but the remaining five destroy the [[gun]] by generation 73.<ref>[[Alan Hensel]]'s [http://www.ibiblio.org/lifepatterns/ lifep.zip] pattern collection.</ref>

Similar patterns based on other glider syntheses can be constructed.<ref name="post12923" />

{|style="margin:auto;width:320px;"
|{{EmbedViewer
|pname = mirage2
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 15 ]]
|caption = A sparse variant of mirage constructed by [[wwei23]] in 2017
}}
|}

==References==
<references>
<ref name="post12923">{{LinkForumThread
|p = 12923
|format = ref
|title = Re: Pure Glider Generators
|author = Bob Shemyakin
|date = August 17, 2014
}}</ref>
</references>

[[Category:Sparks]]

Speed Demonoid

2024-05-05T04:48:26Z

C7X:

{{Spaceship
|name = Speed Demonoid
|pname = speeddemonoid
|c = 1021124
|bx = 872867
|by = 1839173
|dir = Diagonal
|p = 17833792
|m = 8916896
|s = 1746011c/8916896
|z = 3492022c/17833792
|discoverer = Pavel Grankovskiy
|discoverer2 = Dave Greene
|discoveryear = 2020
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|mc = true
|synthesis = 31822
}}
'''Speed Demonoid''' is a self-constructing [[adjustable spaceship]] constructed by [[Pavel Grankovskiy]] with the help of [[Dave Greene]] and completed on September 18, {{year|2020}}.<ref name="post104423" />

Due to a limitation in the design, this initial version of the Speed Demonoid design has an upper limit speed of 2c/9 diagonally, rather than the theoretical maximum of c/4. A redesign of the circuitry was required to correct this limitation.

Below the 2c/9 upper limit, the Speed Demonoid can be adjusted to move at any rational speed, by moving the trailing TRIGGER1 and TRIGGER2 gliders to the correct locations.

On September 26, a new Speed Demonoid variant was constructed to be smoother to simulate in [[HashLife]], and to improve on the 2c/9 upper speed limit mentioned above.<ref name="post104931" /> Speed Demonoid v2 can be trivially adjusted to move at any speed that is a rational fraction number than c/4. A [[Golly]] 3.x/4.0 script is available that will set up a glider recipe to construct a Speed Demonoid for any chosen speed, within certain practical size limitations.<ref name="post108786" />

The {{POTY|year=2020|rank=1|tie=[[Bandersnatch]]}}

== Details ==
The Speed Demonoid achieves its speed by building a [[crab]] spaceship and turning it into a double [[wickstretcher]]. The two wicks are ignited at different times specified by the locations of the TRIGGER1 and TRIGGER2 gliders. With the help of "guard gliders" traveling near the crab spaceship, when the burning wicks reach the crab, they produce target objects at the right location to allow the next copy of the construction-arm and reflector circuitry to be constructed. The TRIGGER1 guard glider allows the fuse to stop burning while the crab spaceship continues onward, and continues stretching the second wick. By contrast, the TRIGGER2 guard glider enables the destruction and eventual complete cleanup of the crab spaceship.

Both TRIGGER1 and TRIGGER2 are precisely synchronized so that they exactly keep up with the recipe gliders, despite being on different lanes and using [[one-time]] [[turner]]s to move instead of conventional [[reflector]]s. Besides igniting the second crabstretcher wick, the TRIGGER2 signal also triggers [[self-destruct circuit]]ry associated with the [[Scorbie Splitter]] and [[Snark]].

The bait still lifes in the self-destruct circuitry were found by Simon Ekström's GoL-destroy search program. A similar design was used in the 10hd and 0hd Demonoids, but has been seen very rarely since then. Other recent Demonoids have used "destruction arms" similar to the one in the original [[Gemini]] spaceship, which incrementally shoot down parent constructor circuitry once it is no longer in use.

== References ==
<references>
<ref name="post104423">{{LinkForumThread
|format = ref
|title = Re: Speed Demonoid (completed)
|p = 104423
|author = Pavel Grankovskiy
|date = September 18, 2020
}}</ref>
<ref name="post104931">{{LinkForumThread
|format = ref
|title = Re: Speed Demonoid
|p = 104931
|author = Pavel Grankovskiy
|date = September 26, 2020
}}</ref>
<ref name="post108786">{{LinkForumThread
|format = ref
|title = Re: Speed Demonoid
|p = 108786
|author = Dave Greene
|date = November 1, 2020
}}</ref>
</references>

[[Category:Glide symmetric spaceships]]
[[Category:Non-monotonic_spaceships]]

Superfountain

2023-02-02T09:14:35Z

C7X:

{{Oscillator
|name = Superfountain
|pname = superfountain
|c = 278
|bx = 46
|by = 25
|p = 4
|m = 4
|h = 151.5
|v = 0.63
|sv = 0.58
|discoverer = Noam Elkies
|discoveryear = 1998
|rulemin = B3/S23
|rulemax = B38/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B37c8/S234c6n7c
|plaintext = true
|rle = true
|animated = true
|apgcode = xp4_okox62s0c4530g8k4871wggmk9b88bl4mgei4ozhn204c68331dd2s34lrco4ghmkk2bb40118q3uhm871zvrwra0ahha4ehvea08821p206w67872278a6zht8046c2oogmm870s3qjlm8brz353xc87064kox146w32
|viewerconfig = #C [[ GPS 2 ZOOM 10 LOOP 4 ]]
}}
'''Superfountain''' is a {{period|4}} [[sparker]] that was found in February {{year|1998}} by [[Noam Elkies]], shown here with a slightly smaller [[stator]] than in its original form. Its name derives from the fact that its lone [[spark]] is more isolated than the lone spark in [[fountain]].

A smaller variant of superfountain, found by [[Nicolay Beluchenko]] in 2006:<ref>Life Lexicon, accessed 2 February 2023.</ref>

{{EmbedViewer
|rle = x = 23, y = 18, rule = B3/S23
11bo3$5bo2bo5bo2bo$3b2o2bob5obo2b2o$5bo11bo$3bob2o9b2obo$bobo3b3o3b3o
3bobo$3obo13bob3o$10bobo$4b3o3bobo3b3o$4bo2bo3bo3bo2bo$3b4o2bobobo2b4o
$3b2o2b3obob3o2b2o$2bo3bo3bobo3bo3bo$3bo2bobobobobobo2bo$4bobob2o3b2ob
obo$5bo11bo!
|viewerconfig = #C [[ GPS 4 ZOOM 14 AUTOSTART T 0 LOOP 4 ]]
|position = center
|style = width:300px;
}}
==References==
<references />
==External links==
{{LinkLexicon|lex_s.htm#superfountain}}
{{LinkCatagolue|xp4_okox62s0c4530g8k4871wggmk9b88bl4mgei4ozhn204c68331dd2s34lrco4ghmkk2bb40118q3uhm871zvrwra0ahha4ehvea08821p206w67872278a6zht8046c2oogmm870s3qjlm8brz353xc87064kox146w32}}
{{Sparker|p=4|type=dot|strength=strong}}

Sidewalk

2022-11-04T04:26:12Z

C7X: Undo revision 117510 by C7X (talk)

{{Stilllife
|name = Sidewalk
|pname = sidewalk
|c = 14
|bx = 6
|by = 5
|fc = 23.6
|rulemin = B/S23
|rulemax = B3678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S2aek3nr
|isorulemax = B2-ac34-aikr5-r678/S012345678
|synthesis = 4
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs14_1no3tg
|niemiecid = 14.507
|pentadecathlonid = 14.43
}}
'''Sidewalk''' (or '''pavement''') is a {{slcells|14}}-[[cell]] [[still life]] made up of two [[island]]s that are by themselves referred to as '''sides'''. An individual side can occasionally be useful as an [[induction coil]].

{|
|-
|[[File:Side.png|framed|A side]]
|{{EmbedViewer
|pname = presidewalk
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 4 HEIGHT 480 ZOOM 64 GPS 1 PAUSE 4 T 2 PAUSE 4 LOOP 3 ]]
|caption = A sidewalk [[predecessor]]. 
|}}
|}

== [[List of common still lifes|Commonness]] ==
It is the thirty-sixth most common object on [[Catagolue]] in the symmetry the object has (C2_2). In asymmetric soups, it is the 150th most common still life.

== [[Glider synthesis]] ==
[[Peter Raynham]] found a {{gliders|4}} synthesis for the still life in {{year|1973}}, which is based on a head-to-head collision between two [[pi-heptomino]]es.<ref>{{CiteLifeline|vol=10|pages=page 2}}</ref>

== See also ==
* [[Eater 1]]
* [[Eleven loop]]
* [[Mango]]
* [[Cthulhu]]

== References ==
<references />

== External links ==
{{LinkLexicon|filename=lex_s.htm#sidewalk}}
{{LinkLexicon|file=lex_s.htm#side|name=Side|accessdate=June 11, 2009}}
{{LinkCatagolue|xs14_1no3tg}}
{{LinkNiemiec|p1-14.htm|patternname=The 619 fourteen-bit still-lifes}}

{{Symmetry|180degree}}

__NOTOC__

Sidewalk

2022-11-04T04:26:00Z

C7X:

{{Stilllife
|name = Sidewalk
|pname = sidewalk
|c = 14
|bx = 6
|by = 5
|fc = 23.6
|rulemin = B/S23
|rulemax = B3678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S2aek3nr
|isorulemax = B2-ac34-aikr5-r678/S012345678
|synthesis = 4
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs14_1no3tg
|niemiecid = 14.507
|pentadecathlonid = 14.43
}}
'''Sidewalk''' (or '''pavement''') is a {{slcells|14}}-[[cell]] [[still life]] made up of two [[island]]s that are by themselves referred to as '''sides'''. An individual side can occasionally be useful as an [[induction coil]].

{|
|-
|[[File:Side.png|framed|A side]]
|{{EmbedViewer
|pname = presidewalk
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 4 HEIGHT 480 ZOOM 64 GPS 1 PAUSE 4 T 2 PAUSE 4 LOOP 3 ]]
|caption = A sidewalk [[predecessor]] composed of two [[Pi-heptomino|pi heptominoes]]. 
|}}
|}

== [[List of common still lifes|Commonness]] ==
It is the thirty-sixth most common object on [[Catagolue]] in the symmetry the object has (C2_2). In asymmetric soups, it is the 150th most common still life.

== [[Glider synthesis]] ==
[[Peter Raynham]] found a {{gliders|4}} synthesis for the still life in {{year|1973}}, which is based on a head-to-head collision between two [[pi-heptomino]]es.<ref>{{CiteLifeline|vol=10|pages=page 2}}</ref>

== See also ==
* [[Eater 1]]
* [[Eleven loop]]
* [[Mango]]
* [[Cthulhu]]

== References ==
<references />

== External links ==
{{LinkLexicon|filename=lex_s.htm#sidewalk}}
{{LinkLexicon|file=lex_s.htm#side|name=Side|accessdate=June 11, 2009}}
{{LinkCatagolue|xs14_1no3tg}}
{{LinkNiemiec|p1-14.htm|patternname=The 619 fourteen-bit still-lifes}}

{{Symmetry|180degree}}

__NOTOC__

File:PiWord.GIF

2022-09-28T03:19:57Z

C7X: C7X uploaded a new version of File:PiWord.GIF

Pseudo-barberpole

2022-09-25T18:00:40Z

C7X: LifeViewer went fast

{{Oscillator
|name = Pseudo-barberpole
|pname = pseudobarberpole
|family = Barberpole
|c = 15
|bx = 12
|by = 12
|p = 5
|m = 5
|h = 16.8
|v = 0.82
|discoverer = Achim Flammenkamp
|discoveryear = 1994
|rulemin = B3/S23
|rulemax = B378/S235678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-eiky/S2-c3jn
|isorulemax = B2cn34-nqry5-aq6-n78/S234-jnz5678
|synthesis = 13
|synthesisRLE = true
|plaintext = true
|rle = true
|animated = yes
|apgcode = xp5_y2g0k413zwo0a02z32
|pentadecathlonid = 15P5.1
|viewerconfig = #C [[ GPS 2 ZOOM 20 LOOP 5 ]]
}}
The '''pseudo-barberpole''' (or '''Achim's p5'''<ref>{{CiteLexicon|file=lex_a.htm#achimsp5|name=Achim's p5|accessdate=December 3, 2018}}</ref>) is a {{period|5}} [[oscillator]] that was found by [[Achim Flammenkamp]] on August 22, {{year|1994}}.<ref name="hickerson" /> With a minimum population of {{cells|15|text=15 cells}}, it is the smallest known period 5 oscillator, followed by [[octagon 2]] with {{cells|16|text=16 cells}}.<ref name="niemiec_p5osc" /><ref name="pentadecathlon_class2" /> On October 23, {{year|2002}} [[Gabriel Nivasch]] found a period 5 oscillator that consists of four radially symmetrically arranged halves of the pseudo-barberpole.<ref name="summers_all-osc" />

