B36/S245
x=0, y = 0, rule = B36/S245
! #C [[ THEME Inverse ]]
#C [[ RANDOMIZE2 RANDSEED 1729 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
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LifeViewer -generated pseudorandom soup
Rulestring
245/36 B36/S245
Rule integer
26696
Character
Stable
Black/white reversal
B012578/S0134678
The rule sqrt replicator rule or B36/S245 is a Life-like cellular automaton in which cells survive from one generation to the next if they have 2, 4, or 5 neighbours and are born if they have 3 or 6 neighbours. Before the end of 2023, this rule was commonly referred to by the inaccurate name logarithmic replicator rule , due to its namesake object being misidentified.[1]
The cellular automaton has rulestring B36/S245, and differs from the "nearby" Move (B368/S245) in the lack of birth on 8 alive neighbours.
The time required to stabilize is generally much shorter than in Conway's Game of Life .
On August 19, 2020 , Peter Naszvadi constructed a Rule 110 unit cell in B36/S245, proving the rule Turing-complete .[2]
Notable patterns
The replicator
The name of this rule comes from an elementary replicator first discovered by Mark Niemiec . Unlike other replicators, (such as the one from HighLife ) this one does not reproduce itself cleanly , instead leaving oscillators behind which result in a more chaotic and slow growth pattern.[3]
x = 19, y = 3, rule = B36/S245
6o7b6o$o4bo7bo4bo$b4o9b4o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 ZOOM 10 ]]
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The namesake replicator with Θ(√t ) growth. It was initially assumed to have log(t) growth, leading to the incorrect and obsolete name.(click above to open LifeViewer ) RLE : here Plaintext : here
Its behaviour can be emulated by the following pattern, discovered by AforAmpere on April 11, 2020 in an isotropic non-totalistic rule:[4]
x = 3, y = 2, rule = B2a3eny4at/S01c2ci3i4e5e
bo$obo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 ZOOM 10 ]]
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A small replicator that emulates the one above(click above to open LifeViewer )
This emulates the 4 -state elementary cellular automaton in a range-1 neighbourhood, with rule integer 508169473510261892743356039977344.
Growth bounds
Per the convention in Rule 120 , let b2 (n) be the number obtained from writing n in binary and reading this result as a base-4 number. (ie. 1110 = 10112 , so b2 (7) = 10114 = 6910 )[n 1]
In AforAmpere's emulator shown above,
the bottom edge increases to width 1 on generation 2 , then to width n on generation f(n) = 2*b2 (n-1)+b2 (⌊n-1 2 ⌋)+5 .
(lim infn→∞ (f(n) n2 ) = 3 4 , lim supn→∞ (f(n) n2 ) = 9 4 )
the top edge increases to width n on generation g(n) = 3*b2 (⌊n 2 ⌋+1)+6*b2 (⌊n+2-2⌊log2 (n+2)⌋ 2 ⌋)+2*(n mod 2)+5 .
(lim infn→∞ (g(n) n2 ) = 3 8 , lim supn→∞ (g(n) n2 ) = 3 4 )
In the t th iteration, the pattern's total height has the asymptotic bounds 2*√t < h(t) < 2*√5*t √3 .
The rule's original name stemmed from this asymptotic growth rate being interpreted as logarithmic in character, rather than square-root growth.
Spaceships
The rule has known elementary spaceships of eighteen speeds (where those in bold have occurred naturally );
orthogonal: c/2 , c/3 , c/4 , c/5 , 2c/5 , c/6 , c/7 , 2c/7 ,[5] 3c/8 ,[6] 4c/23 .
