LifeWiki:Object counts: Difference between revisions

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moved pseudo objects to separate table
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The behaviour of all configurations up to 8 [[cell]]s have been classified. All 9-cell patterns have been tested, but objects whose period is a factor of 12 were not classified. "Single cluster" configurations up to 10 cells have been tested, although again objects whose period is a factor of 12 were not classified.<ref name="t3604" />
The behaviour of all configurations up to 8 [[cell]]s have been classified. All 9-cell patterns have been tested, but objects whose period is a factor of 12 were not classified. "Single cluster" configurations up to 10 cells have been tested, although again objects whose period is a factor of 12 were not classified.<ref name="t3604" />
{|class="wikitable" style="text-align: center"
{|class="wikitable" style="text-align: center"
|+ style="text-align: left;" | Strict objects
!colspan="2"|cells||1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||16||17||18||19||20||21||22||23||24||25||26||27||28||29||30||31||32||33||34||35||36||37||38||39||40||41||42||43||44||45||46||47||48||49||50||51||52||53||54||55||56||57||58||59||60||61||62||63||64||65||66||67||68||69||70||71||72||73||74||75||76||77||78||79||80||81||82||83||84||85||86||87||88||89||90||91||92||93||94||95||96||97||98||99||100||101||102||103||104||105||106||107||108||109||110||111||112||113||114||115||116||117||118||119||120||121||122||123||124||125||126||127
!colspan="2"|cells||1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||16||17||18||19||20||21||22||23||24||25||26||27||28||29||30||31||32||33||34||35||36||37||38||39||40||41||42||43||44||45||46||47||48||49||50||51||52||53||54||55||56||57||58||59||60||61||62||63||64||65||66||67||68||69||70||71||72||73||74||75||76||77||78||79||80||81||82||83||84||85||86||87||88||89||90||91||92||93||94||95||96||97||98||99||100||101||102||103||104||105||106||107||108||109||110||111||112||113||114||115||116||117||118||119||120||121||122||123||124||125||126||127
|-
|-
|colspan="2"|'''still lifes''' (<tt>{{OEIS|A019473|tt=tt}}</tt>)||0||0||0||2||1||5||4||9||10||25||46||121||240||619||1353||3286||7773||19044||45759||112243||273188||672172||1646147||4051732||9971377||24619307||60823008||150613157||373188952||926068847||2299616637||5716948683||14223867298||35422864104
|colspan="2"|'''still lifes''' (<tt>{{OEIS|A019473|tt=tt}}</tt>)||0||0||0||2||1||5||4||9||10||25||46||121||240||619||1353||3286||7773||19044||45759||112243||273188||672172||1646147||4051732||9971377||24619307||60823008||150613157||373188952||926068847||2299616637||5716948683||14223867298||35422864104
|-
|-
|rowspan="7"|'''oscillators'''||'''p2''' (<tt>{{OEIS|A056614|tt=tt}}</tt>)||0||0||1||0||0||3||0||1||1||1||1||6||3||20||29||98||199||484||1083||2722||6596
|rowspan="7"|'''oscillators'''
|'''p2''' (<tt>{{OEIS|A056614|tt=tt}}</tt>)||0||0||1||0||0||3||0||1||1||1||1||6||3||20||29||98||199||484||1083||2722||6596
|-
|-
|'''p3'''||0||0||0||0||0||0||0||0||0||0||0||1||1||1||0||7||8||39||66||216
|'''p3'''||0||0||0||0||0||0||0||0||0||0||0||1||1||1||0||7||8||39||66||216
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|'''all other periods'''||0||0||0||0||0||0||0||0||0
|'''all other periods'''||0||0||0||0||0||0||0||0||0
|-
|-
|rowspan="8"|'''spaceships'''||'''(1,0)c/2'''<ref name="amling-c/2--pop-le-127" />||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||1||1||2||1||4||2||9||6||13||14||17||27||20||36||47||56||62||97||103||157||171||244||306||345||516||467||879||749||1334||1202||1816||1943||2511||3046||3835||4657||5726||6961||8576||10441||13116||16086||19755||24958||29547||37214||44477||55371||66544||82723||99474||123749||148721||184427||221313||273406||331180||408743||497303||615118||750032||917054||1127615||1370036
|rowspan="8"|'''spaceships'''
