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OCA:Grounded Life

2024-03-23T23:14:48Z

MEisSCAMMER: /* Soup search */ grammar and thousands of billions --> trillions

{{Rule
|name = Grounded Life
|b = 35
|s = 23
|char = Chaotic
|ruleinteger = 6184
|reversal = B0123478/S0124678
}}
'''Grounded Life''' is a [[Life-like cellular automaton]] in which a [[cell]] survives from one generation to the next if it has 2 or 3 [[Neighbourhood|neighbors]], and is born if it has 3 or 5 neighbors. Under this rule, patterns tend to stabilize much more quickly than in standard [[Life]],<ref name="post5304" /> which is one of the reasons for its name.

==Patterns==
The two most common objects in Grounded Life are the [[block]] and the [[blinker]].

Some patterns work as they do in [[Life]], but many instead die off completely, such as the [[beehive]], [[boat]], [[T-tetromino]], [[pi-heptomino]], and [[stairstep hexomino]].

===Still lifes===

Because Grounded Life adds one birth transition from Life, all still lives in Grounded Life are still lives in Conway's Game of Life, but the reverse is not true. For example, the [[boat]] fails in Grounded Life.

Many small still lifes under the standard Life rules have dead cells with five alive neighbours, so the list of still lifes for the two rules are extremely different for both small and large cell counts. The smallest patterns that are still lifes in the standard Life rules but not in Grounded Life are boat (with 5 cells), beehive (with 6 cells) and [[loaf]], [[long boat]] and [[fishhook]] (with 7 cells). Thus, the smallest asymmetric still life is [[hook with tail]].

Also, any pattern using a [[house]], [[bookend]], or [[bun]] as an induction coil that is a still life under the standard rules, any extended forms of the [[ship]] or [[boat]], any still life in Life that contains a [[pre-block]] [[motif]] (that is not part of a [[hook]] or stabilised by an aircraft carrier-like formation) or a still life where a 2-cell long line stabilises a 4-cell line by induction are not still lifes in Grounded Life.

All still lifes up to 12 bits have occurred naturally. Only two still lifes with 13 bits have not occurred naturally, namely {{LinkCatagolue|xs13_25a88gzwca1|rule=b35s23|style=raw}} and {{LinkCatagolue|xs13_32akg8426|rule=b35s23|style=raw}}. Notably, [[barge]], [[aircraft carrier]] and [[carrier bridge carrier]] are much more common than in Life, with carrier bridge carrier being about 1,500 times as common as it is in Life, making it the most common 12-cell still life by far.

===Oscillators===

[[Natural]]ly occurring objects in this rule include oscillators of periods 2, 3, 4, 5, 8 and 26. There are also [[semi-natural]] oscillators of periods 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 18, 21, 24, 26, 29, 33, 46, 82, and 142. Alien oscillators are also much more common than in similar{{which}} rules, especially 8P8 (a mirrored [[short table]]) and 8P4 (a [[pre-pulsar]] predecessor in Life).

Notably, the [[washing machine]] is much more common in this rule, even in asymmetric soups.
It is the 56th most common object in asymmetric soups and the 21st most common object in D4_x1 soups. [[Toad]]s and [[clock]]s are also significantly more common, and blinkers are more common than blocks.
{{EmbedViewer
|rle = x = 14, y = 12, rule = B35/S23
$9bo$8bobo$7bo3bo$8bo2bo$9b3o2$4bo$3bobo$3bobo$4b2o!
|position = center
|caption = Typical formation of a washing machine with a [[bun]] (Which evolves to the [[fleet]] sequence) and a [[bakery]] sequence, that does not work in Life. This also highlights the fact that washing machines tend to form with [[beacon]]s.
|viewerconfig = #C [[ HEIGHT 600 ZOOM 20 AUTOSTART GPS 10 THEME BOOK T 0 PAUSE 2 T 77 PAUSE 2 LOOP 100 ]]
|style = width:300px;
}}