diagonal: c/3, c/4 ,[7] c/5 ,[5] [8] c/6 ,[5] c/7 , c/8
knightwise: (2,1)c/5[5] and (2,1)c/6 .[9]
type
direction
speed
period
first known
discoverer
minimal known
discoverer
elementary
orthogonal
c/2
2
17P2H1V0
unknown
4
51P4H2V0
unknown
26P4H2V0
DroneBetter, 2024
6
48P6H3V0
DroneBetter, 2024[5]
8
43P8H4V0
DroneBetter, 2024[5]
10
156P10H5V0
DroneBetter, 2024[5]
12
73P12H6V0
DroneBetter, 2024[5]
20
43P20H10V0
Jason Summers, 2002
52
86P52H26V0
Jason Summers, 2002
c/3
3
28P3H1V0
unknown
6
71P6H2V0
DroneBetter, 2024[5]
61P6H2V0
DroneBetter, 2024
9
154P9H3V0
DroneBetter, 2024[5]
c/4
4
13P4H1V0
unknown
8
93P8H2V0
DroneBetter, 2024[5]
c/5
5
246P5H1V0
unknown
69P5H1V0
JMM, 2024
10
314P10H2V0
DroneBetter, 2024[5]
2c/5
5
380P5H2V0
unknown
208P5H2V0
Darren Li , 2024[5]
c/6
6
32P6H1V0
unknown
c/7
7
44P7H1V0
Evan Clark, 2006
2c/7
7
504P7H2V0
DroneBetter, 2024[5]
423P7H2V0
Darren Li, 2024[6]
14
68P14H4V0
DroneBetter, 2024[5]
3c/8
8
1372P8H3V0
Darren Li, 2024[6]
4c/23
23
14P23H4V0
unknown
diagonal
c/3d
3
60P3H1V1
unknown
c/4d
4
60P4H1V1
unknown
c/5d
5
146P5H1V1
DroneBetter, 2024[5]
c/6d
6
718P6H1V1
DroneBetter, 2024[5]
c/7d
7
Jellyfish (5P7H1V1)
Nathan Thompson , 1994
c/8d
8
64P8H1V1
DroneBetter, 2024[6]
knightwise
(2,1)c/5
5
544P5H2V1
DroneBetter, 2024[5]
(2,1)c/6
6
421P6H2V1
LaundryPizza03 , 2020[9]
corderoid
orthogonal
7c/150
300
58P300H14V0
Dean Hickerson , 1997
52P300H14V0
Benet Nasch, 2022[10]
7c/252
504
2715P504H14V0
FWKnightship,[11] Peter Naszvadi ,[12] toroidalet,[13] 2022
7c/501
2004
9980P2004H28V0
FWKnightship,[14] Peter Naszvadi,[15] 2022
7c/600
1200
280P1200H28V0
Dean Hickerson, 1997
x = 852, y = 265, rule = B36/S245
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305bob2obo10b3o12b3o111b2o2b2obo6bobo3bobo95bob2ob2o64b2o4bo45b3o14bob3o$305b6o12b3o8b3o114bobo11b3ob3o98b2o66b3o3b2o45bo2bo11b3o3bo$305bob2obo12b2o10b2o116bo118b2o64b3o50b4o10b4o3bo$304bo6bo10b2o12b2o114bo119b3o65b2o52bo8bobobo4bo$305b6o11b2obo8bob2o113b4o183bobo48bob4o7bo2b2o2bo$307b2o14bob2o6b2obo114b3o234bob2o2bo5b3o4bob2o$305bo4bo11bo2b2o6b2o2bo113bo2bo117bobo61bob2o47bo3b3o6b2ob2ob3obo$304bo2b2o2bo11bo2bo6bo2bo117bo117b3o63b2o49bo3bo4b2ob2obobobo$305b6o12bo2bo6bo2bo114bobobo114bo2bo62bob2o45bob5o5bo$304bo2b2o2bo11b2o10b2o115bo2b2o112b5o63bo46bobobob2o4bo8b2o$305bob2obo12bobo8bobo116b2o114bo2b2o62b3o44bob2o2bo5b3o7bo$304b2o4b2o9b2obo2b2o2b2o2bob2o113b2o114b2ob3o109bo10bobo6bo$305b2o2b2o11bo4b2o2b2o4bo114bo116b2o62bob2o45b2ob2o7b2o7bo$306bo2bo12b5o6b5o112bob4o112