== Commonness ==
{{main|List of common oscillators}}
As of July 2022, this is one of two 15-cell oscillators, and one of six 15-cell periodic objects (still lifes, oscillators and spaceships) which are yet to arise naturally from an asymmetric soup on [[Catagolue]], with the other oscillator being the [[nonapole]].<ref>{{LinkForumThread|t=5549|title=Small Unnatural Objects Watchlist|format=ref}}</ref>[[Category:Small unnatural periodic objects]]

== Glider synthesis ==
Goldtiger997 found a {{gliders|16}} [[Glider synthesis|synthesis]] based on a sample soup from [[Adam P. Goucher]]'s [[Catagolue]] on April 22, 2017.<ref name="goldtiger997_20170422" /> Martin Grant found an unrelated {{gliders|13}} synthesis that can also act as a component on June 20, 2018.<ref>{{LinkForumThread|f=2|t=1155|p=61175|title=Re: Synthesising Oscillators|format=ref}}</ref>

== Gallery ==
{|style="margin:auto;width:360px;"
|{{EmbedViewer
|pname = radialpseudobarberpole
|position = center
|viewerconfig = #C [[ GPS 3 THUMBSIZE 2 ]]
|caption = A radially symmetric relative of the pseudo-barberpole
}}
|}

== See also ==
* [[Barberpole]]
* [[Smallest period 5 oscillators]]
* [[Highest volatility period 5 oscillators]]

== References ==
<references>
<ref name="hickerson">{{CiteHickersonOscillators}}</ref>
<ref name="niemiec_p5osc">{{cite web
|url = http://codercontest.com/mniemiec/p5osc.htm
|title = Life Period-5 Oscillators
|author = Mark Niemiec
|date = 1998
|accessdate = February 15, 2009
}}</ref>
<ref name="pentadecathlon_class2">{{cite web
|url = https://web.archive.org/web/20210716141058/http://pentadecathlon.com/objects/class2/class2.php?part=1
|title = Class 2 Objects Catalog
|accessdate = March 14, 2009
}}</ref>
<ref name="summers_all-osc">{{CiteSummersPattern|name=all-osc}}</ref>
<ref name="goldtiger997_20170422">{{LinkForumThread
|p = 42887
|title = Re: Soup search results
|author = Goldtiger997
|date = 2017-04-22
|format = ref
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_p.htm#pseudobarberpole}}
* {{LinkCatagolue|xp5_y2g0k413zwo0a02z32}}
* {{LinkPentadecathlonObject|15P5.1}}

{{Symmetry|diagonal2}}
{{Sparker|p=5|type=domino|strength=moderate}}
{{seminatural}}
__NOTOC__

Oblique spaceship

2022-09-11T06:44:53Z

C7X:

{{Glossary}}
An '''oblique spaceship''' is a [[spaceship]] which moves neither orthogonally nor diagonally.

The simplest type is a [[knightship]], so called because it moves parallel to a knight in chess. By analogy with the corresponding [https://en.wikipedia.org/wiki/fairy_chess_piece fairy chess pieces], the following other terms may be used to designate spaceships with different [[slope]]s:

{| class="wikitable" style="margin-left: auto; margin-right: auto;"
|-
! Type
! Ship
! Movement
! Maximum speed (Life)
! Example
|-
| (2''m'',''m'')/''n''
| knightship
| knightwise
| (2,1)c/6
| [[Sir Robin]]*
|-
| (3''m'',''m'')/''n''
| camelship
| camelwise
| (3,1)c/8
| [[Camelship]]
|-
| (4''m'',''m'')/''n''
| giraffeship
| giraffewise
| (4,1)c/10
| ''none found''
|-
| (5''m'',''m'')/''n''
| ibisship
| ibiswise
| (5,1)c/12
| [[Gemini]]
|-
| (6''m'',''m'')/''n''
| flamingoship
| flamingowise
| (6,1)c/14
| ''none found''
|-
| (3''m'',2''m'')/''n''
| zebraship
| zebrawise
| (3,2)c/10
| ''none found''
|-
| (4''m'',3''m'')/''n''
| antelopeship
| antelopewise
| (4,3)c/14
| ''none found''
|-
! colspan="5" | ...
|-
| (23''m'',5''m'')/''n''
|
|
| (23,5)c/56
| [[waterbear]]
|-
|}
<nowiki>*</nowiki>''Spaceship is elementary''

A full list of spaceships in Life can be seen at [[List of spaceships]]. Further spaceships in arbitrary isotropic non-totalistic rules are catalogued at [[LifeWiki:Smallest Spaceships Supporting Specific Speeds|the 5s project]]; these can be emulated to produce a spaceship with equivalent [[slope]] in Life using the [[0E0P metacell]], but no examples have been explicitly constructed yet.

==History==
In 1982, Berlekamp showed that there must exist spaceships of any given rational slope in Life, although no explicit oblique examples were constructed.<ref>D. Eppstein, [https://arxiv.org/pdf/cs/0004003.pdf Searching for Spaceships] (2000, p.4). Accessed 11 September 2022.</ref> The first oblique spaceship was [[Andrew Wade]]'s ibisship [[Gemini]], based on the [[Chapman-Greene construction arm]].<ref name="post141232" /> [[Dave Greene]] proceeded to build variants, called [[Geminoid]]s, travelling in a variety of directions.

In early 2014, a collaborative effort was launched to build a [[half-baked knightship]], which translates itself by (6, 3) each period and is therefore a knightship. [[Chris Cain]] optimised the construction to yield a smaller and faster [[parallel HBK]].

In December {{year|2014}}, [[Brett Berger]] constructed the first fast oblique spaceship in Conway's Game of Life, the [[waterbear]], moving at a velocity of (23,5)c/79. It has a bounding box very slightly smaller than the [[parallel HBK]]. With a period of 158, it is the lowest-period oblique spaceship other than [[Sir Robin]].

In March 2018, [[Adam P. Goucher]] and [[Tomas Rokicki]] discovered [[Sir Robin]], the first elementary oblique ship. It is the fastest knightship and lowest-period oblique ship possible, and also the smallest known oblique ship.

In December 2018, [[Chris Cain]] completed a new diagonal loop design for a small-step oblique spaceship, a true [[camelship]] with a (3,1) step size in each cycle instead of the (3072,1024) step distance of the [[Gemini 3|adjusted Gemini]] spaceship.

==Other rules==
[[File:Pedestrianlife oblique spaceship.png|framed|right|(5,2)c/190 oblique spaceship in [[Pedestrian Life]] (B38/S23)]]

Many automata extremely similar to Life have oblique ships and related technology. For example, [[Pedestrian Life]] has a naturally-occuring family of (5,2)c/190 ships, as well as a natural (101,3)c/1884 puffer; [[tDryLife]] has a slope 3 ship puffer that can be stabilized into a spaceship.

These natural spaceships and puffers are qualitatively different from any in Life, which are either large engineered constructions or, in the case of [[Sir Robin]], the result of extensive computer search.

==See also==
* [[Knightship]]
* [[Types of spaceships]]

==External links==
{{LinkLexicon|lex_o.htm#oblique|name=Oblique}}

==References==
<references>
<ref name="post141232">{{LinkForumThread
|accessdate = February 4, 2022
|date = February 4, 2022
|format = ref
|title = Re: Thread for basic questions
|author = Dave Greene
|p = 141232
}}</ref>
</references>

Talk:Spaceships in Conway's Life

2022-09-08T19:06:13Z

C7X:

I think "External links" would be most appropriate here -- I'd generally use "Further Reading" for offline(ish) resources, like books and magazine/journal articles. "References" is more for citations. [[User:Apple Bottom|Apple Bottom]] ([[User talk:Apple Bottom|talk]]) 09:28, 18 February 2018 (UTC)

==File upload==
Is there a way to upload the files onto this wiki in case the external link goes down in the future? [[User:C7X|C7X]] ([[User talk:C7X|talk]]) 19:06, 8 September 2022 (UTC)

Lifeline Volume 2

2022-09-08T19:03:12Z

C7X: Spelling from scan

__NOTOC__{{LifeLine|vol=2|date=June 1971}}

<center><pre>A QUARTERLY NEWSLETTER FOR ENTHUSIASTS OF JOHN CONWAY'S GAME OF LIFE

O OOOOO OOOOO OOOOO O OOOOO O O OOOOO
O O O O O O OO O O
O O OOO OOO O O O O O OOO
O O O O O O O OO O
OOOOO OOOOO O OOOOO OOOOO OOOOO O O OOOOO

Number 2 JUNE 1971</pre>

• Editor and Publisher: [[Robert T. Wainwright]] •</center>

====Page 1====
The response to [[Lifeline|LIFELINE]] Number One and Martin Gardner's announcement in the April issue of ''Scientific American'' regarding this endeavor has been overwhelming! More than 340 inquiries have been received from readers in many industrial organizations, schools, and universities in fourteen different countries - and mail is still flowing in. The administrative burden accounts for what may seem to some of you (especially the early respondents) an indifference on my part. Following the establishment of a mailing list of subscribers, I will attempt to answer many of your individual inquiries via LIFELINE, an informal but relatively rapid and specific response to your area of interest.

LIFELINE Number Two extends and refines the ideas presented in the first issue and incorporates information from many of your responses. The main objective of this issue is to further the base of classification and common definition using your own developments as examples.

The fates of the unknown [[heptomino]]es E, F, H, and I were first sent in by Robert Bison of Hopewell Jct., N.Y. and subsequently confirmed by David W. Bray of Syracuse, N.Y., [[Charles Corderman|Charles L. Corderman]] of Winchester, Mass., Gary Goodman of Stanford, Calif., Stephen B. Gray of Los Angeles, Calif., Maxwell E. Manowski of New York (FPO), and [[Don Woods]] of Natick, Mass. The histories and final '[[census]]' (an apt term coined by Woods) of these four interesting Life objects are shown here:

{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! colspan="3" | Fates of the last four unknown heptominoes
|-
! Heptomino
! Age
! Census
|-
| E
| 343
| 5 [[block]]s, 4 [[beehive]]s, 1 [[blinker]], and 1 [[glider]]
|-
| F
| 437
| 3 blocks, 1 [[tub]], 1 [[boat]], 1 beehive, 1 [[pond]], 7 blinkers (1 + 3/4 [[traffic light|traffic lts.]]), and 1 glider
|-
| H and I
| 247
| 3 blocks, 1 boat, 1 beehive, 1 ship, and 2 gliders
|}

To save unnecessary effort on the part of those receiving [[Lifeline Volume 1|issue Number One]] later than April, I appended a note to the effect that these results were known. Like seven other heptominoes (No. 1, Table 2), they all give birth to one or more gliders during their history. Interestingly, the direction of glider escape in all cases is to the northeast from the initial positions originally shown.

With many more objects being discovered in Classes I, II, and V it becomes tempting to subclassify them within the system proposed in issue Number One. The writer had previously arranged all Life objects into six primary classes based upon characteristics of their history and now proposes further definition (subclassification).