Many alien oscillators exist in this rule, several of which are shown below:
{{EmbedViewer
|rle = x = 0, y = 0, rule = B35/S23History
94F$F24.F17.F20.F28.F$F24.F17.F20.F28.F$F2.2D13.2A.2A2.F2.2D6.A6.F4.D
15.F28.F$F.D2.D5.2A4.A2.2A.A.F.D2.D3.3A.A.A2.F3.2D3.3A9.F28.F$F4.D3.3A
2.A2.A4.2A.F4.D8.2A2.F2.D.D4.A4.4A2.F28.F$F3.D4.A2.3A3.A3.A2.F2.2D6.A
.3A2.F.D2.D9.4A2.F28.F$F2.D7.2A4.2A4.A.F4.D4.2A.A4.F.5D3.A4.4A2.F11.6A
11.F$F.D14.A.2A2.A.F.D2.D4.A7.F4.D3.3A3.4A2.F28.F$F.4D12.2A.2A2.F2.2D
5.A7.F4.D15.F9.A8.A9.F$F24.F17.F20.F8.A.A6.A.A8.F$F24.F17.F20.F7.A.A8.
A.A7.F$65F6.A.A10.A.A6.F$F21.F41.F7.A12.A7.F$F2.2D4.A6.A5.F9.2D30.F4.
A7.D3.D6.A4.F$F.D2.D3.2A4.2A5.F8.D2.D29.F4.A6.2D2.2D6.A4.F$F.D6.2A4.2A
5.F8.D2.D4.6A6.2A.2A8.F4.A5.D.D.D.D6.A4.F$F.3D5.A4.A6.F9.2D4.A.4A.A6.
A.A9.F4.A7.D3.D6.A4.F$F.D2.D16.F8.D2.D4.6A6.2A.2A8.F4.A7.D3.D6.A4.F$F
.D2.D4.A4.A6.F8.D2.D4.A4.A19.F4.A7.D3.D6.A4.F$F2.2D6.A2.A7.F9.2D30.F7.
A4.D3.D3.A7.F$F10.4A7.F41.F6.A.A10.A.A6.F$F10.A2.A7.43F7.A.A8.A.A7.F$
F10.A2.A7.F41.F8.A.A6.A.A8.F$F10.A2.A7.F2.2D4.D32.F9.A8.A9.F$F10.4A7.
F.D2.D2.2D7.2A15.2A6.F28.F$F10.A2.A7.F4.D.D.D7.2A15.2A6.F11.6A11.F$F9.
A4.A6.F3.D4.D32.F28.F$F21.F2.D5.D32.F28.F$F9.A4.A6.F.D6.D32.F28.F$F8.
2A4.2A5.F.4D3.D12.2A5.2A11.F28.F$F8.2A4.2A5.F17.A4.A5.A4.A7.F28.F$F8.
A6.A5.F16.3A3.A5.A3.3A6.F28.F$F21.F16.A.A2.A7.A2.A.A6.30F$31F33.F28.F
$F29.F33.F28.F$F29.F8.A.A2.A7.A2.A.A6.F28.F$F20.2D3.2D2.F8.3A3.A5.A3.
3A6.F28.F$F19.D2.D.D2.D.F9.A4.A5.A4.A7.F28.F$F22.D4.D.F13.2A5.2A11.F28.
F$F20.2D3.2D2.F33.F21.2A5.F$F22.D4.D.F33.F5.2A9.2A3.A.A4.F$F19.D2.D.D
2.D.F33.F4.A.A9.A.A2.3A4.F$F20.2D3.2D2.F8.2A15.2A6.F4.3A9.2A10.F$F3.3A
6.3A14.F8.2A15.2A6.F28.F$F4.A8.A15.F33.F28.F$F18.46F6.A21.F$F6.2A2.2A
6.F44.F5.A.A4.D3.2D10.F$F6.2A2.2A6.F44.F5.3A3.2D2.D2.D9.F$F18.F44.F10.
D.D2.D12.F$F18.F44.F9.D2.D2.3D10.F$F18.F37.2A5.F9.5D.D2.D9.F$F6.2A2.2A
6.F10.3A24.2A5.F12.D2.D2.D2.3A4.F$F6.2A2.2A6.F10.2A7.2D3.2D3.3A5.2A5.
F12.D3.2D3.A.A4.F$F18.F10.3A5.D2.D.D2.D2.3A12.F22.A5.F$F4.A8.A4.F12.2A
7.D.D20.F28.F$F3.3A6.3A3.F6.2A4.2A6.D2.3D18.F28.F$F18.F6.2A11.D3.D2.D
17.F11.2A9.3A3.F$F18.F7.3A8.D4.D2.D17.F5.3A2.A.A9.A.A3.F$F18.F8.2A8.4D
2.2D12.3A3.F5.A.A3.2A9.2A4.F$F18.F7.3A21.2A5.3A3.F6.2A20.F$F18.F31.2A
11.F28.F$F18.F31.2A11.F28.F$F18.F44.F28.F$F18.F44.F28.F$F18.F44.F28.F
$94F$F36.F55.F$F36.F55.F$F36.F55.F$F36.F13.2A21.2A17.F$F36.F13.A.A19.
A.A17.F$F36.F14.2A19.2A18.F$F36.F22.2A3.2A26.F$F36.F21.A.A3.A.A25.F$F
2.2D3.2D7.3A7.3A7.F21.3A3.3A25.F$F.D2.D.D2.D6.A2.A5.A2.A7.F22.A5.A26.
F$F.D2.D4.D6.A.A7.A.A7.F6.2A35.2A10.F$F2.2D4.D8.2A7.2A8.F6.A.A33.A.A10.
F$F.D2.D2.D28.F7.2A33.2A11.F$F.D2.D.D10.2A7.2A8.F55.F$F2.2D2.4D6.A.A7.