|'''(1,0)c/2'''<ref name="amling-c/2--pop-le-127" />||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||1||1||2||1||4||2||9||6||13||14||17||27||20||36||47||56||62||97||103||157||171||244||306||345||516||467||879||749||1334||1202||1816||1943||2511||3046||3835||4657||5726||6961||8576||10441||13116||16086||19755||24958||29547||37214||44477||55371||66544||82723||99474||123749||148721||184427||221313||273406||331180||408743||497303||615118||750032||917054||1127615||1370036
|-
|-
|'''(1,0)c/3'''<ref name="amling-c/3--pop-le-52" />||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||2||1||0||0||1||1||0||0||0||1||1||3
|'''(1,0)c/3'''<ref name="amling-c/3--pop-le-52" />||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||2||1||0||0||1||1||0||0||0||1||1||3
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{|class="wikitable" style="text-align: center"
{|class="wikitable" style="text-align: center"
|+ style="text-align: left;" | Pseudo objects
!colspan="2"|cells||1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||16||17||18||19||20||21||22||23||24||25||26||27||28||29||30||31||32||33||34||35||36||37||38||39||40||41||42||43||44||45||46||47||48||49||50||51||52||53||54||55||56||57||58||59||60||61||62||63||64||65||66||67||68||69||70||71||72||73||74||75||76||77||78||79||80||81||82||83||84||85||86||87||88||89||90||91||92||93||94||95||96||97||98||99||100||101||102||103||104||105||106||107||108||109||110||111||112||113||114||115||116||117||118||119||120||121||122||123||124||125||126||127
!colspan="2"|cells||1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||16||17||18||19||20||21||22||23||24||25||26||27||28||29||30||31||32||33||34||35||36||37||38||39||40||41||42||43||44||45||46||47||48||49||50||51||52||53||54||55||56||57||58||59||60||61||62||63||64||65||66||67||68||69||70||71||72||73||74||75||76||77||78||79||80||81||82||83||84||85||86||87||88||89||90||91||92||93||94||95||96||97||98||99||100||101||102||103||104||105||106||107||108||109||110||111||112||113||114||115||116||117||118||119||120||121||122||123||124||125||126||127
|-
|-
|colspan="2"|'''pseudo still lifes''' (<tt>{{OEIS|A056613|tt=tt}}</tt>)||0||0||0||0||0||0||0||1||1||7||16||55||110||279||620||1645||4067||10843||27250||70637||179011||462086||1184882||3069135||7906676||20463274||52816265||136655095||353198379||914075620||2364815358||6123084116||15851861075||41058173683
|rowspan="3"|'''pseudo still lifes'''
|'''all''' (<tt>{{OEIS|A056613|tt=tt}}</tt>)||0||0||0||0||0||0||0||1||1||7||16||55||110||279||620||1645||4067||10843||27250||70637||179011||462086||1184882||3069135||7906676||20463274||52816265||136655095||353198379||914075620||2364815358||6123084116||15851861075||41058173683
|-
|-
|rowspan="7"|'''pseudo oscillators'''||'''p2'''||0||0||0||0||0||0||0||0||0||1||2||14||17||46||78||225||484||1519||3350||9460||22134
|'''triple'''||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||1||11||26
|-
|'''quad'''||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||1
|-
|rowspan="7"|'''pseudo oscillators'''
|'''p2'''||0||0||0||0||0||0||0||0||0||1||2||14||17||46||78||225||484||1519||3350||9460||22134
|-
|-
|'''p3'''||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||2||5||20||44||90||265
|'''p3'''||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||2||5||20||44||90||265
Line 57: Line 67:
|'''all other periods'''||0||0||0||0||0||0||0||0||0||0||0||0||0
|'''all other periods'''||0||0||0||0||0||0||0||0||0||0||0||0||0
|-
|-
|rowspan="8"|'''pseudo spaceships'''||'''(1,0)c/2'''<ref name="amling-c/2--pop-le-127" />||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0
|rowspan="8"|'''pseudo spaceships'''
|'''(1,0)c/2'''<ref name="amling-c/2--pop-le-127" />||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0
|-
|-
|'''(1,0)c/3'''<ref name="amling-c/3--pop-le-52" />||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0
|'''(1,0)c/3'''<ref name="amling-c/3--pop-le-52" />||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0

Revision as of 04:51, 22 February 2024

This table contains counts of strict still lifes, oscillators and spaceships with specific population. It is an expansion of [1], however whereas that includes lower bounds from the number of known examples, values are only included here when they have been proven.