====Page 2====
{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! colspan="6" | AN EXPANDED CLASSIFICATION SYSTEM FOR FINITE LIFE OBJECTS
|-
! Primary Class
! colspan="2" | Subclassified According To:
! Subclass
! Example*
! Size
|-
| rowspan="8" | I-[[Still life|Still Lifes]]
| rowspan="8" | Degree of symmetry
| 2-way orthogonal, 2-way diagonal, 90° rotational
| I.A
| block
| 4
|-
| 2-way orthogonal, 180° rotational
| I.B.1
| beehive
| 6
|-
| 2-way diagonal, 2-way diagonal, 90° rotational
| I.B.2
| ship
| 6
|-
| 90° rotational
| I.B.3
| [[spiral]]
| 20
|-
| 1-way orthogonal
| I.C.1
| [[hat]]
| 9
|-
| 1-way diagonal
| I.C.2
| boat
| 5
|-
| 180° rotational
| I.C.3
| [[snake]]
| 6
|-
| none
| I.D
| [[eater 1|fishhook]]
| 7
|-
| rowspan="6" | II-[[Oscillator]]s
| rowspan="6" | Type of periodic activity
| [[flip-flop]]s (all period two)
| II.A
| blinker
| 3
|-
| [[billiard table configuration]]s
| II.B
| [[pinwheel]]
| 35
|-
| inductors
| II.C
| [[tumbler]]
| 16
|-
| pulsators
| II.D
| [[pentadecathlon|pentadecathalon]]
| 12
|-
| [[shuttle]]s
| II.E
| [[queen bee shuttle|queen bee]]
| 20
|-
| miscellaneous
| II.F
| [[cuphook|M.I.T. osc.]]
| 18
|-
| rowspan="2" | III-[[Spaceship]]s
| rowspan="2" | Motion of spaceship
| orthogonal
| III.A
| [[lightweight spaceship|lt.wt.s.s.]]
| 8
|-
| diagonal
| III.B
| [[glider]]
| 5
|-
| rowspan="2" | IV-Propagators
| rowspan="2" | Nature of activity
| [[gun|spaceship guns]]
| IV.A
| [[Gosper glider gun|the Gun]]
| 36
|-
| [[puffer|puffer trains]]
| IV.B
| ?
| ?
|-
| rowspan="7" | V-Unstable (all objects not in above)
| rowspan="7" | Final census
| dies (Θ)
| V.A
| [[bit]]
| 1
|-
| Class I
| V.B
| [[pre-block|latent block]]
| 3
|-
| Class II
| V.C
| blinker pred.
| 4
|-
| Class III
| V.D.1
| [[R-pentomino]]
| 5
|-
| Class III (only)
| V.D.2
| glider pred.
| 5
|-
| Class IV
| V.E
| Gun pred.
| 26
|-
| unknown
| V.F
| [[acorn]]**
| 7
|-
| colspan="6" | * smallest known object (for Classes II, III, IV - minimum phase)
|-
| colspan="6" | ** 'apparently' unknown - see text, page six
|}

====Page 3====
A modified classification system is presented on page two which attempts to recognize the specific, key characteristics of finite Life objects of each class. The examples shown represent, for each subclass, the smallest object (minimum number of bits) known to the writer. Most examples given are well known and have been previously described in either ''Scientific American'' or LIFELINE Number One. Those that are new are described in this newsletter. If anyone knows of smaller objects than any of these I will publish them in the next issue.

In general the number of new Class I objects reported is too large and common to mention. The '[[spiral]]' was suggested by the writer merely to provide an example of a small Class I.B.3 object since none had previously been mentioned. The '[[hat]]' a name given by [[Charles Corderman|Corderman]] and known by several other readers can be used to construct larger stable forms and is probably the smallest Class I.C.1 object. Class I.D objects exhibiting no symmetry whatsoever are the least common.

[[Image:Lifeline_vol02_fig01.png|framed|center|Some interesting examples of [[still life]] symmetry Left to right: [[Hat]], [[Eater 1|Fishhook]], [[Spiral]], [[Shillelagh]], [[tub with tail|Tub w/tail]]]]

The '[[eater 1|fishhook]]', a name independently coined by Clement A. Lessner III of W. Lafayette, Ind. and William P. Webb of San Rafael, Calif., was sent in by a number of readers and certainly must be the smallest possible nonsymmetrical still life. The two made of eight bits were given by Corderman and Hugh Thompson of Lefrak City, N.Y., who suggested the name '[[shillelagh]]'.

[[Image:Lifeline_vol02_fig02.png|framed|right|The hustler]] Many Class II.A objects were reported, again too numerous and common to mention. Class II.B objects are fairly easy to develop starting with an empty m by n area (billiard table) bounded by '[[induction coil|inductor coils]]' and experimenting with various random patterns within. But if one excludes [[period]] two oscillators from this subclass, only a few are known. Other than the familiar [[Hertz oscillator]] (period eight) and [[pinwheel]] (period four) only the '[[hustler]]' of an uneven period of three shown here has been added to this subclass. Note the now familiar fishhook used as an inductor coil for the crooked sides of the billiard table. Classes II.C and II.D are very uncommon and to date no one has reported anything new in either of these groups.

====Page 4====
[[Image:Lifeline_vol02_fig03.png|framed|left|The hungry bee]]If one uses the Gun, many Class II.E objects may be constructed, for example, the pentadecathlon '[[eater|eating]]' gliders (February column, page 114 . Incidentally, the illustration as shown is incorrect. The pentadecathlon and glider nearest it should be moved to the right one unit and in addition, an extra bit should be placed in the cell directly to the southeast of the glider). Earl C. Abbe of McLean, Va. has similarly positioned a [[queen bee]] near the glider stream. In this case however, the object eating the gliders will die if it is not fed every thirty [[generation]]s!

Abbe has also placed two [[shuttle]]s between two [[block]]s to create a 'queen bees' oscillator of period thirty. Does anyone know of an 'active element' which can be used for these type of constructions other than the glider or shuttle?

[[Image:Lifeline_vol02_fig04.png|framed|center|Queen bees]]

The miscellaneous category II.F is unusual and had the single addition presented below with all its phases shown. Charles Trawick of Decatur, Ga, calls his discovery '[[candelabra]]' and, like the [[cuphook|M.I.T. oscillator]] (No.1,p.5) is also of period three.

[[Image:Lifeline_vol02_fig05.png|framed|center|Candelabra]]

Not surprisingly, no new spaceships (Class III) were reported. However, several intriguing (and delightfully simple) infinite patterns have been discovered that move orthogonally at the speed of light! These are discussed later in this newsletter. Notice Class III is now subdivided by the object's direction of motion.

Class IV, consisting only of the Gun, may (for the fun of it) be subclassified by type of activity into spaceship guns and puffer trains. In a sense, all Class III.A objects are puffer trains whose 'sparks' die rather than create any Class I or II objects. More will be said about puffer trains later.

====Page 5====
[[Image:Lifeline_vol02_fig08.png|right|framed|A small [[predecessor|predesesor]] to the blinker]] Class V includes anything not in Classes I through IV and is now subdivided according to the object's final census. The single bit is, of course, the smallest object (Class V.A) that dies. I coined theta (Θ), the Greek symbol for death and which appears on the ecology flags, to represent this subclass. A [[pre-block|latent block]] ([[Image:Lifeline_vol02_fig06.png]]) is the smallest object (Class V.B) that becomes a still life. The blinker predecessor shown here is not only one of the smallest objects (Class V.C) that becomes periodic but does so in only a single generation. The [[tetromino]] ([[Image:Lifeline_vol02_fig07.png]]) and two other four-bit objects, of course, form the [[traffic light]] but only after a varying number (nine or more) of [[generation]]s. These three objects were the subject of issue Number One (p.6) and are discussed later in this issue. Can you identify the five other four-bit objects besides the one shown here that become a blinker?

[[Image:Lifeline_vol02_fig09.png|left|framed|A pure glider generating heptomino]] Class V.D objects are less common and very fascinating because of the one or more gliders created during their history. They include the [[R-pentomino]], a hexomino, and the eleven heptominoes mentioned earlier. Of these, three heptominoes are of the '[[pure glider generator]]' variety (Class V.D.2) one of which is shown at the left. Although not an omino, the five-bit object to the right is one of the several smallest known predecessors to the glider. Glider α ([[Image:Lifeline_vol02_fig10.png]]) and glider β ([[Image:Lifeline_vol02_fig11.png]]) are not included in the list even though they do evolve into a glider. Can you identify any of these objects including the two other heptominoes before I present them in the next issue?

Many readers have reported Class V.D.2 objects like the [[4-8-12 diamond]] and [[bi-loaf (pure glider generator)|biloaf]] presented in the first issue and also described by Martin Gardner in the April column. Shown below are two symmetrical objects yielding two gliders each and three nonsymmetrical single glider generators. 'No name' was sent in by Bray and also Roger H. Rosenbaum of Seattle, Wash., who supplied the two long undecominoes. You may recognize the third one as appearing in the spaceship conversion last issue. There seems to be an inordinate number (four now including the one mentioned last issue, p.3) of undecominoes in this subclass. Dale Edwin Cole of San Bernardino, Calif. sent in his '[[bi-clock|biclock]]'.

[[Image:Lifeline_vol02_fig12.png|framed|center|Some more pure glider generators Left to right: no name, three undecominoes, biclock]]

You might be interested in following the pattern made up entirely of ominoes at the top of the next page for a real surprise!

====Page 6====

[[Image:Lifeline_vol02_fig15.png|framed|center|A family of ominoes with interesting great grandchildren]]

[[Image:Lifeline_vol02_fig13.png|framed|right|The smallest known ancestor of the Gun]] No one responded to the challenge of finding a minimum predecessor pattern for the Gun (Class V.E). The 26-bit pattern mentioned in March (p.3) is shown here and the challenge still stands: Does a 25 or less bit pattern exist? This was given as the example for Class V.E even though it is not a true object since the idea was to get the minimum configuration (object or pattern). However, there undoubtedly are true objects that evolve into the Gun. More will be said about the meaning of an object later.

[[Image:Lifeline_vol02_fig14.png|framed|left|The 'acorn']] Class V.F is a catchall for anything whose outcome is not known. Notice the old Class VI is now defunct. The example mentioned on page two and shown to the left is a mere seven-bit object that is for all practical purposes unknown (to all but a few) because of its unusual history. Unless you have the resources of a large computer (and program), the patience, and are willing to spend a lot of time please do not try to determine its fate. As a surprise for LIFELINE Number Three, I will give its discoverer as well as present the fate of the '[[acorn]]' - a term I coined after seeing its final census. It is given as a Class V.F example only to show how a simple object can, until census verified, be classified as unknown (just like the four heptominoes previously given.)

====Page 7====
A large unexplored area of Life that is fast gaining popularity (with some real surprises!) involves 'transfinite objects'. In general, these are objects consisting of an infinite stable portion and (if activated) a finite unstable portion which 'feeds' on the stable portion. The stable portion may be a single infinite object (or an infinite set of finite objects) of Class I, II, III, or IV. The object (or set) may be infinite in one dimension (a [[fuse]]) or infinite in two dimensions (an [[agar]]). In a sense, transfinite objects (activated) may be considered very large Class V objects. But, for the fuses, the active portion exhibits characteristics of:

1. Periodicity.

2. Motion (speed).

3. Some visible rate of change of population (decreasing, constant, or increasing).

and most importantly:

4. An infinite life (as do classes I thru IV)

Fuses, therefore, seem most like the hypothetical puffer trains with the difference (very significant) being that they (the fuses) have an infinite mass provided (gratis) whereas a genuine puffer train, like the Gun, creates its own mass.

If the stable portion is infinite in two dimensions (an agar), the active portion will be an ever expanding oval boundary around an area which may continue to 'ferment'. Examples of the stable portion of these types of objects, many of which are familiar to you, are shown:

{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! Stable portion
! Fuse example
! Agar example
|-
| Class I
| diagonal
| '[[chicken wire]]'
|-
| Class II
| [[barberpole|barber pole]]
| oscillating field*
|-
| Class III
| [[flotilla]]
| field of spaceships*
|-
| Class IV
| 'multibarreled Gun'
| none
|-
| colspan="3" | * described with specific examples in the newsletter
|}

Note that in all cases, the examples given are true (single) objects and in order to exist must be infinite. In some cases, methods are known to stabilize the boundary thereby making it possible to construct a finite object of the desired size - for instance, the 'fencepost' ([[Image:Lifeline_vol02_fig16.png]]) for the diagonal. Whatever their class, transfinite objects, and fuses especially, display a variety of interesting phenomena.

The number of fuses reported is increasing rapidly so I will present here only those that display some variation on what we have previously seen reported with these objects. [Regarding fuses, Woods points out an error in the ''Scientific American'' illustration (April, page 116) in fuse b. The bottom row of two bits should be one row lower in order to work properly.]

The top of page eight shows two orthogonal fuses both of which, unlike all of the diagonal ones, 'burn' slower than the speed of light. '[[Washerwoman]]' was sent in by Abbe and every 18 generations converts two tubs into a pair of 'clotheslines' (traffic lights). 'Honey farm-II' supplied by the writer converts three fenceposts into a beehive every 12 generations.