A.A7.F55.F$F16.A2.A5.A2.A7.F55.F$F16.3A7.3A7.F55.F$F36.F55.F$F36.F10.
2A27.2A14.F$F36.F9.A.2A25.2A.A13.F$F36.F9.3A8.D4.D3.2D8.3A13.F$F36.F19.
2D3.2D2.D2.D23.F$F36.F18.D.D2.D.D5.D23.F$F36.F20.D.D2.D4.D24.F$F36.F9.
3A8.D.5D2.D9.3A13.F$38F9.A.2A7.D4.D2.D9.2A.A13.F$F36.F10.2A8.D4.D2.4D
7.2A14.F$F23.2A11.F55.F$F23.2A11.F55.F$F36.F55.F$F36.F55.F$F36.F55.F$
F6.D2.2D7.2A3.2A11.F7.2A33.2A11.F$F5.2D.D2.D6.A4.2A11.F6.A.A33.A.A10.
F$F4.D.D.D2.D7.A4.A11.F6.2A35.2A10.F$F6.D2.2D12.2A11.F22.A5.A26.F$F6.
D.D2.D12.A11.F21.3A3.3A25.F$F6.D.D2.D13.5A3.2A.F21.A.A3.A.A25.F$F6.D2.
2D15.A.2A3.2A.F22.2A3.2A26.F$F36.F14.2A19.2A18.F$F36.F13.A.A19.A.A17.
F$F36.F13.2A21.2A17.F$F27.A.A6.F55.F$F28.2A6.F55.F$F36.F55.F$94F$F30.
F27.F33.F$F2.2D5.D20.F10.2A15.F21.A11.F$F.D2.D3.2D20.F10.2A15.F20.A.A
10.F$F4.D2.D.D20.F27.F21.A11.F$F3.D2.D2.D20.F27.F33.F$F2.D3.5D6.3A10.
F27.F33.F$F.D7.D8.A11.F8.A18.F19.2A12.F$F.4D4.D5.A2.2A10.F7.A.A8.2A7.
F3.D3.2D10.2A12.F$F15.3A.A2.2A6.F7.A.2A6.A2.A6.F2.2D2.D2.D9.A4.3A6.F$
F15.A.2A3.2A6.F8.2A.A5.3A7.F.D.D5.D15.2A3.A2.F$F22.3A5.F10.A5.A.A5.2A
.F3.D3.2D4.A7.2A6.A.A.F$F25.A4.F17.A6.2A.F3.D5.D2.A.A6.2A7.A2.F$F18.3A
4.A4.F27.F3.D2.D2.D3.A3.2A14.F$F18.3A4.A4.F27.F3.D3.2D8.3A4.A8.F$F10.
A9.A9.F27.F23.2A8.F$F7.A.2A10.3A6.F.2A6.A17.F23.2A8.F$F2.2A3.2A21.F.2A
5.A.A5.A10.F33.F$F3.A26.F7.3A5.A.2A8.13F21.F$F4.A25.F6.A2.A6.2A.A19.F
10.A10.F$F3.2A5.2A18.F7.2A8.A.A9.2D4.2D2.F9.A.A9.F$F10.A19.F18.A9.D2.
D2.D2.D.F10.A10.F$F11.A18.F31.D2.D2.D.F21.F$F6.2A3.2A17.F30.D4.3D.F21.
F$F4.2A.A22.F29.D7.D.F21.F$F4.A25.F15.2A11.D5.D2.D.F21.F$F30.F15.2A11.
4D3.2D2.F21.F$F30.F39.F21.F$94F!
|viewerconfig = #C [[ HEIGHT 1150 WIDTH 800 ZOOM 8 GRID OFF THEME LifeHistory AUTOSTART GPS 8 ]]
|position = center
|caption = A [[stamp collection]] of natural and semi-natural oscillators. From left to right, top to bottom, they are:
{{LinkCatagolue|xp2_62bd46|rule=b35s23|patternname=12P2|style=raw}} and [[Washing machine]] (rare examples of [[billiard table]]s in Grounded Life. Note that washing machine still works in Life, but is notably more common in this rule and is thus mentioned.), 
{{LinkCatagolue|xp3_2ir0qcez03|rule=b35s23|patternname=14P3|style=raw}} (a natural oscillator resembling the [[caterer]]), 
{{LinkCatagolue|xp4_hrh|rule=b35s23|patternname=8P4|style=raw}} (a [[pre-pulsar]] predecessor in rules without B5e as it is dependant on that transition. It resembles 8P8.), 
{{LinkCatagolue|xp4_ffff|rule=b35s23|patternname=12P4|style=raw}} (dependent on the B5a transition; the pattern dies in Life due to the lack of it. Also most common in [[one-cell-thick pattern]]s and C4_4, instead of its native symmetry, D8_4. ), 