bo3bo61bo46bobo3bo8bo6bo$305bo4bo11bo3bo2b2o2bo3bo116bo114bo2bo61bo44b6o8b2o2bo4bo$323b2obobo2bobob2o115b2obo116bo61bo43b2o2bobob2o5bo2bob2ob2o$322b2o4bo2bo4b2o115b2obo115bo59bobo43b3obo2bo8bobo3bo$327b2o2b2o119b3obo114bo60bo2bo41bobo6bo5b2obo3bo$452b3o176bo3bo42b2o10bobobo$325b2o6b2o116bo179b3o45bo11b3o$325b2o6b2o117b3o177b2o46bo4b3obobo$631bo56b4o$324bo2b6o2bo118b2o172b2o53b2o3b3o$324b3o6b3o118b3o170bo2bo52bobobo$325b2o2b2o2b2o119b2o170bo3bo50b2obo4bo$323bo3b2o2b2o3bo115bo2bo169bobo2bo51bo7bo$324bo3bo2bo3bo116bo2bo169b3o51bobo7bo$323bo4bo2bo4bo116bo2bo171bo50bobo4b3o$325bobo4bobo120b2o167b2o2b2o48b2o6b2o$326bobo2bobo119bo2bo167bo3b2o51b2obob3o$325bo8bo117bo2bo167b3obo53bobo2bo$326bo6bo120bo167b2o2b2o50bo4b2o$324bo3bo2bo3bo286bo3bo52bobo$324bo4b2o4bo116b2o169bo54bo$324bo10bo117bo169b3o48bo2bo$324bo3b4o3bo115bobo170bo50b2o$324bob3o2b3obo114bo171b2o$324bo2b2o2b2o2bo114b4o165b2obo49b3o$323bo3bob2obo3bo114b2o165bo2b2o45bo2b2o$322bo3bob4obo3bo113bo2b3o162bo47bo2b3o$323bo2b8o2bo113b7o161b2o46b2o2b3o$323b2o10b2o114b2obo211b2o4b2o$323bobobo4bobobo113b2o2b2o216bo$322bob2o2bo2bo2b2obo116bo210bobo2bo$323bo2b3o2b3o2bo117bo209bob2o2b2o$322b5o6b5o324bob5o2bo$322b2o2bo6bo2b2o115b2o207bo2b6o$322b2ob3o4b3ob2o117bobo207b2o$324bobo6bobo117b2o2b2o202b2obobo$452b3obo199b2obo2bo$452bo205bobobo$323bo12bo116b2o201bo2bobo$323b4o6b4o118bo198bobo2bob2o$322bo4bo4bo4bo116bobo197b3o4b2o$321b4o10b4o116b2o199bobob3o$322b3o10b3o116bo199bob3o$455bo197bob5o$322bobo10bobo115b2o198b2ob4o$320bo2b2o10b2o2bo311bobobobo$322b4o8b4o312b2o$324bo10bo314b3o$323bo12bo314b2o$321bo2bo10bo2bo306b4obo$323b2o10b2o306bo2b2ob2o$325b2o6b2o307bo2b4o$325bo8bo308bobo2bo$322b3o10b3o303b2o2b2o2bo$325bo8bo308b4obo$328b4o310bo$327b2o2b2o$326b2o4b2o$325b3ob2ob3o$323bobobob2obobobo$322b2o2bo6bo2b2o$321b2o3b2o4b2o3b2o$320bobo4b6o4bobo$320b2o2bobob4obobo2b2o$327b2o2b2o2$326b3o2b3o$324bo2b2o2b2o2bo$324b2ob6ob2o$327b6o$324bo10bo$325bobo4bobo$327bob2obo$325bo8bo$328b4o$328b4o$328bo2bo$327bo4bo$327bob2obo$326bo2b2o2bo$325bo2bo2bo2bo$325b2o6b2o$324bo10bo$326bo6bo$327bo4bo$323bobo8bobo$322bob2o8b2obo$322bobobo6bobobo$322bobo10bobo$324bo10bo$323bo12bo$322b3o10b3o$325b2o6b2o2$324b2o3b2o3b2o$324bo2b6o2bo$323bo2bob4obo2bo$323b2o2bo4bo2b2o$324b4ob2ob4o$324b2o3b2o3b2o$324bob8obo$323b3ob6ob3o$323bo12bo$324bobo6bobo$320b2o2bo10bo2b2o$323bobobo4bobobo$321bobo2bo6bo2bobo$324b2o8b2o2$323bo3bo4bo3bo$323bo12bo$325bo8bo$321bob2o10b2obo$321b3obo8bob3o$323bo12bo$323bo12bo$321b2o14b2o$323bo12bo$321b3o12b3o$321bo16bo$324bo10bo$323bo12bo$324bobo2b2o2bobo$323b2o2b6o2b2o$324bo2bo4bo2bo$326bobo2bobo$323b2obobo2bobob2o$323bo3b2o2b2o3bo$323bo2b3o2b3o2bo$326bo6bo$325bob2o2b2obo$327bob2obo$327b2o2b2o2$327bo4bo3$329b2o$329b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 WIDTH 3430 HEIGHT 1085 ZOOM 4 ]]