The behaviour of all configurations up to 8 cells have been classified. All 9-cell patterns have been tested, but objects whose period is a factor of 12 were not classified. "Single cluster" configurations up to 10 cells have been tested, although again objects whose period is a factor of 12 were not classified.[2]

Strict objects
cells 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127
still lifes (A019473) 0 0 0 2 1 5 4 9 10 25 46 121 240 619 1353 3286 7773 19044 45759 112243 273188 672172 1646147 4051732 9971377 24619307 60823008 150613157 373188952 926068847 2299616637 5716948683 14223867298 35422864104
oscillators p2 (A056614) 0 0 1 0 0 3 0 1 1 1 1 6 3 20 29 98 199 484 1083 2722 6596
p3 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 7 8 39 66 216
p4 0 0 0 0 0 0 0 0 0 0 0 2
p5 0 0 0 0 0 0 0 0 0 0 0
p6 0 0 0 0 0 0 0 0
p12 0 0 0 0 0 0 0 0
all other periods 0 0 0 0 0 0 0 0 0
spaceships (1,0)c/2[3] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 1 4 2 9 6 13 14 17 27 20 36 47 56 62 97 103 157 171 244 306 345 516 467 879 749 1334 1202 1816 1943 2511 3046 3835 4657 5726 6961 8576 10441 13116 16086 19755 24958 29547 37214 44477 55371 66544 82723 99474 123749 148721 184427 221313 273406 331180 408743 497303 615118 750032 917054 1127615 1370036
(1,0)c/3[4] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 1 1 0 0 0 1 1 3
(1,0)c/4[5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
(2,0)c/4[1] 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 5 0 9 2 7 2
(1,1)c/4 0 0 0 0 1 0 0 0 0
(2,0)c/5[6] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
spaceships with periods 6 or 12 0 0 0 0 0 0 0 0
all other types 0 0 0 0 0 0 0 0 0
Pseudo objects
cells 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127
pseudo still lifes all (A056613) 0 0 0 0 0 0 0 1 1 7 16 55 110 279 620 1645 4067 10843 27250 70637 179011 462086 1184882 3069135 7906676 20463274 52816265 136655095 353198379 914075620 2364815358 6123084116 15851861075 41058173683
triple 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 11 26
quad 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
pseudo oscillators p2 0 0 0 0 0 0 0 0 0 1 2 14 17 46 78 225 484 1519 3350 9460 22134
p3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 20 44 90 265
p4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
p5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
p6 0 0 0 0 0 0 0 0 0 0 0 0
p12 0 0 0 0 0 0 0 0 0 0 0 0
all other periods 0 0 0 0 0 0 0 0 0 0 0 0 0
pseudo spaceships (1,0)c/2[3] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(1,0)c/3[4] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(1,0)c/4[5] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(2,0)c/4[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
(1,1)c/4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(2,0)c/5[6] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
pseudo spaceships with periods 6 or 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
all other types 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

See also

References

  1. ↑ 1.0 1.1 1.2 Life Object Counts at Mark D. Niemiec's Life Page
  2. ↑ Nick Gotts (November 28, 2018). Systematic survey of small patterns (discussion thread) at the ConwayLife.com forums
  3. ↑ 3.0 3.1 Keith Amling (January 15, 2024). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  4. ↑ 4.0 4.1 Keith Amling (December 1, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  5. ↑ 5.0 5.1 Keith Amling (November 22, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
  6. ↑ 6.0 6.1 Keith Amling (November 15, 2023). Re: LLSSS min pop search results spam (discussion thread) at the ConwayLife.com forums
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