====Page 8====
[[Image:Lifeline_vol02_fig17.png|framed|center|Washerwoman]]

[[Image:Lifeline_vol02_fig18.png|framed|center|Honey farm-II]]

Many fuses may be constructed by using objects other than the simple, single diagonal. Shown below are two such fuses which, at the speed of light, convert their fuse material into Class I and Class III (!) objects respectively. The first one converts its wavy diagonal (half-pond pieces) into a [[pond]] every six generations making it one of the two only known fuses that burns with a period not of multiple four. The other converts its double fuse into a glider every four generations thus creating a stream of gliders (20 generations apart in space). Question: what is the closest possible spacing for a stream of gliders in the same 'flight path'?

[[Image:Lifeline_vol02_fig19.png|framed|center|Two unusual fuses]]

====Page 9====
{{EmbedViewerLifeline
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2bo2bo4bo2bo4bo2bo$o6b2o6b2o6bo$3b2o6b2o6b2o$bo4bo2bo4bo2bo4bo$bo4bo2b
o4bo2bo4bo$3b2o6b2o6b2o$o6b2o6b2o6bo$2bo2bo4bo2bo4bo2bo$2bo2bo4bo2bo4b
o2bo$o6b2o6b2o6bo$3b2o6b2o6b2o$bo4bo2bo4bo2bo4bo$bo4bo2bo4bo2bo4bo$3b
2o6b2o6b2o$o6b2o6b2o6bo$2bo2bo4bo2bo4bo2bo$2bo2bo4bo2bo4bo2bo$o6b2o6b
2o6bo$3b2o6b2o6b2o$bo4bo2bo4bo2bo4bo$bo4bo2bo4bo2bo4bo$3b2o6b2o6b2o$o
6b2o6b2o6bo$2bo2bo4bo2bo4bo2bo!
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#C [[ THUMBZOOM 64 ]]
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I would now like to describe five unusual agars (not activated) all of which are periodic. The one shown to the right oscillates with a period of two. '[[Squaredance]]', a name I gave (because the bit pairs seem to move in and out around an open square) was sent in by Woods who actually named it the 'quilt'. The one below-left sent in by Steve Tower (no address given) looks as if it will completely die out (Θ). It does but only after creating an appropriate dispersion of bit pairs to replace it. Another oscillator discovered by Tower is truly unique for it is of period three! Each of its phases are shown. Can you detect anything unusual about this oscillator (besides the period) before it is revealed in [[Lifeline Volume 3|Issue Three]]?

{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig20.png|framed|center|Surviving bits]]
| [[Image:Lifeline_vol02_fig21.png|framed|center|The three phases of an oscillator field]]
|}

The last two agars (which were referred to on page four) are actually spaceships! The first of these shown at the left below was discovered by Robert Kraus of Chicago, Ill. Each member can be made any length desired (greater than four) by extending the two 'fins'. The second one discovered by the writer only comes in two sizes. The smaller version (not shown) is four units long and without the single bit. Both of these period one objects move orthogonally at the speed of light!

[[Image:Lifeline_vol02_fig23.png|framed|center|Two spaceship flotillas moving at the speed of light]]

====Page 10====
The next three examples actually involve finite fuses but in all cases the length of the fuse may be increased in multiples of four to achieve the same effect. They all illustrate how a glider's direction may be altered using fuses. I will, in a scenario of events, show how three fuses can be placed to demonstrate these findings. The creative staff includes (in order of occurrence) Rosenbaum, Webb, and Woods. The sequence of exhibits on this and the opposite page show, first, the three fuses at generation zero, then a glider (created by the short clean fuse) heading in generation eight towards the diagonal fuse (burning at both ends) where in generation twelve it is altered in flight and directed toward the 'synapse fuse' which gets activated by the glider (a signal) transmitting the signal thru the network (shown at generation 44) until reaching the other end where the signal is returned in generation 66 (as a glider displaced in time and space).

[[Image:Lifeline_vol02_fig24.png|framed|left|Generation: 0]] One of the most appealing features of fuses, from an experimental standpoint, is their ease of tracking. As stated in issue Number One (p.6) you need only a good supply of graph paper and not as much patience. The fact that fuses are periodic means that after a fairly small number of generations you can determine the period and identify each phase.

For anyone new to the game, LIFEFILE contains, among other things, a brief description of a convenient and reliable method for manually calculating Life object histories. Also, for anyone with access to a computer, but no program, I have provided an efficient program (FORTRAN source listing) written by Paul Boltwood of Ottawa, Ontario. The program calculates about three generations per second on an 80 by 80 matrix.

====Page 11====
{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig25.png|framed|center|Generation: 8]]
| [[Image:Lifeline_vol02_fig26.png|framed|center|Generation: 12]]
| [[Image:Lifeline_vol02_fig27.png|framed|center|Generation: 44]]
| [[Image:Lifeline_vol02_fig28.png|framed|center|Generation: 66]]
|}

====Page 12====
At this time we must deal with the inevitable question: what do we mean by an 'object'? My own criteria (arbitrary, of course) for determining if a [[pattern]] (of bits) is a single object are these:

1. Patterns whose bits are all connected (either orthogonally and/or diagonally) are objects.

2. Spatially connected patterns (a collection of objects, each of which is defined as above) are single objects if an empty cell between two or more of the 'subparts', and because of the subparts, is either a birth cell (when, without the subparts, would not have been) or a non-birth cell (when, without all the subparts, would have been.)

In other words, the subparts must have a mutual effect upon each other. The pattern at the left below {Figure 2.18, first pattern} is not a single object, but its next generation, center below, is a single object (by the definition just given). The smallest example of a stable spatially connected object is the '[[aircraft carrier]]' (Conway's term) shown at the right below.

{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig29.png|framed|center|A pattern]]
| [[Image:Lifeline_vol02_fig30.png|framed|center|An object]]
| [[Image:Lifeline_vol02_fig31.png|framed|center|Aircraft carrier]]
|}

Obvious exceptions to this definition include all objects in Classes II.E and IV.A because they are, by definition, '[[shuttle]]s' whose activity necessitates a movement thru open space. On page two my example given for Class V.E was purposely called a pattern (No.1,p.3) since it is not a true object. The idea there was to find the minimum pattern (object or not). Finally, members of Classes II.C, II.D, and the [[beacon]] may be considered objects since at least one of their phases meets the definition. This definition is important (at least for Class V objects) to preserve any meaning for the E.F. ratio discussed in March (page 6) since it excludes defining as an object (as was suggested by several readers) such things as 'a glider a long distance away from and heading towards a blinker, say'.

[[Image:Lifeline_vol02_fig32.png|framed|right|Three relatives (E.F. value)]] This brings us to the challenges proposed last issue of finding objects with maximum M.I.P. and E.F. ratios. Philip M. Cohen of Aliquippa, Pa. and Woods pointed out the only two other four-bit objects with an M.I.P. value of 5.0. These are shown at the right along with the [[T-tetromino|tetromino]] to illustrate their varying E.F. values. The third one, incidentally, sets the record for all four-bit objects.

Shown at the top of the next page are eight predecessor objects to the [[R-pentomino]]. The first three (a, b, and c) are the ones (all orthogonally-diagonally connected) that the writer had in mind when discussing this subject in March. The other five, all spatially connected, were sent in by Cohen (f), Corderman (a, c, and h), and Woods (a, b, d, e, f, and g). Three of these (a, c, and h) are all '[[grandfather]]s' to the R-pentomino and therefore have an E.F. value (the one Woods had in mind) of 221.0. Does anyone know of a five-bit great grandfather to the R-pentomino?

====Page 13====
[[Image:Lifeline_vol02_fig33.png|framed|center|A host of predecessors to the R-pentomino]]

[[Image:Lifeline_vol02_fig34.png|framed|right|Diehard]]Another interesting measure is the ratio of age to initial population for Class V.A objects. For example, five generations is the longest any four-bit object can last before dying (E.F.=1.25) and apparently eight generations is the longest any five-bit object can survive before death (E.F.=1.6). Can you identify either of these? Rosenbaum has discovered the object at the right of a mere eight bits that manages to stay alive 118 generations before death (E.F.=14.75)! Even though E.F.[V.A. max ≤ E.F.V max for objects of the same size, I think this represents a very interesting challenge by virtue of the final extinction requirement. Any information received regarding this or the other two ratios will be presented in [[Lifeline Volume 3|issue Three]].

Practically any variation to [[Conway's Game of Life|Life]] that you can think of is probably being investigated by at least one individual. I would now like to mention several areas of Life and Cellular Automata Theory in general that are being investigated. It is still too early to report many detailed results on these subjects, however.

Several readers have tried playing Life on boards finite in either one or two dimensions which is analogous to playing on a cylindrical or a toroidal (doughnut) surface. The most noteworthy of these involves the work of Donovan Smith of El Cerritor, Calif. who has investigated families of 'necklaces' and 'radicals' as he calls them, on 4 by n toroidal surfaces (see example).

{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig35.png|framed|center|A necklace]]
| [[Image:Lifeline_vol02_fig36.png|framed|center|A radical]]
|}

Oscillators with periods greater than two are very common (usually a multiple of four) and shown below at the left is one Smith discovered of period five (!) which begins in generation seven starting with a 4 by 12 necklace. Interestingly, the very same finite surface will support a period four oscillator sent in by Trawick shown below at the right.

[[Image:Lifeline_vol02_fig37.png|framed|center|Two oscillators supported on a 4 by 12 torus Left: Period 5      Right: Period 4]]

====Page 14====
Many phenomena exhibit interesting twists on a closed board. For instance, two [[overweight spaceship]]s (November column, page 118) of any identical length could travel together along the surface of a cylinder twelve units in circumference. A [[spaceship]] like the one described on page nine could travel unescorted endlessly across a 6 by 7 surface at the speed of light!

Two person games seem to be popular as evidenced by the large number of readers either requesting information or actually submitting ideas for games that they have developed. Rules for such games are easy to think up and the ones proposed vary widely. I will present here one of the many games suggested because it seems to have been played for awhile (tested) so has been refined from the original idea. Also, it embodies the concept of many other games sent in.

[[Immigration|IMMIGRATION]], a two-person game invented by Woods, is played as follows:

# Equipment - a 25 by 25 board (used as a finite matrix like the toroidal surface just described) and a good supply of two different colored counters (chips or stones).
# To setup - each player alternately places one of his 'people' (counters) on the board until each has placed five people.
# Rules to play - colors are irrelevant in determining survivals and births which use the same rules as in the regular version. Since a birth requires three neighbors (an odd number) the majority color (i.e. the color with two or three) determines the color of the newborn 'child'. Remember, the 98 border squares also have eight neighbors. Every ten generations the player with the most people places (immigrates) one extra person of his color in any empty cell. Then the other player does the same with his color. If neither player has a majority, they continue advancing thru additional generations until the tie is broken. The 'every ten generations' then applies to the tenth generation following the tie-breaking one. Unlike most other games IMMIGRATION involves a degree of skill (via the every tenth generation choice placement) and, as Woods says, 'also threatens stable Life forms'. The game is won when, at the time for immigration, only one color remains on the board. If both colors are extinct the game is a draw. Experience has shown that some basic strategies may be developed to increase the chances of winning.

Life may also be played as some readers have done, on a hexagonal tessellation which can be translated into an equivalent game on a square tessellation by suitable definition of neighborhood (see below).

{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig38.png|framed|center|The hexagonal tesselation]]
| [[Image:Lifeline_vol02_fig39.png|framed|center|An equivalent tesselation]]
|}

====Page 15====
{{EmbedViewerLifeline
|rle = x = 4, y = 4, rule = B2-p/S2H
2o$o$2obo$2bo!
|position = right
|viewerconfig = #C [[ THUMBSIZE 4 HEIGHT 640 WIDTH 640 ]]
#C [[ THUMBZOOM 64 ]]
#C [[ X 0 Y 0 ]]
#C [[ ZOOM 24 ]]
#C [[ ANGLE 60 ]]
#C [[ COLOR ARROW Black ]]
#C [[ ARROWZOOMRANGE -2048 2048 ]]
#C [[ ARROW -0.75 0 -2.75 -2 20 ]]
|caption = A 'hexaglider'
|alternate = [[Image:Lifeline_vol02_fig40.png]]
}}
Notice the neighborhood is now six rather than eight cells and therein lies the big question: what rules do we use? Ken Preston, Jr. of Norwalk, Conn. using the following set of rules has reported the existence of a Class III object similar to a lightweight spaceship (!): Survival requires two (and only two) bits anywhere in the six-cell neighborhood. Birth requires two bits in the neighborhood but not if they are opposite each other (i.e. in the illustration on the previous page, bits in cells 1 and 2 or in 1 and 3 would give birth but bits in cells 1 and 4 would not). The object shown at the right every six generations moves three units in the direction indicated (one of the three major axes). A filled hexagon (whose sides are alternately of length four and three) after 116 generations forms six 'hexagliders' (my term) which successfully escape. Six more are formed in generation 406 but are immediately 'gobbled up'. Still six more appear in generation 470 and succeed in escaping as did the original six. Preston has yet to determine its eventual fate.