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known elementary spaceships of minimal width and population for each speed, period and symmetry(click above to open LifeViewer )
In 1997 , Dean Hickerson discovered two replicator-based spaceships traveling at 7c/150 orthogonal and 7c/300 orthogonal respectively:
x = 38, y = 17, rule = B36/S245
15bobo$16bo4bobo$12bo3bo4bobo12bo$12bo2bobo2bo3bo9b2obo$12bo2bobo2bo3b
o9b2obo$12bo3bo4bobo12bo$16bo4bobo$15bobo4$b4o$3bo17bo$o2bo15b2obo$o2b
o15b2obo$3bo17bo$b4o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 2 ZOOM 12 ]]
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14c/300o(click above to open LifeViewer ) RLE : here Plaintext : here Catagolue : here
x = 280, y = 163, rule = B36/S245
170bo$171bo$170bo16bo$127b3o38b2obo14bob2o$168b2obo14bob2o$170bo16bo$
171bo$170bo7$171bobo$170b2obo$169bo2bo15b2o$169b3o16bobo$169b3o16bobo$
169bo2bo15b2o$170b2obo$171bobo6$236bobo$170bo32bo15b2o14bo2b2o36b2o$
171bo31bo14bobo14bo3b2o34bobo$170bo16bo15bo14bobo14bo3b2o34bobo$168b2o
bo14bob2o29b2o14bo2b2o36b2o$127b3o38b2obo14bob2o46bobo$170bo16bo$171bo
$170bo6$237bo$94bo27bo27bo27bo41bo15bob2o37bo$93bob2o24bob2o24bob2o24b
ob2o38bob2o13b5o35bob2o$93bob2o24bob2o24bob2o24bob2o38bob2o13b5o35bob
2o$94bo27bo27bo27bo41bo15bob2o37bo$237bo4$4o24b4o24b4o48bo3b2o$81b2o
25bob2o2b2o$10b2o26b2o26b2o13b3o23b3o6b2o19b2o$9bobo25bobo25bobo38bobo
b2ob3o2b2o16bobo$9bobo25bobo25bobo38bobob2ob3o2b2o16bobo$10b2o26b2o26b
2o39b3o6b2o19b2o97bobo$108bob2o2b2o103b2o14bo2b2o36b2o$108bo3b2o89bo
14bobo14bo3b2o34bobo$203bo14bobo14bo3b2o34bobo$203bo15b2o14bo2b2o36b2o
$236bobo2$110bo$108b2obobo$20b2o86bo3b3o$19b4o84b2obo2bobobo$19b2o84b
2obo3bo2b4o18bo$20bo83bobo5bob4obo15b2obo$104bobo5bob4obo15b2obo$105b
2obo3bo2b4o18bo$85bo21b2obo2bobobo$85bo22bo3b3o$85bo22b2obobo$110bo15$
26bo$25bo59bo$26bobo56bo18bo$27bo57bo18bo$105b2o16bo13bo$102bob4o13b2o
bo10b2obo$102bob4o13b2obo10b2obo$105b2o16bo13bo$104bo$104bo4$241bo$
203bo15b2o12b3ob4ob2ob2o29b2o$203bo14bobo12bo3bo7bobo27bobo$203bo14bob
o12bo3bo7bobo27bobo$106bo11b2o99b2o12b3ob4ob2ob2o29b2o$10b2o26b2o26b2o
37b3o15b2o12b2o102bo$9bobo25bobo25bobo36b2o12b2o2bobo11bobo$9bobo25bob