{{LinkCatagolue|xp11_xg8k81111118k8gzs0121y61210sz70g8gy6g8g07zx1252gggggg2521|rule=b35s23|patternname=56P11|style=raw}} (resemblant of [[Achim's p11]]), 
{{LinkCatagolue|xp6_7ey0e7z01u44u1z0872278ze7y07e|rule=b35s23|patternname=46P6|style=raw}} (Four [[rock]] toads hassling unknown active region, also a strong [[emulator|middleweight]] [[spark]]er), 
{{LinkCatagolue|xp8_2d7777d2|rule=b35s23|patternname=14P8|style=raw}} (extensible, although only in discrete lengths or with proper [[induction coil]]s. Also dependent on the B5a transition; the pattern dies in Life due to the lack of it), 
{{LinkCatagolue|xp8_rar|rule=b35s23|patternname=8P8|style=raw}} (a mirrored [[short table]]), 
{{LinkCatagolue|xp33_131oowoo131zxoowooz464y2464|rule=b35s23|patternname=32P33|style=raw}} (four [[block]]s hassling four [[T-tetromino]]s), 
{{LinkCatagolue|xp21_33yb33zc6cw97y179wc6cz6c6wisy1siw6c6zooyboo|rule=b35s23|patternname=60P21|style=raw}} (four blocks hassling 8 [[pi-heptomino]]es), 
{{LinkCatagolue|xp26_ggw77toz1bee|rule=b35s23|patternname=18P26|style=raw}} (the highest-period oscillator to have appeared naturally), 
{{LinkCatagolue|xp26_cccy177zwggy1ooozw33|rule=b35s23|patternname=24P26|style=raw}} (an oscillator composed of interacting beehive sparks; appears in 1 in 1250 C4_4 soups), 
{{LinkCatagolue|xp46_caey5ea4w756z0caczydckcz0o8ow8ksy5skczw11|rule=b35s23|patternname=48P46|style=raw}} (a [[shuttle]] of [[loaf]] and [[beehive]] sparks), 
{{LinkCatagolue|xp82_79d2y12d97ze9b4y14b9e|rule=b35s23|patternname=36P82|style=raw}} (A [[T-nose]]), 
{{LinkCatagolue|xp142_y3356y1g8oxo8gy1653zckoy8131x131y8okczzx6572yl2756zx6ae4yl4ea6z0ggytggz321y8ocoxocoy8123zy3ca6y211x11y26ac|rule=b35s23|patternname=104P142|style=raw}} (A [[B-heptomino]] shuttle, also the highest period oscillator to have appeared semi-naturally), 
{{LinkCatagolue|xp18_y133z35xbvzy313133x33zy5123|rule=b35s23|patternname=32P18|style=raw}} (four blocks hassling an unknown active region), 
{{LinkCatagolue|xp24_4cgw6423z01hg8ow3d8zw1|rule=b35s23|patternname=24P24|style=raw}} (A group of 4 [[phi spark]]s hassling each other, also a flipper), 
{{LinkCatagolue|xp24_woowdnp8sze1110scczw111|rule=b35s23|patternname=30P24|style=raw}} (A flipper), 
{{LinkCatagolue|xp29_y533zy269ek8y0gcqa4xggzggy2gy31y211z11x4ab61y025eiczyaoo|rule=b35s23|patternname=44P29|style=raw}} (Has four [[transparent object|transparent]] blocks), 
and {{LinkCatagolue|xp13_y4252z0gy173gg04ccwg8gz121w664011osy11zy58k8|rule=b35s23|patternname=40P13|style=raw}} (4 [[crotchet]] [[spark]]s hassled by 4 [[tub]]s and a block)
  