Several ambitious readers are attempting to play Life in a three-dimensional matrix. The greatest problem here, I think, is choosing a set of rules for the 26-cell neighborhood. One reader, Harvey Lerman of Maitland, Fla., suggests the following method which attempts to make use of Conway's sound two-dimensional rules:

# Consider the three orthogonal planes thru a cell.
# Use Conway's rules on each plane separately.
# If the cell survives in at least two (Lerman is also considering all three) of the planes then it survives in three dimensions.
# Likewise for birth.

Whichever rule it is really not too difficult to compute and plot (each layer, say) but you definitely are more limited in grid (computer core) size and it is extremely difficult to conceptualize what is going on.

Martin Gardner in the February column (page 113) mentions proof of the existence of '[[Garden of Eden]]' (GoE) patterns. Recall, these are configurations that have no predecessor patterns so therefore could never be formed unless given in the initial (zero) generation. At that time we were assured that such patterns existed within a field 10^9 cells on a side. Two developments (one theoretical and the other experimental) since then have considerably reduced the area of search but unfortunately do not really help in finding such a GoE pattern. [[John Conway]] has succeeded in showing such patterns, 'orphans' as he calls them, exist on square boards of sides less than 4000. In connection with searching for GoE patterns, Gray has written such a program which uses brute force to examine and tabulate many candidate patterns. He has succeeded in proving that no GoE exist within a 4 by 4 square - a feat which required identifying predecessor patterns (fathers) for all the 65,536 possible 4 by 4 patterns (including rotations and reflections.) This effort required 90 minutes of computer (special purpose solid logic) time during which about 20 million 6 by 6 random patterns were created!

====Page 16====
Along this same line, several readers have inquired about 'backward synthesis' algorithms for determining predecessor patterns. To my knowledge, nothing has been done in this regard. If anyone has, I will be pleased to report their work in the next issue of LIFELINE.

It is not practical to report here the details on all the other variations on Life which readers have sent in. As the level of interest or effort in any particular area increases, I will include these in the newsletter. I solicit your ideas and suggestions on how more of the detailed information can be effectively disseminated. In the meantime, LIFEFILE, the appendix to LIFELINE, will be used to fill this need.

In closing LIFELINE Number Two, I think it appropriate to give some indication as to the subjects planned for future issues which the writer has in mind and is already developing. These are not in any particular order, and in some cases not too descriptive, but all are definitely food for thought.

COMING EVENTS:

* methods of stabilizing the boundary of transfinite objects
* spiral fuses
* some more interesting scenarios of Life's events
* an entire field of gliders
* 'fly by fuses'
* F.I.P. - another ratio
* [[spark]]s
* a catalog of glider-derived objects
* implications of aging - another rule for death
* measuring the density and center of mass of an object or pattern
* '[[constellation]]s'
* some potential spaceships
* Life family trees
* 'channel' phenomena
* self-repairable Life objects
* '[[tagalong|tag alongs]]'
* minimum predecessor patterns
* seeded agars
* some potential spaceship guns (!)
* entropy of a system of bits
* primordial broths
* illusions of motion exhibited by certain Life objects
* 'beehive', a period 30 agar
* 'antibodies' that thrive on glider streams
* constructing a computer with glider guns

====Page 17====
<center><pre>O OOO OOO OOO OOO OOO O OOO
O O O O O O O O
O O OO OO OO O O OO
O O O O O O O O
OOO OOO O OOO O OOO OOO OOO

A COMPREHENSIVE FILE OF INFORMATION GENERATED BY LIFE EXPERIMENTERS</pre></center>

LIFEFILE this issue regards ways of calculating Life histories. Many readers have requested computer programs and nearly as many have supplied source listings in addition to algorithms, hints, etc. that they are using. I have decided to present here two sound and efficient Life algorithms. The first of these described below is simply a procedure for tracking patterns manually using graph paper. The second, given on the next page, is a source listing of a FORTRAN (IV G) program written by Boltwood and slightly modified by the writer to change the input requirement and output display. The algorithm, to my knowledge, is the most efficient one in use. Input requires a header card followed by a set of cards containing the pattern for generation zero.

<pre>Header Card: cc 01-05: limit of calculation (gen. no)
06-10: frequency of printing
11-15: top row of initial pattern</pre>

<pre>Example: 0 1
123456789012345
75 4 31</pre>

This specifies the termination of calculation at gen. 75 (unless pattern dies out sooner) and output printed every 4 gens. The pattern supplied on the set of cards begins in row 31.

Set of pattern cards: The first card corresponds to top row in pattern and the following cards for each row. The card columns correspond to output columns. A '0' (or any non-blank character) may be punched for @ bit.

{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! A suggested manual method for 'playing Life'
|-
|
# Start generation zero by marking all 'live' cells with a 'O'.
# Scan* the pattern and mark all birth cells (those with exactly three neighbors) with a '.'.
# Check each bit for the possibility of death (those with other than two or three neighbors) and mark with a 'X'.
# Copy all 'O' and '.' to a new area for the next generation. Go back to step two.

[[Image:Lifeline_vol02_fig41.png|framed|center|Example]]
|-
| * scanning can be done by either or both of these methods:

a. scan each empty cell of every row (or column) passing adjacent to and thru the pattern.

b. scan each empty cell immediately around the pattern and within the pattern
|}

====Page 18====
Boltwood's Life program in FORTRAN:

<pre> IMPLICIT INTEGER (A-Z)
COMMON Q,ST,IT,C(6400)
INTEGER R(80)
DATA BL,BIT/' ','0'/
Q=80
QQ=Q*Q
DO 1 1=1,QQ
D(1)=Q
ST=9999
Q2=Q/2
REAC(5,8) CY,PI,I
FORMAT(315)
REAC(5,9,END=11)
FORMAT(80A1)
DO 10 K=1,0
IF(R(K).BQ.BL) GO TO 10
L=I*Q+K-I
D(L)=ST
ST=L
CONTINUE
I=I+1
GO TO 5
WRITE(6,3)
FORMAT('1')
IT=0
CALL PRT
DO 4 IT=1,CY
CALL NEXGEN(&6)
IF(MOD(IT,PI).EQ.0) CALL PRT
GO TO 2
WRITE(6,7) IT
FORMAT(' DIED AT ITERATION ',I4)
STOP
END

SUBROUTINE PRT
IMPLICIT INTEGER (A-Z)
COMMON Q,ST,IT,D(1)
INTEGER R(80)
DATA BL,BIT/' ','O'/
O=0
L=10000
B=ST
IF(K.EQ.9999) GO TO 21
J=MOD(K-1,Q)
IF(J.GT.B) B=J
IF(J.LT.A) A=J
IF=(K.GT.U) U=K
IF(K.LT.L) L=K
R=D(K)
GO TO 22
21 WRITE (6,23) IT
23 FORMAT(//' GENERATION', I5)
WRITE (6,28)
28 FORMAT(4X,'.........1.........2.........3.........4.........5.........6.........7.........8')
U=(U-1)/Q
L=(L-1)/Q
DO 27 K=1,Q
27 P(K)=BL
DO 24 I=L,U
DO 25 J=A,B
P(J)=BL
25 IF(D(I*Q+J+1).NE.O) P(J)=B IT
24 WRITE (6,26) I,P,I
26 FORMAT(1X,I3,80A1,I2)
WRITE (6,28)
RETURN
END

SUBROUTINE NEXGEN(*)
IMPLICIT INTEGER (A-Z)
COMMON Q,ST,IT,D(1)
INTEGER NK(8),NNK(8)
NB=-9999
B8=N8
K=ST
1 IF(K.EQ.9999) GO TO 6
CALL NEIBR(K,NK,&13)
NN=0
DO 2 I=1,8
NKI=NK(I)
IF(D(NKI).LE.0) GO TO 3
NN=NN+1
GO TO 2
3 IF(D(NKI).LT.0) GO TO 2
CALL NEIBR(NKI,NNK,&13)
NNN=0
DO 4 J=1,8
4 IF(C(NNK(J)).GT.0) NNN=NNN+1
IF(NNN.NE.3) GO TO 5
D(NKI)=NB
ND=-NKI
GO TO 2
5 D(NKI)=BB
BB=-NKI
2 CONTINUE
IF(NN.EQ.2.OR.NN.EQ.3) GO TO 12
13 D(K)=D(K)+10000
K=D(K)-10000
GO TO 1
12 K=D(K)
GO TO 1
6 CONTINUE
16 IF(ST.EQ.9999) RETURN 1
IF(D(ST).LT.10000) GO TO 14
I=ST
ST=D(ST)-10000
D(I)=0
GO TO 16
14 K=D(ST)
DK=ST
15 IF(K.EQ.9999) GO TO 11
IF(D(K).LT.10000) GO TO 20
D(DK)=D(K)-10000
D(K)=0
K=D(DK)
GO TO 15
11 IF(NB.EQ.-9999 GO TO 17
K=-NB
8 IF(K.EQ.-9999) GO TO 17
D(K)=-D(K)
CK=K
K=D(K)
GO TO 8
7 D(CK)=ST
ST=-NB
17 K=-BB
IF(K.EQ.9999) RETURN
I=K
K=-D(K)
D(I)=0
GO TO 9
END

SUBROUTINE NEIBR(K,NK,*)
IMPLICIT INTEGER (A-Z)
COMMON Q
INTEGER NK(8)
Q1=Q-1
K1=K-1
I=K1/C
J=MOD(KI,Q)
IF(I.EQ.0.OR.I.EW.W1.OR.J.EQ.0.OR.J.EQ.Q1) RETURN 1
NK(1)=K1
NK(2)=K1+2
NK(3)=K1+Q
NK(4)=NK(3)+1
NK(5)=NK(4)+1
NK(6)=K1-Q
NK(7)=NK(6)+1
NK(8)=NK(7)+1
RETURN
END</pre>

==Page Scans==
<gallery>
Image:Lifeline_vol_2.png|Page 1
Image:Lifeline_vol_2_p2.jpg|Page 2
Image:Lifeline_vol_2_p3.jpg|Page 3
Image:Lifeline_vol_2_p4.jpg|Page 4
Image:Lifeline_vol_2_p5.jpg|Page 5
Image:Lifeline_vol_2_p6.jpg|Page 6
Image:Lifeline_vol_2_p7.jpg|Page 7
Image:Lifeline_vol_2_p8.jpg|Page 8
Image:Lifeline_vol_2_p9.jpg|Page 9
Image:Lifeline_vol_2_p10.jpg|Page 10
Image:Lifeline_vol_2_p11.jpg|Page 11
Image:Lifeline_vol_2_p12.jpg|Page 12
Image:Lifeline_vol_2_p13.jpg|Page 13
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Image:Lifeline_vol_2_p15.jpg|Page 15
Image:Lifeline_vol_2_p16.jpg|Page 16
Image:Lifeline_vol_2_p17.jpg|Page 17
Image:Lifeline_vol_2_p18.jpg|Page 18
</gallery>

Lifeline Volume 2

2022-09-08T18:58:33Z

C7X: Typo not present in scan

__NOTOC__{{LifeLine|vol=2|date=June 1971}}

<center><pre>A QUARTERLY NEWSLETTER FOR ENTHUSIASTS OF JOHN CONWAY'S GAME OF LIFE

O OOOOO OOOOO OOOOO O OOOOO O O OOOOO
O O O O O O OO O O
O O OOO OOO O O O O O OOO
O O O O O O O OO O
OOOOO OOOOO O OOOOO OOOOO OOOOO O O OOOOO

Number 2 JUNE 1971</pre>

• Editor and Publisher: [[Robert T. Wainwright]] •</center>

====Page 1====
The response to [[Lifeline|LIFELINE]] Number One and Martin Gardner's announcement in the April issue of ''Scientific American'' regarding this endeavor has been overwhelming! More than 340 inquiries have been received from readers in many industrial organizations, schools, and universities in fourteen different countries - and mail is still flowing in. The administrative burden accounts for what may seem to some of you (especially the early respondents) an indifference on my part. Following the establishment of a mailing list of subscribers, I will attempt to answer many of your individual inquiries via LIFELINE, an informal but relatively rapid and specific response to your area of interest.