o25bobo36b2o12b2o2bobo11bobo$10b2o26b2o26b2o13b3o21b3o15b2o12b2o$81b2o
23bo11b2o$4o24b4o24b4o3$234bo$235bo11bo$94bo27bo27bo27bo41bo14bo3bo4bo
bo30bo$93bob2o24bob2o24bob2o24bob2o38bob2o11b2o4b2o2bo3bo27bob2o$93bob
2o24bob2o24bob2o24bob2o38bob2o11b2o4b2o2bo3bo27bob2o$94bo27bo27bo27bo
41bo14bo3bo4bobo30bo$235bo11bo$234bo4$170bo2$163b2o6bob3o$161b2o7bo3bo
12bo$127b3o30bo3bo2b6obob2o8bob2o51bo$160bo3bo2b6obob2o8bob2o29b2o12b
3ob4ob2ob2o29b2o$161b2o7bo3bo12bo15bo14bobo12bo3bo7bobo27bobo$163b2o6b
ob3o27bo14bobo12bo3bo7bobo27bobo$203bo15b2o12b3ob4ob2ob2o29b2o$170bo
70bo5$169bo3b2o$169b3ob2obo$164bob2o4b3obo$164bo3b2o2b2ob3o10b2o$164b
3o4bobo14bobo$164b3o4bobo14bobo$164bo3b2o2b2ob3o10b2o$164bob2o4b3obo$
169b3ob2obo$169bo3b2o5$170bo2$163b2o6bob3o$161b2o7bo3bo12bo$160bo3bo2b
6obob2o8bob2o$127b3o30bo3bo2b6obob2o8bob2o$161b2o7bo3bo12bo$163b2o6bob
3o2$170bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ HEIGHT 500 WIDTH 700 THUMBSIZE 2 ZOOM 2 ]]
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28c/1200o(click above to open LifeViewer ) RLE : here Plaintext : here
Linear growth
Replicators can also be used to create a gun for the c/7 diagonal ship:
x = 74, y = 45, rule = B36/S245
55b2o$55bobo$16bo38bobo$14b4o37bobo$13bo2bobo36bobo$13bo2bobo36b2o$14b
4o$16bo9$69b4o$68bo4bo$2b2o64b6o$bo2bo$bo2bo$6o$bo2bo28b6o$2b2o29bo4bo
$34b4o11$50b2o$49bobo$49bobo$49bobo$23bo25bobo$22b4o24b2o$21bobo2bo$
21bobo2bo$22b4o$23bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ MAXGRIDSIZE 9 HEIGHT 600 WIDTH 800 THUMBSIZE 2 ZOOM 8 ]]
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(click above to open LifeViewer ) RLE : here Plaintext : here
On May 28, 2021, Luka Okanishi constructed the following period-408 4c/23 spaceship gun without synthesizing from smaller ships.[16]
x = 110, y = 64, rule = B36/S245
23b2obo2b2obo2bo38bo2bob2o2bob2o$23bob3obobo2b2o38b2o2bobob3obo$13bo2b
o6bob3obobo2b2o38b2o2bobob3obo6bo2bo$14b2obo5b2obo2b2obo2bo38bo2bob2o
2bob2o5bob2o$12b3obo76bob3o$15bo78bo12$29bo50bo$28b4o46b4o$27bobo2bo
44bo2bobo$5b3o19bobo2bo44bo2bobo19b3o$3bob2obo19b4o46b4o19bob2obo$5bo
23bo50bo23bo$4b3o47b2o47b3o$52bob2obo$52b2o2b2o$52bob2obo$54b2o$54b2o$
7b2obo88bob2o$5b4o5bo80bo5b4o$4bo2bo2b2ob2o80b2ob2o2bo2bo$4bo2bo2b2ob
2o80b2ob2o2bo2bo$5b4o5bo80bo5b4o$7b2obo88bob2o2$53b4o$54b2o$52bob2obo$
53bo2bo$54b2o$35b2o36b2o$35b2o16b4o16b2o$33bo4bo32bo4bo$2b4o28bo2bo34b
o2bo28b4o$2bo2bo26b2ob2ob2o13bo16b2ob2ob2o26bo2bo$2bo2bo27bob2obo13bob
o16bob2obo27bo2bo$2bo2bo45bobo50bo2bo$3b2o47b2o51b2o$52bobo$52bo5$2bo