|style = width:300px;
}}

104P142 can be [[monomer]]ised to create 38P142 or [[polymer]]ised to create an [[agar]]:<ref name="post165772"/>

{{EmbedViewer
|rle = x = 25, y = 14, rule = B35/S23
2o21b2o$obo19bobo$b2o19b2o5$9bo5bo$8b3o3b3o$8bobo3bobo$9b2o3b2o$b2o19b
2o$obo19bobo$2o21b2o!
|position = center
|caption = 38P142, which has [[mod]] 71 and is a [[flipper]].
|viewerconfig = #C [[ THEME Book STARTFROM 142 ]]
|style = width:300px;
}}

{{EmbedViewer
|rle = x = 139, y = 139, rule = B35/S23
57b2o21b2o$57bobo19bobo$58b2o19b2o$66b2o3b2o$67bo3bo$64bobo5bobo$66bo
5bo$50b2o13bo7bo13b2o$50bobo33bobo$51b2o33b2o5$55bo27bo$57bo23bo$53bob
2o25b2obo$53b2o29b2o4$53b2o29b2o$53bob2o25b2obo$57bo23bo$55bo27bo$32b
2o71b2o$32bobo69bobo$33b2o69b2o$41b2o3b2o43b2o3b2o$42bo3bo45bo3bo$39bo
bo5bobo39bobo5bobo$41bo5bo17bo7bo17bo5bo$25b2o13bo7bo17bo5bo17bo7bo13b
2o$25bobo36bobo5bobo36bobo$26b2o39bo3bo39b2o$66b2o3b2o4$30bo27bo21bo
27bo$32bo23bo25bo23bo$28bob2o25b2obo17bob2o25b2obo$28b2o29b2o17b2o29b
2o4$28b2o29b2o17b2o29b2o$28bob2o25b2obo17bob2o25b2obo$32bo23bo25bo23bo
$30bo27bo21bo27bo$7b2o121b2o$7bobo119bobo$8b2o119b2o$16b2o3b2o43b2o3b
2o43b2o3b2o$17bo3bo45bo3bo45bo3bo$14bobo5bobo39bobo5bobo39bobo5bobo$
16bo5bo17bo7bo17bo5bo17bo7bo17bo5bo$2o13bo7bo17bo5bo17bo7bo17bo5bo17bo
7bo13b2o$obo36bobo5bobo39bobo5bobo36bobo$b2o39bo3bo45bo3bo39b2o$41b2o
3b2o43b2o3b2o4$5bo27bo21bo27bo21bo27bo$7bo23bo25bo23bo25bo23bo$3bob2o
25b2obo17bob2o25b2obo17bob2o25b2obo$3b2o29b2o17b2o29b2o17b2o29b2o4$3b
2o29b2o17b2o29b2o17b2o29b2o$3bob2o25b2obo17bob2o25b2obo17bob2o25b2obo$
7bo23bo25bo23bo25bo23bo$5bo27bo21bo27bo21bo27bo4$41b2o3b2o43b2o3b2o$b
2o39bo3bo45bo3bo39b2o$obo36bobo5bobo39bobo5bobo36bobo$2o13bo7bo17bo5bo
17bo7bo17bo5bo17bo7bo13b2o$16bo5bo17bo7bo17bo5bo17bo7bo17bo5bo$14bobo
5bobo39bobo5bobo39bobo5bobo$17bo3bo45bo3bo45bo3bo$16b2o3b2o43b2o3b2o
43b2o3b2o$8b2o119b2o$7bobo119bobo$7b2o121b2o$30bo27bo21bo27bo$32bo23bo
25bo23bo$28bob2o25b2obo17bob2o25b2obo$28b2o29b2o17b2o29b2o4$28b2o29b2o
17b2o29b2o$28bob2o25b2obo17bob2o25b2obo$32bo23bo25bo23bo$30bo27bo21bo
27bo4$66b2o3b2o$26b2o39bo3bo39b2o$25bobo36bobo5bobo36bobo$25b2o13bo7bo
17bo5bo17bo7bo13b2o$41bo5bo17bo7bo17bo5bo$39bobo5bobo39bobo5bobo$42bo
3bo45bo3bo$41b2o3b2o43b2o3b2o$33b2o69b2o$32bobo69bobo$32b2o71b2o$55bo
27bo$57bo23bo$53bob2o25b2obo$53b2o29b2o4$53b2o29b2o$53bob2o25b2obo$57b
o23bo$55bo27bo5$51b2o33b2o$50bobo33bobo$50b2o13bo7bo13b2o$66bo5bo$64bo
bo5bobo$67bo3bo$66b2o3b2o$58b2o19b2o$57bobo19bobo$57b2o21b2o!
|position = center
|caption = 104P142-based agar, which can be stabilised with [[ship]]s.
|viewerconfig = #C [[ HEIGHT 950 WIDTH 800 THEME Book STARTFROM 142 ]]
|style = width:300px;
}}

===Spaceships===

Of particular note is the fact that neither the [[glider]] nor any of the [[xWSS]]es work in Grounded Life (all of them die off), giving the rule its name. No known spaceships work in both Life and Grounded Life. The most common spaceship according to [[Catagolue]] is the [[OCA:Glider 3736|glider 3736]].