LIFELINE Number Two extends and refines the ideas presented in the first issue and incorporates information from many of your responses. The main objective of this issue is to further the base of classification and common definition using your own developments as examples.

The fates of the unknown [[heptomino]]es E, F, H, and I were first sent in by Robert Bison of Hopewell Jct., N.Y. and subsequently confirmed by David W. Bray of Syracuse, N.Y., [[Charles Corderman|Charles L. Corderman]] of Winchester, Mass., Gary Goodman of Stanford, Calif., Stephen B. Gray of Los Angeles, Calif., Maxwell E. Manowski of New York (FPO), and [[Don Woods]] of Natick, Mass. The histories and final '[[census]]' (an apt term coined by Woods) of these four interesting Life objects are shown here:

{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! colspan="3" | Fates of the last four unknown heptominoes
|-
! Heptomino
! Age
! Census
|-
| E
| 343
| 5 [[block]]s, 4 [[beehive]]s, 1 [[blinker]], and 1 [[glider]]
|-
| F
| 437
| 3 blocks, 1 [[tub]], 1 [[boat]], 1 beehive, 1 [[pond]], 7 blinkers (1 + 3/4 [[traffic light|traffic lts.]]), and 1 glider
|-
| H and I
| 247
| 3 blocks, 1 boat, 1 beehive, 1 ship, and 2 gliders
|}

To save unnecessary effort on the part of those receiving [[Lifeline Volume 1|issue Number One]] later than April, I appended a note to the effect that these results were known. Like seven other heptominoes (No. 1, Table 2), they all give birth to one or more gliders during their history. Interestingly, the direction of glider escape in all cases is to the northeast from the initial positions originally shown.

With many more objects being discovered in Classes I, II, and V it becomes tempting to subclassify them within the system proposed in issue Number One. The writer had previously arranged all Life objects into six primary classes based upon characteristics of their history and now proposes further definition (subclassification).

====Page 2====
{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! colspan="6" | AN EXPANDED CLASSIFICATION SYSTEM FOR FINITE LIFE OBJECTS
|-
! Primary Class
! colspan="2" | Subclassified According To:
! Subclass
! Example*
! Size
|-
| rowspan="8" | I-[[Still life|Still Lifes]]
| rowspan="8" | Degree of symmetry
| 2-way orthogonal, 2-way diagonal, 90° rotational
| I.A
| block
| 4
|-
| 2-way orthogonal, 180° rotational
| I.B.1
| beehive
| 6
|-
| 2-way diagonal, 2-way diagonal, 90° rotational
| I.B.2
| ship
| 6
|-
| 90° rotational
| I.B.3
| [[spiral]]
| 20
|-
| 1-way orthogonal
| I.C.1
| [[hat]]
| 9
|-
| 1-way diagonal
| I.C.2
| boat
| 5
|-
| 180° rotational
| I.C.3
| [[snake]]
| 6
|-
| none
| I.D
| [[eater 1|fishhook]]
| 7
|-
| rowspan="6" | II-[[Oscillator]]s
| rowspan="6" | Type of periodic activity
| [[flip-flop]]s (all period two)
| II.A
| blinker
| 3
|-
| [[billiard table configuration]]s
| II.B
| [[pinwheel]]
| 35
|-
| inductors
| II.C
| [[tumbler]]
| 16
|-
| pulsators
| II.D
| [[pentadecathlon|pentadecathalon]]
| 12
|-
| [[shuttle]]s
| II.E
| [[queen bee shuttle|queen bee]]
| 20
|-
| miscellaneous
| II.F
| [[cuphook|M.I.T. osc.]]
| 18
|-
| rowspan="2" | III-[[Spaceship]]s
| rowspan="2" | Motion of spaceship
| orthogonal
| III.A
| [[lightweight spaceship|lt.wt.s.s.]]
| 8
|-
| diagonal
| III.B
| [[glider]]
| 5
|-
| rowspan="2" | IV-Propagators
| rowspan="2" | Nature of activity
| [[gun|spaceship guns]]
| IV.A
| [[Gosper glider gun|the Gun]]
| 36
|-
| [[puffer|puffer trains]]
| IV.B
| ?
| ?
|-
| rowspan="7" | V-Unstable (all objects not in above)
| rowspan="7" | Final census
| dies (Θ)
| V.A
| [[bit]]
| 1
|-
| Class I
| V.B
| [[pre-block|latent block]]
| 3
|-
| Class II
| V.C
| blinker pred.
| 4
|-
| Class III
| V.D.1
| [[R-pentomino]]
| 5
|-
| Class III (only)
| V.D.2
| glider pred.
| 5
|-
| Class IV
| V.E
| Gun pred.
| 26
|-
| unknown
| V.F
| [[acorn]]**
| 7
|-
| colspan="6" | * smallest known object (for Classes II, III, IV - minimum phase)
|-
| colspan="6" | ** 'apparently' unknown - see text, page six
|}

====Page 3====
A modified classification system is presented on page two which attempts to recognize the specific, key characteristics of finite Life objects of each class. The examples shown represent, for each subclass, the smallest object (minimum number of bits) known to the writer. Most examples given are well known and have been previously described in either ''Scientific American'' or LIFELINE Number One. Those that are new are described in this newsletter. If anyone knows of smaller objects than any of these I will publish them in the next issue.

In general the number of new Class I objects reported is too large and common to mention. The '[[spiral]]' was suggested by the writer merely to provide an example of a small Class I.B.3 object since none had previously been mentioned. The '[[hat]]' a name given by [[Charles Corderman|Corderman]] and known by several other readers can be used to construct larger stable forms and is probably the smallest Class I.C.1 object. Class I.D objects exhibiting no symmetry whatsoever are the least common.

[[Image:Lifeline_vol02_fig01.png|framed|center|Some interesting examples of [[still life]] symmetry Left to right: [[Hat]], [[Eater 1|Fishhook]], [[Spiral]], [[Shillelagh]], [[tub with tail|Tub w/tail]]]]

The '[[eater 1|fishhook]]', a name independently coined by Clement A. Lessner III of W. Lafayette, Ind. and William P. Webb of San Rafael, Calif., was sent in by a number of readers and certainly must be the smallest possible nonsymmetrical still life. The two made of eight bits were given by Corderman and Hugh Thompson of Lefrak City, N.Y., who suggested the name '[[shillelagh]]'.

[[Image:Lifeline_vol02_fig02.png|framed|right|The hustler]] Many Class II.A objects were reported, again too numerous and common to mention. Class II.B objects are fairly easy to develop starting with an empty m by n area (billiard table) bounded by '[[induction coil|inductor coils]]' and experimenting with various random patterns within. But if one excludes [[period]] two oscillators from this subclass, only a few are known. Other than the familiar [[Hertz oscillator]] (period eight) and [[pinwheel]] (period four) only the '[[hustler]]' of an uneven period of three shown here has been added to this subclass. Note the now familiar fishhook used as an inductor coil for the crooked sides of the billiard table. Classes II.C and II.D are very uncommon and to date no one has reported anything new in either of these groups.

====Page 4====
[[Image:Lifeline_vol02_fig03.png|framed|left|The hungry bee]]If one uses the Gun, many Class II.E objects may be constructed, for example, the pentadecathlon '[[eater|eating]]' gliders (February column, page 114 . Incidentally, the illustration as shown is incorrect. The pentadecathlon and glider nearest it should be moved to the right one unit and in addition, an extra bit should be placed in the cell directly to the southeast of the glider). Earl C. Abbe of McLean, Va. has similarly positioned a [[queen bee]] near the glider stream. In this case however, the object eating the gliders will die if it is not fed every thirty [[generation]]s!

Abbe has also placed two [[shuttle]]s between two [[block]]s to create a 'queen bees' oscillator of period thirty. Does anyone know of an 'active element' which can be used for these type of constructions other than the glider or shuttle?

[[Image:Lifeline_vol02_fig04.png|framed|center|Queen bees]]

The miscellaneous category II.F is unusual and had the single addition presented below with all its phases shown. Charles Trawick of Decatur, Ga, calls his discovery '[[candelabra]]' and, like the [[cuphook|M.I.T. oscillator]] (No.1,p.5) is also of period three.

[[Image:Lifeline_vol02_fig05.png|framed|center|Candleabra]]

Not surprisingly, no new spaceships (Class III) were reported. However, several intriguing (and delightfully simple) infinite patterns have been discovered that move orthogonally at the speed of light! These are discussed later in this newsletter. Notice Class III is now subdivided by the object's direction of motion.

Class IV, consisting only of the Gun, may (for the fun of it) be subclassified by type of activity into spaceship guns and puffer trains. In a sense, all Class III.A objects are puffer trains whose 'sparks' die rather than create any Class I or II objects. More will be said about puffer trains later.

====Page 5====
[[Image:Lifeline_vol02_fig08.png|right|framed|A small [[predecessor|predesesor]] to the blinker]] Class V includes anything not in Classes I through IV and is now subdivided according to the object's final census. The single bit is, of course, the smallest object (Class V.A) that dies. I coined theta (Θ), the Greek symbol for death and which appears on the ecology flags, to represent this subclass. A [[pre-block|latent block]] ([[Image:Lifeline_vol02_fig06.png]]) is the smallest object (Class V.B) that becomes a still life. The blinker predecessor shown here is not only one of the smallest objects (Class V.C) that becomes periodic but does so in only a single generation. The [[tetromino]] ([[Image:Lifeline_vol02_fig07.png]]) and two other four-bit objects, of course, form the [[traffic light]] but only after a varying number (nine or more) of [[generation]]s. These three objects were the subject of issue Number One (p.6) and are discussed later in this issue. Can you identify the five other four-bit objects besides the one shown here that become a blinker?

[[Image:Lifeline_vol02_fig09.png|left|framed|A pure glider generating heptomino]] Class V.D objects are less common and very fascinating because of the one or more gliders created during their history. They include the [[R-pentomino]], a hexomino, and the eleven heptominoes mentioned earlier. Of these, three heptominoes are of the '[[pure glider generator]]' variety (Class V.D.2) one of which is shown at the left. Although not an omino, the five-bit object to the right is one of the several smallest known predecessors to the glider. Glider α ([[Image:Lifeline_vol02_fig10.png]]) and glider β ([[Image:Lifeline_vol02_fig11.png]]) are not included in the list even though they do evolve into a glider. Can you identify any of these objects including the two other heptominoes before I present them in the next issue?

Many readers have reported Class V.D.2 objects like the [[4-8-12 diamond]] and [[bi-loaf (pure glider generator)|biloaf]] presented in the first issue and also described by Martin Gardner in the April column. Shown below are two symmetrical objects yielding two gliders each and three nonsymmetrical single glider generators. 'No name' was sent in by Bray and also Roger H. Rosenbaum of Seattle, Wash., who supplied the two long undecominoes. You may recognize the third one as appearing in the spaceship conversion last issue. There seems to be an inordinate number (four now including the one mentioned last issue, p.3) of undecominoes in this subclass. Dale Edwin Cole of San Bernardino, Calif. sent in his '[[bi-clock|biclock]]'.

[[Image:Lifeline_vol02_fig12.png|framed|center|Some more pure glider generators Left to right: no name, three undecominoes, biclock]]

You might be interested in following the pattern made up entirely of ominoes at the top of the next page for a real surprise!

====Page 6====

[[Image:Lifeline_vol02_fig15.png|framed|center|A family of ominoes with interesting great grandchildren]]

[[Image:Lifeline_vol02_fig13.png|framed|right|The smallest known ancestor of the Gun]] No one responded to the challenge of finding a minimum predecessor pattern for the Gun (Class V.E). The 26-bit pattern mentioned in March (p.3) is shown here and the challenge still stands: Does a 25 or less bit pattern exist? This was given as the example for Class V.E even though it is not a true object since the idea was to get the minimum configuration (object or pattern). However, there undoubtedly are true objects that evolve into the Gun. More will be said about the meaning of an object later.

[[Image:Lifeline_vol02_fig14.png|framed|left|The 'acorn']] Class V.F is a catchall for anything whose outcome is not known. Notice the old Class VI is now defunct. The example mentioned on page two and shown to the left is a mere seven-bit object that is for all practical purposes unknown (to all but a few) because of its unusual history. Unless you have the resources of a large computer (and program), the patience, and are willing to spend a lot of time please do not try to determine its fate. As a surprise for LIFELINE Number Three, I will give its discoverer as well as present the fate of the '[[acorn]]' - a term I coined after seeing its final census. It is given as a Class V.F example only to show how a simple object can, until census verified, be classified as unknown (just like the four heptominoes previously given.)