2bo14bobo64bobo14bo2bo$2bo2bo14b2obo62bob2o14bo2bo$o2b2o2bo11bo4bo60bo
4bo11bo2b2o2bo$obo2bobo11bo4bo60bo4bo11bobo2bobo$20b2obo62bob2o$2b4o
14bobo12b2o36b2o12bobo14b4o$3b2o29bo2bo34bo2bo29b2o$35b2o36b2o$35b2o
36b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ MAXGRIDSIZE 9 HEIGHT 700 WIDTH 960 THUMBSIZE 2 ZOOM 8 ]]
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On September 23, 2022, FWKnightship constructed a 14c/504 orthogonal replicator-based puffer ,[11] which Peter Naszvadi [12] and toroidalet [13] both found spaceship versions of on the following day. Also on September 24, FWKnightship found a second puffer with a speed of 28c/2004 orthogonal,[14] which Naszvadi completed into a spaceship two days later.[15]
Notes
See also
Rule 120 , another one-dimensional cellular automaton exhibiting Θ(√t ) growth.
References
↑ DroneBetter (November 22, 2023). Regarding the name of the """logarithmic""" replicator rule (discussion thread) at the ConwayLife.com forums
↑ Peter Naszvadi (August 19, 2020). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums
↑ David Eppstein. "Replicators: B36/S245 ". Replicators . Retrieved on June 2, 2019.
↑ AforAmpere (April 11, 2020). Re: Miscellaneous Discoveries in Other Cellular Automata (discussion thread) at the ConwayLife.com forums
↑ 5.00 5.01 5.02 5.03 5.04 5.05 5.06 5.07 5.08 5.09 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 DroneBetter (March 3, 2024). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ 6.0 6.1 6.2 6.3 DroneBetter (April 27, 2024). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ B36/S245 at David Eppstein 's Glider Database
↑ May13 (March 3, 2024). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ 9.0 9.1 LaundryPizza03 (December 21, 2020). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ the attribution page , December 15, 2022
↑ 11.0 11.1 FWKnightship (September 23, 2022). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ 12.0 12.1 Peter Naszvadi (September 24, 2022). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ 13.0 13.1 toroidalet (September 24, 2022). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ 14.0 14.1 FWKnightship (September 24, 2022). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ 15.0 15.1 Naszvadi (September 26, 2022). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
↑ Luka Okanishi (May 28, 2021). Re: B36/S245 (discussion thread) at the ConwayLife.com forums
External links