Known [[spaceship]] speeds are c/2o, c/3o, c/4o, c/5o, c/6o, 2c/5o, c/4d and c/5d.

The three smallest spaceships in {{rl|Pseudo Life}} also work.
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
2b3o$bo3bo$o2bo2bo$3ob3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -4 THEME Book STARTFROM 10 ]]
|position = center
|caption = 13P5H2V0 (glider 3736) (Robert Wainwright, 1994)
|style = width:100px;
|apgcode = xq5_359a953/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
2bo$b3o$o3bo$bo2bo$3b2obo$6bo$4bobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 6 ]]
|position = center
|caption = 14P3H1V0 (glider 4793) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq3_0oogheez17/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
3bo$b2ob2o$o2bo2bo$obobobo$3bo$bo3bo$bobobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 18P2H1V0 (glider 4716) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq2_4urhru4zw202/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
o3b2o6bo$2ob4o5bo$o5b2o2b5o$3bo3b3obo$3bob2ob2obo$5b3o$6b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 27P4H1V0 (glider 13284) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq4_05p3gz420s8gazdtf/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
2bo$o2bo$o2b4ob2o$bo4bo$2bo3bo$3b2obo3bo$8bob3o$8b2o$10bo2bo$9bo3bo$9bo$9bo4bo$10bo$11b3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y 0 THEME Book STARTFROM 4 ]]
|position = center
|caption = 35P4H1V1 (Sokwe, 2010)
|style = width:100px;
|apgcode = xq4_xgg0qen6vf72z021tpn1z2e631/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
17b2o2$15b2o$14bobo$13b2o$11b4o2bo4bo$11bobo3bo2bobo$10b3obo2bobo2bo$6bo6b2ob
2ob2o$4bobo3b3o3bo$2b3o6bo4b2o$bo5b2o7b2o$5o2b2o2b2obo2bo$b4o4bo2b2o$2b3o5bo
2bo$3bo7b3o$11bob2o$12b2o$9bo3bo$7b3o3bo$8b2o$9b4o$10b2o$11bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 600 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 90P4H1V1
|style = width:100px;
|apgcode = xq4_y9go4c11zy0g0oxknlbd0of0ca07z4etttw668g5co4037zx1xggo035v2zy4136e2/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
11bo$10bobo$8b2o$6bo$6bo3bo3bo$5bob4o2bo$3b2obo2bo2b3o$5bo2b2obob3o$2b
o2bob3o3bo2bo$2bo2b5obo3bo$bo2b2o9b2o$o6bobo3bob4o$bo4bo7b2o$5b4o2bo3b
o$4bob2o4bo4b3o$7bob5o$8bob2o$11bo2bo$11bo2bo$14bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 600 Y -2 THEME Book STARTFROM 5 ]]
|position = center
|caption = 78P5H1V1
|style = width:100px;
|apgcode = xq5_ow11t6i0ok88z163hlxoo92ce8ggs4zw1611act0o8krd2zy3c4701/b35s23
}}}}
{{gallery bottom}}

In particular, many [[tagalong]]s for 90P4H1V1 and 18P2H1V0 are known. This is due to their easily-connectable-to spark.