====Page 7====
A large unexplored area of Life that is fast gaining popularity (with some real surprises!) involves 'transfinite objects'. In general, these are objects consisting of an infinite stable portion and (if activated) a finite unstable portion which 'feeds' on the stable portion. The stable portion may be a single infinite object (or an infinite set of finite objects) of Class I, II, III, or IV. The object (or set) may be infinite in one dimension (a [[fuse]]) or infinite in two dimensions (an [[agar]]). In a sense, transfinite objects (activated) may be considered very large Class V objects. But, for the fuses, the active portion exhibits characteristics of:

1. Periodicity.

2. Motion (speed).

3. Some visible rate of change of population (decreasing, constant, or increasing).

and most importantly:

4. An infinite life (as do classes I thru IV)

Fuses, therefore, seem most like the hypothetical puffer trains with the difference (very significant) being that they (the fuses) have an infinite mass provided (gratis) whereas a genuine puffer train, like the Gun, creates its own mass.

If the stable portion is infinite in two dimensions (an agar), the active portion will be an ever expanding oval boundary around an area which may continue to 'ferment'. Examples of the stable portion of these types of objects, many of which are familiar to you, are shown:

{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! Stable portion
! Fuse example
! Agar example
|-
| Class I
| diagonal
| '[[chicken wire]]'
|-
| Class II
| [[barberpole|barber pole]]
| oscillating field*
|-
| Class III
| [[flotilla]]
| field of spaceships*
|-
| Class IV
| 'multibarreled Gun'
| none
|-
| colspan="3" | * described with specific examples in the newsletter
|}

Note that in all cases, the examples given are true (single) objects and in order to exist must be infinite. In some cases, methods are known to stabilize the boundary thereby making it possible to construct a finite object of the desired size - for instance, the 'fencepost' ([[Image:Lifeline_vol02_fig16.png]]) for the diagonal. Whatever their class, transfinite objects, and fuses especially, display a variety of interesting phenomena.

The number of fuses reported is increasing rapidly so I will present here only those that display some variation on what we have previously seen reported with these objects. [Regarding fuses, Woods points out an error in the ''Scientific American'' illustration (April, page 116) in fuse b. The bottom row of two bits should be one row lower in order to work properly.]

The top of page eight shows two orthogonal fuses both of which, unlike all of the diagonal ones, 'burn' slower than the speed of light. '[[Washerwoman]]' was sent in by Abbe and every 18 generations converts two tubs into a pair of 'clotheslines' (traffic lights). 'Honey farm-II' supplied by the writer converts three fenceposts into a beehive every 12 generations.

====Page 8====
[[Image:Lifeline_vol02_fig17.png|framed|center|Washerwoman]]

[[Image:Lifeline_vol02_fig18.png|framed|center|Honey farm-II]]

Many fuses may be constructed by using objects other than the simple, single diagonal. Shown below are two such fuses which, at the speed of light, convert their fuse material into Class I and Class III (!) objects respectively. The first one converts its wavy diagonal (half-pond pieces) into a [[pond]] every six generations making it one of the two only known fuses that burns with a period not of multiple four. The other converts its double fuse into a glider every four generations thus creating a stream of gliders (20 generations apart in space). Question: what is the closest possible spacing for a stream of gliders in the same 'flight path'?

[[Image:Lifeline_vol02_fig19.png|framed|center|Two unusual fuses]]

====Page 9====
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I would now like to describe five unusual agars (not activated) all of which are periodic. The one shown to the right oscillates with a period of two. '[[Squaredance]]', a name I gave (because the bit pairs seem to move in and out around an open square) was sent in by Woods who actually named it the 'quilt'. The one below-left sent in by Steve Tower (no address given) looks as if it will completely die out (Θ). It does but only after creating an appropriate dispersion of bit pairs to replace it. Another oscillator discovered by Tower is truly unique for it is of period three! Each of its phases are shown. Can you detect anything unusual about this oscillator (besides the period) before it is revealed in [[Lifeline Volume 3|Issue Three]]?

{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig20.png|framed|center|Surviving bits]]
| [[Image:Lifeline_vol02_fig21.png|framed|center|The three phases of an oscillator field]]
|}

The last two agars (which were referred to on page four) are actually spaceships! The first of these shown at the left below was discovered by Robert Kraus of Chicago, Ill. Each member can be made any length desired (greater than four) by extending the two 'fins'. The second one discovered by the writer only comes in two sizes. The smaller version (not shown) is four units long and without the single bit. Both of these period one objects move orthogonally at the speed of light!

[[Image:Lifeline_vol02_fig23.png|framed|center|Two spaceship flotillas moving at the speed of light]]

====Page 10====
The next three examples actually involve finite fuses but in all cases the length of the fuse may be increased in multiples of four to achieve the same effect. They all illustrate how a glider's direction may be altered using fuses. I will, in a scenario of events, show how three fuses can be placed to demonstrate these findings. The creative staff includes (in order of occurrence) Rosenbaum, Webb, and Woods. The sequence of exhibits on this and the opposite page show, first, the three fuses at generation zero, then a glider (created by the short clean fuse) heading in generation eight towards the diagonal fuse (burning at both ends) where in generation twelve it is altered in flight and directed toward the 'synapse fuse' which gets activated by the glider (a signal) transmitting the signal thru the network (shown at generation 44) until reaching the other end where the signal is returned in generation 66 (as a glider displaced in time and space).

[[Image:Lifeline_vol02_fig24.png|framed|left|Generation: 0]] One of the most appealing features of fuses, from an experimental standpoint, is their ease of tracking. As stated in issue Number One (p.6) you need only a good supply of graph paper and not as much patience. The fact that fuses are periodic means that after a fairly small number of generations you can determine the period and identify each phase.

For anyone new to the game, LIFEFILE contains, among other things, a brief description of a convenient and reliable method for manually calculating Life object histories. Also, for anyone with access to a computer, but no program, I have provided an efficient program (FORTRAN source listing) written by Paul Boltwood of Ottawa, Ontario. The program calculates about three generations per second on an 80 by 80 matrix.

====Page 11====
{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig25.png|framed|center|Generation: 8]]
| [[Image:Lifeline_vol02_fig26.png|framed|center|Generation: 12]]
| [[Image:Lifeline_vol02_fig27.png|framed|center|Generation: 44]]
| [[Image:Lifeline_vol02_fig28.png|framed|center|Generation: 66]]
|}

====Page 12====
At this time we must deal with the inevitable question: what do we mean by an 'object'? My own criteria (arbitrary, of course) for determining if a [[pattern]] (of bits) is a single object are these:

1. Patterns whose bits are all connected (either orthogonally and/or diagonally) are objects.

2. Spatially connected patterns (a collection of objects, each of which is defined as above) are single objects if an empty cell between two or more of the 'subparts', and because of the subparts, is either a birth cell (when, without the subparts, would not have been) or a non-birth cell (when, without all the subparts, would have been.)

In other words, the subparts must have a mutual effect upon each other. The pattern at the left below {Figure 2.18, first pattern} is not a single object, but its next generation, center below, is a single object (by the definition just given). The smallest example of a stable spatially connected object is the '[[aircraft carrier]]' (Conway's term) shown at the right below.

{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig29.png|framed|center|A pattern]]
| [[Image:Lifeline_vol02_fig30.png|framed|center|An object]]
| [[Image:Lifeline_vol02_fig31.png|framed|center|Aircraft carrier]]
|}

Obvious exceptions to this definition include all objects in Classes II.E and IV.A because they are, by definition, '[[shuttle]]s' whose activity necessitates a movement thru open space. On page two my example given for Class V.E was purposely called a pattern (No.1,p.3) since it is not a true object. The idea there was to find the minimum pattern (object or not). Finally, members of Classes II.C, II.D, and the [[beacon]] may be considered objects since at least one of their phases meets the definition. This definition is important (at least for Class V objects) to preserve any meaning for the E.F. ratio discussed in March (page 6) since it excludes defining as an object (as was suggested by several readers) such things as 'a glider a long distance away from and heading towards a blinker, say'.

[[Image:Lifeline_vol02_fig32.png|framed|right|Three relatives (E.F. value)]] This brings us to the challenges proposed last issue of finding objects with maximum M.I.P. and E.F. ratios. Philip M. Cohen of Aliquippa, Pa. and Woods pointed out the only two other four-bit objects with an M.I.P. value of 5.0. These are shown at the right along with the [[T-tetromino|tetromino]] to illustrate their varying E.F. values. The third one, incidentally, sets the record for all four-bit objects.

Shown at the top of the next page are eight predecessor objects to the [[R-pentomino]]. The first three (a, b, and c) are the ones (all orthogonally-diagonally connected) that the writer had in mind when discussing this subject in March. The other five, all spatially connected, were sent in by Cohen (f), Corderman (a, c, and h), and Woods (a, b, d, e, f, and g). Three of these (a, c, and h) are all '[[grandfather]]s' to the R-pentomino and therefore have an E.F. value (the one Woods had in mind) of 221.0. Does anyone know of a five-bit great grandfather to the R-pentomino?

====Page 13====
[[Image:Lifeline_vol02_fig33.png|framed|center|A host of predecessors to the R-pentomino]]

[[Image:Lifeline_vol02_fig34.png|framed|right|Diehard]]Another interesting measure is the ratio of age to initial population for Class V.A objects. For example, five generations is the longest any four-bit object can last before dying (E.F.=1.25) and apparently eight generations is the longest any five-bit object can survive before death (E.F.=1.6). Can you identify either of these? Rosenbaum has discovered the object at the right of a mere eight bits that manages to stay alive 118 generations before death (E.F.=14.75)! Even though E.F.[V.A. max ≤ E.F.V max for objects of the same size, I think this represents a very interesting challenge by virtue of the final extinction requirement. Any information received regarding this or the other two ratios will be presented in [[Lifeline Volume 3|issue Three]].

Practically any variation to [[Conway's Game of Life|Life]] that you can think of is probably being investigated by at least one individual. I would now like to mention several areas of Life and Cellular Automata Theory in general that are being investigated. It is still too early to report many detailed results on these subjects, however.

Several readers have tried playing Life on boards finite in either one or two dimensions which is analogous to playing on a cylindrical or a toroidal (doughnut) surface. The most noteworthy of these involves the work of Donovan Smith of El Cerritor, Calif. who has investigated families of 'necklaces' and 'radicals' as he calls them, on 4 by n toroidal surfaces (see example).

{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig35.png|framed|center|A necklace]]
| [[Image:Lifeline_vol02_fig36.png|framed|center|A radical]]
|}

Oscillators with periods greater than two are very common (usually a multiple of four) and shown below at the left is one Smith discovered of period five (!) which begins in generation seven starting with a 4 by 12 necklace. Interestingly, the very same finite surface will support a period four oscillator sent in by Trawick shown below at the right.

[[Image:Lifeline_vol02_fig37.png|framed|center|Two oscillators supported on a 4 by 12 torus Left: Period 5      Right: Period 4]]

====Page 14====
Many phenomena exhibit interesting twists on a closed board. For instance, two [[overweight spaceship]]s (November column, page 118) of any identical length could travel together along the surface of a cylinder twelve units in circumference. A [[spaceship]] like the one described on page nine could travel unescorted endlessly across a 6 by 7 surface at the speed of light!

Two person games seem to be popular as evidenced by the large number of readers either requesting information or actually submitting ideas for games that they have developed. Rules for such games are easy to think up and the ones proposed vary widely. I will present here one of the many games suggested because it seems to have been played for awhile (tested) so has been refined from the original idea. Also, it embodies the concept of many other games sent in.

[[Immigration|IMMIGRATION]], a two-person game invented by Woods, is played as follows:

# Equipment - a 25 by 25 board (used as a finite matrix like the toroidal surface just described) and a good supply of two different colored counters (chips or stones).
# To setup - each player alternately places one of his 'people' (counters) on the board until each has placed five people.
# Rules to play - colors are irrelevant in determining survivals and births which use the same rules as in the regular version. Since a birth requires three neighbors (an odd number) the majority color (i.e. the color with two or three) determines the color of the newborn 'child'. Remember, the 98 border squares also have eight neighbors. Every ten generations the player with the most people places (immigrates) one extra person of his color in any empty cell. Then the other player does the same with his color. If neither player has a majority, they continue advancing thru additional generations until the tie is broken. The 'every ten generations' then applies to the tenth generation following the tie-breaking one. Unlike most other games IMMIGRATION involves a degree of skill (via the every tenth generation choice placement) and, as Woods says, 'also threatens stable Life forms'. The game is won when, at the time for immigration, only one color remains on the board. If both colors are extinct the game is a draw. Experience has shown that some basic strategies may be developed to increase the chances of winning.