{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 31, y = 32, rule = B35/S23
11bo$10b2o$9b4o$8b2o$7b3o3bo$9bo3bo$12b2o$11bob2o$3bo7b3o$2b3o5bo2bo$
b4o4bo2b2o$5o2b2o2b2obo$bo5b2o$2b3o6bo4bo$4bobo3b2o2bo2b2o$6bo6b2o2bo
$13b2o$17b4o$13bo2b4o$13bo9b3o$15b7obo2bo$17b2o4bo$18b3o$19b3o$21bo2b
2o$18bo2bo2bo$18bobo3b3o2bo$25bo2b3o$25bo3b2o$26bob3o$25b4o$27bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 HEIGHT 500 Y -4 THEME Book STARTFROM 10 ]]
|position = center
|caption = Smallest 90P4H1V1 tagalong found.
|style = width:100px;
|apgcode = xq4_ssm36qz01w157wepojzy0244702iqrra20czy84680730c40gg60c88gzychubp4211w7f731zyd7hgguc4zyf31/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 34, y = 35, rule = B35/S23
11bo$10b3o$9b3obo$8b4obo$9b3ob2o2$14b2o$4bo6b2o$3b2o6b2o$2b4o4bo$b2o6b
o4bo$3o4b2o2bob2o$2bo3bobob2o$4b7o4b2ob2o$7bo3bo2b3o$20bo$13bo4bobo$14b
2ob2ob2o$14bo2b2ob3o2b2o$17b2obob2o$17bo2bob2o2bo$20bo2b3o3b2o$28b2ob
o$19b3o6bo$19bo4b3obo$19bo4b4obo$20bo6b2o$23bob2obobo$22b2o3bo$21b3o2b
obo3bo$29b2o2bo$30bo2bo$30bo2bo2$31b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 HEIGHT 500 Y -2 THEME Book STARTFROM 6 ]]
|position = center
|caption = Another 90P4H1V1 tagalong.
|style = width:100px;
|apgcode = xq4_s11sgz0104gdqlkg7318gzw48c70h99og2q30gzy3220136v0f70468zya22033p80d6ieb6220so8zye880661y01731zyf178vf72/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 9, rule = B35/S23
2b3o$b2ob2o$2o3b2o$b2ob2o$b5o2$2bobo2$2b3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = Smallest 18P2H1V0 tagalong, at 3 cells.
|style = width:100px;
|apgcode = xq2_4urhru4zwa8a/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 25, rule = B35/S23
2b3o$b2ob2o$2o3b2o$b2ob2o$b5o2$2bobo2$2b3o2$3bo$2bo$bobo$bobo2$b3o2$2bo$bo$ob
o$obo2$3o2$bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = Infinitely extensible 18P2H1V0 tagalong.
|style = width:100px;
|apgcode = xq2_4urhru4zwa8az0c2dzg9l1z545z534/b35s23
}}}}
{{gallery bottom}}

As of late 2023, there is an ongoing search for spaceships that work in both [[Life]] and Grounded Life, as none are known yet. Such searches have had no results as of March 2024.

=== Puffers ===

There is a naturally occurring orthogonal [[glide-symmetric]] c/2 [[puffer]] with period 136, leaving three [[blinker]]s in a half-[[interchange]] formation and two [[block]]s every 68 ticks. Combining two or more puffers can give other puffers and spaceships.<ref name="post12942" /><ref name="post17286" /> The puffer engine also works in [[Pseudo Life]] (B357/S238) (where it becomes a p248 puffer). As of 2023, all known natural infinite growth relies on this puffer.
On September 10, 2021, FWKnightship posted a 24c/48 siderake emitting 2c/5 spaceships.<ref name="post135647" />

{{EmbedViewer
|rle = x = 81, y = 16, rule = B35/S23
16b2o$16b2o2$57bo$57bo$57b2o14b3o$12b2o39bo18b4o$3o3b3o3b2o33bo3b3o2b
2ob2o10b4o3b2o$25bo11b3o7bo4b2o4b3o11b2o5b2o$4bo20b2o10bobo7bo4bo4bob
2o14b2ob2o$4bo18b4o10b3o12bo3bo4bo13b4o$4bo18b2o25b3o7b4o12bo$17bo42b
o$17bo2bo19b2o18bobo$16bo3bo19b2o$17bobo!
|viewerconfig = #C [[ HEIGHT 360 WIDTH 900 THUMBSIZE 2 ZOOM 10 GPS 12 AUTOSTART TRACKLOOP 136 1/2 0/2 ]]
|position = center
|caption = A period-136 orthogonal c/2 puffer<ref name="post12942" />
|style = width:300px;
|apgcode = yl68_1_17_f843afff9c5c3cef7d244e5948674525/b35s23
}}

{{EmbedViewer
|rle = x = 8, y = 14, rule = B35/S23
o2b3o$2ob4o$b3o2b2o$2b3obo$5bo2$2o$2o2$5bo$2b3obo$b3o2b2o$2ob4o$o2b3o
!
|viewerconfig = #C [[ HEIGHT 360 WIDTH 900 THUMBSIZE 2 ZOOM 16 GPS 12 AUTOSTART TRACKLOOP 136 1/2 0/2 ]]
|position = center
|caption = A semi-natural p32 spaceship based on this puffer, using two engines.
|style = width:300px;
|apgcode = xq32_36cfbje4z66xgzc63fdc72/b35s23
}}

===Beehive/block reburnable fuse===
One of the most useful reactions is the following [[reburnable]] [[block fuse]], in which a beehive spark interacts with a chain of blocks, moving it further down the chain. It moves at a [[speed]] of 3c/4 orthogonal and has [[period]] 4.<ref name="post35738" />