Life may also be played as some readers have done, on a hexagonal tessellation which can be translated into an equivalent game on a square tessellation by suitable definition of neighborhood (see below).

{| style="margin-left:auto;margin-right:auto"
|-
| [[Image:Lifeline_vol02_fig38.png|framed|center|The hexagonal tesselation]]
| [[Image:Lifeline_vol02_fig39.png|framed|center|An equivalent tesselation]]
|}

====Page 15====
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Notice the neighborhood is now six rather than eight cells and therein lies the big question: what rules do we use? Ken Preston, Jr. of Norwalk, Conn. using the following set of rules has reported the existence of a Class III object similar to a lightweight spaceship (!): Survival requires two (and only two) bits anywhere in the six-cell neighborhood. Birth requires two bits in the neighborhood but not if they are opposite each other (i.e. in the illustration on the previous page, bits in cells 1 and 2 or in 1 and 3 would give birth but bits in cells 1 and 4 would not). The object shown at the right every six generations moves three units in the direction indicated (one of the three major axes). A filled hexagon (whose sides are alternately of length four and three) after 116 generations forms six 'hexagliders' (my term) which successfully escape. Six more are formed in generation 406 but are immediately 'gobbled up'. Still six more appear in generation 470 and succeed in escaping as did the original six. Preston has yet to determine its eventual fate.

Several ambitious readers are attempting to play Life in a three-dimensional matrix. The greatest problem here, I think, is choosing a set of rules for the 26-cell neighborhood. One reader, Harvey Lerman of Maitland, Fla., suggests the following method which attempts to make use of Conway's sound two-dimensional rules:

# Consider the three orthogonal planes thru a cell.
# Use Conway's rules on each plane separately.
# If the cell survives in at least two (Lerman is also considering all three) of the planes then it survives in three dimensions.
# Likewise for birth.

Whichever rule it is really not too difficult to compute and plot (each layer, say) but you definitely are more limited in grid (computer core) size and it is extremely difficult to conceptualize what is going on.

Martin Gardner in the February column (page 113) mentions proof of the existence of '[[Garden of Eden]]' (GoE) patterns. Recall, these are configurations that have no predecessor patterns so therefore could never be formed unless given in the initial (zero) generation. At that time we were assured that such patterns existed within a field 10^9 cells on a side. Two developments (one theoretical and the other experimental) since then have considerably reduced the area of search but unfortunately do not really help in finding such a GoE pattern. [[John Conway]] has succeeded in showing such patterns, 'orphans' as he calls them, exist on square boards of sides less than 4000. In connection with searching for GoE patterns, Gray has written such a program which uses brute force to examine and tabulate many candidate patterns. He has succeeded in proving that no GoE exist within a 4 by 4 square - a feat which required identifying predecessor patterns (fathers) for all the 65,536 possible 4 by 4 patterns (including rotations and reflections.) This effort required 90 minutes of computer (special purpose solid logic) time during which about 20 million 6 by 6 random patterns were created!

====Page 16====
Along this same line, several readers have inquired about 'backward synthesis' algorithms for determining predecessor patterns. To my knowledge, nothing has been done in this regard. If anyone has, I will be pleased to report their work in the next issue of LIFELINE.

It is not practical to report here the details on all the other variations on Life which readers have sent in. As the level of interest or effort in any particular area increases, I will include these in the newsletter. I solicit your ideas and suggestions on how more of the detailed information can be effectively disseminated. In the meantime, LIFEFILE, the appendix to LIFELINE, will be used to fill this need.

In closing LIFELINE Number Two, I think it appropriate to give some indication as to the subjects planned for future issues which the writer has in mind and is already developing. These are not in any particular order, and in some cases not too descriptive, but all are definitely food for thought.

COMING EVENTS:

* methods of stabilizing the boundary of transfinite objects
* spiral fuses
* some more interesting scenarios of Life's events
* an entire field of gliders
* 'fly by fuses'
* F.I.P. - another ratio
* [[spark]]s
* a catalog of glider-derived objects
* implications of aging - another rule for death
* measuring the density and center of mass of an object or pattern
* '[[constellation]]s'
* some potential spaceships
* Life family trees
* 'channel' phenomena
* self-repairable Life objects
* '[[tagalong|tag alongs]]'
* minimum predecessor patterns
* seeded agars
* some potential spaceship guns (!)
* entropy of a system of bits
* primordial broths
* illusions of motion exhibited by certain Life objects
* 'beehive', a period 30 agar
* 'antibodies' that thrive on glider streams
* constructing a computer with glider guns

====Page 17====
<center><pre>O OOO OOO OOO OOO OOO O OOO
O O O O O O O O
O O OO OO OO O O OO
O O O O O O O O
OOO OOO O OOO O OOO OOO OOO

A COMPREHENSIVE FILE OF INFORMATION GENERATED BY LIFE EXPERIMENTERS</pre></center>

LIFEFILE this issue regards ways of calculating Life histories. Many readers have requested computer programs and nearly as many have supplied source listings in addition to algorithms, hints, etc. that they are using. I have decided to present here two sound and efficient Life algorithms. The first of these described below is simply a procedure for tracking patterns manually using graph paper. The second, given on the next page, is a source listing of a FORTRAN (IV G) program written by Boltwood and slightly modified by the writer to change the input requirement and output display. The algorithm, to my knowledge, is the most efficient one in use. Input requires a header card followed by a set of cards containing the pattern for generation zero.

<pre>Header Card: cc 01-05: limit of calculation (gen. no)
06-10: frequency of printing
11-15: top row of initial pattern</pre>

<pre>Example: 0 1
123456789012345
75 4 31</pre>

This specifies the termination of calculation at gen. 75 (unless pattern dies out sooner) and output printed every 4 gens. The pattern supplied on the set of cards begins in row 31.

Set of pattern cards: The first card corresponds to top row in pattern and the following cards for each row. The card columns correspond to output columns. A '0' (or any non-blank character) may be punched for @ bit.

{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! A suggested manual method for 'playing Life'
|-
|
# Start generation zero by marking all 'live' cells with a 'O'.
# Scan* the pattern and mark all birth cells (those with exactly three neighbors) with a '.'.
# Check each bit for the possibility of death (those with other than two or three neighbors) and mark with a 'X'.
# Copy all 'O' and '.' to a new area for the next generation. Go back to step two.

[[Image:Lifeline_vol02_fig41.png|framed|center|Example]]
|-
| * scanning can be done by either or both of these methods:

a. scan each empty cell of every row (or column) passing adjacent to and thru the pattern.

b. scan each empty cell immediately around the pattern and within the pattern
|}

====Page 18====
Boltwood's Life program in FORTRAN:

<pre> IMPLICIT INTEGER (A-Z)
COMMON Q,ST,IT,C(6400)
INTEGER R(80)
DATA BL,BIT/' ','0'/
Q=80
QQ=Q*Q
DO 1 1=1,QQ
D(1)=Q
ST=9999
Q2=Q/2
REAC(5,8) CY,PI,I
FORMAT(315)
REAC(5,9,END=11)
FORMAT(80A1)
DO 10 K=1,0
IF(R(K).BQ.BL) GO TO 10
L=I*Q+K-I
D(L)=ST
ST=L
CONTINUE
I=I+1
GO TO 5
WRITE(6,3)
FORMAT('1')
IT=0
CALL PRT
DO 4 IT=1,CY
CALL NEXGEN(&6)
IF(MOD(IT,PI).EQ.0) CALL PRT
GO TO 2
WRITE(6,7) IT
FORMAT(' DIED AT ITERATION ',I4)
STOP
END

SUBROUTINE PRT
IMPLICIT INTEGER (A-Z)
COMMON Q,ST,IT,D(1)
INTEGER R(80)
DATA BL,BIT/' ','O'/
O=0
L=10000
B=ST
IF(K.EQ.9999) GO TO 21
J=MOD(K-1,Q)
IF(J.GT.B) B=J
IF(J.LT.A) A=J
IF=(K.GT.U) U=K
IF(K.LT.L) L=K
R=D(K)
GO TO 22
21 WRITE (6,23) IT
23 FORMAT(//' GENERATION', I5)
WRITE (6,28)
28 FORMAT(4X,'.........1.........2.........3.........4.........5.........6.........7.........8')
U=(U-1)/Q
L=(L-1)/Q
DO 27 K=1,Q
27 P(K)=BL
DO 24 I=L,U
DO 25 J=A,B
P(J)=BL
25 IF(D(I*Q+J+1).NE.O) P(J)=B IT
24 WRITE (6,26) I,P,I
26 FORMAT(1X,I3,80A1,I2)
WRITE (6,28)
RETURN
END

SUBROUTINE NEXGEN(*)
IMPLICIT INTEGER (A-Z)
COMMON Q,ST,IT,D(1)
INTEGER NK(8),NNK(8)
NB=-9999
B8=N8
K=ST
1 IF(K.EQ.9999) GO TO 6
CALL NEIBR(K,NK,&13)
NN=0
DO 2 I=1,8
NKI=NK(I)
IF(D(NKI).LE.0) GO TO 3
NN=NN+1
GO TO 2
3 IF(D(NKI).LT.0) GO TO 2
CALL NEIBR(NKI,NNK,&13)
NNN=0
DO 4 J=1,8
4 IF(C(NNK(J)).GT.0) NNN=NNN+1
IF(NNN.NE.3) GO TO 5
D(NKI)=NB
ND=-NKI
GO TO 2
5 D(NKI)=BB
BB=-NKI
2 CONTINUE
IF(NN.EQ.2.OR.NN.EQ.3) GO TO 12
13 D(K)=D(K)+10000
K=D(K)-10000
GO TO 1
12 K=D(K)
GO TO 1
6 CONTINUE
16 IF(ST.EQ.9999) RETURN 1
IF(D(ST).LT.10000) GO TO 14
I=ST
ST=D(ST)-10000
D(I)=0
GO TO 16
14 K=D(ST)
DK=ST
15 IF(K.EQ.9999) GO TO 11
IF(D(K).LT.10000) GO TO 20
D(DK)=D(K)-10000
D(K)=0
K=D(DK)
GO TO 15
11 IF(NB.EQ.-9999 GO TO 17
K=-NB
8 IF(K.EQ.-9999) GO TO 17
D(K)=-D(K)
CK=K
K=D(K)
GO TO 8
7 D(CK)=ST
ST=-NB
17 K=-BB
IF(K.EQ.9999) RETURN
I=K
K=-D(K)
D(I)=0
GO TO 9
END

SUBROUTINE NEIBR(K,NK,*)
IMPLICIT INTEGER (A-Z)
COMMON Q
INTEGER NK(8)
Q1=Q-1
K1=K-1
I=K1/C
J=MOD(KI,Q)
IF(I.EQ.0.OR.I.EW.W1.OR.J.EQ.0.OR.J.EQ.Q1) RETURN 1
NK(1)=K1
NK(2)=K1+2
NK(3)=K1+Q
NK(4)=NK(3)+1
NK(5)=NK(4)+1
NK(6)=K1-Q
NK(7)=NK(6)+1
NK(8)=NK(7)+1
RETURN
END</pre>

==Page Scans==
<gallery>
Image:Lifeline_vol_2.png|Page 1
Image:Lifeline_vol_2_p2.jpg|Page 2
Image:Lifeline_vol_2_p3.jpg|Page 3
Image:Lifeline_vol_2_p4.jpg|Page 4
Image:Lifeline_vol_2_p5.jpg|Page 5
Image:Lifeline_vol_2_p6.jpg|Page 6
Image:Lifeline_vol_2_p7.jpg|Page 7
Image:Lifeline_vol_2_p8.jpg|Page 8
Image:Lifeline_vol_2_p9.jpg|Page 9
Image:Lifeline_vol_2_p10.jpg|Page 10
Image:Lifeline_vol_2_p11.jpg|Page 11
Image:Lifeline_vol_2_p12.jpg|Page 12
Image:Lifeline_vol_2_p13.jpg|Page 13
Image:Lifeline_vol_2_p14.jpg|Page 14
Image:Lifeline_vol_2_p15.jpg|Page 15
Image:Lifeline_vol_2_p16.jpg|Page 16
Image:Lifeline_vol_2_p17.jpg|Page 17
Image:Lifeline_vol_2_p18.jpg|Page 18
</gallery>