{{EmbedViewer
|rle = x = 58, y = 4, rule = B35/S23:T59,10
19bo2b2o$2ob2ob2ob2ob2ob2obo4b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob
2ob2ob2ob2ob2obo4b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$19bo2b2o!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 ]]
|position = center
|caption = The beehive/block fuse
|style = width:300px;
}}

Once the beehive reaches the end, it will reverse direction while shortening the chain, and will eventually annihilate it given enough time. This can be stopped with a [[pond]]:<ref name="post160876" />

{{EmbedViewer
|rle = x = 32, y = 13, rule = B35/S23
bo27b2o$obob2ob2ob2ob2ob2ob2ob2ob2obo2bo$obob2ob2ob2ob2ob2ob2ob2ob2ob
o2bo$bo27b2o6$bo$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$obob2ob2ob2ob2ob2ob2o
b2ob2ob2o$bo!
|viewerconfig = #C [[ AUTOSTART ZOOM 15 WIDTH 1000 GPS 6 LOOP 145 T 0 PAUSE 2 ]]
|position = center
}}

A beehive followed by <tt>n</tt> blocks turns into two vertically spaced blocks in <tt>{{frac|2*n2+23*n+42|3}}</tt> generations if <tt>n ≡ 2 (mod 3)</tt>, and is otherwise a [[diehard]] lasting <tt>{{frac|2*n2 + 23*n + {{frac|55 if n%3 {{=}}{{=}} 0 else 52|3}}|3}}</tt> generations.

These chains can interact in different ways to form logic gates.<ref name="post164488" />

{{EmbedViewer
|rle = x = 95, y = 79, rule = B35/S23
53b2o$53b2o$12b2o$11bobo2b2o35b2o17b2o$11b2o3bo36bobo16bobo$17bo36b2o
17b2o$3bo12b2o$2bobob2ob2ob2obo5b2ob2ob2ob2ob2ob2o$2bobob2ob2ob2obo5b
2ob2ob2ob2ob2obobo2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob
2o$3bo12b2o19b2o2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob2o
$17bo$11b2o3bo20b2o$11bobo2b2o19b2o15b2o17b2o$12b2o39bobo16bobo12b2o$
37b2o14b2o17b2o13b2o$37b2o$53b2o32b2o$37b2o14b2o32b2o$37b2o$87b2o$37b
2o48b2o$37b2o$87b2o$37b2o48b2o$37b2o$33b2o6b2o39b2o3b2o$32bobo6bobo38b
2o3b2o$32b2o3b2o3b2o$37b2o43b2o3b2o$81bobo3bobo$37b2o42b2o5b2o$37b2o$
88b2o$37b2o50bo$18b2o17b2o49bo$17bo2bob2o64b2o$17bo2bob2o13b2o$18b2o17b
2o49b2o$88b2o$37b2o$5b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2bobo49b2o$4bobob2o
b2ob2ob2ob2ob2ob2ob2ob2o2b2o50b2o$4b2o61b2o$67b2o19b2o$18b2o68b2o$4b2o
11bo2bob2o$4b2o11bo2bob2o23b2o22b2ob2ob2ob2ob2o3b2o$18b2o27bo23b2ob2o
b2ob2ob2o3b2o$4b2o42bo$4b2o43bobob2ob2ob2ob2ob2o21b2o$50b2ob2ob2ob2ob
2ob2o21b2o$4b2o64b2o$4b2o22b2ob2ob2ob2ob2ob2ob2o22bobo15b2o$27bobob2o
b2ob2ob2ob2ob2o23b2o15b2o$4b2o21b2o$4b2o46b2o12b2o$2o6b2o17b2o23bobo11b
2o$2o6b2o17b2o24b2o2$27b2o$b2o4b2o18b2o$obo4bobo$2o6b2o17b2o$4b2o21b2o
$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o21b2o$4b2o2$4b2o21b2o$4b2o21b2o2$
4b2o$3bo2bo$3bo2bo$4b2o!
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 WIDTH 1000 ZOOM 6 GPS 6 LOOP 300 ]]
|position = center
|caption = A collection of beehive/block fuse reactions linked to each other.
|style = width:300px;
}}

Alternatively, a blinker following a [[pre-beehive]] also allows for a [[clean]] ignition of the block fuse, although different circuitry is needed. Similarly to the reburnable form, it moves at a speed of 3c/4 and has period 4. It also produces [[corner dot]]s.<ref name="post166070" />

{{EmbedViewer
|rle = x = 0, y = 0, rule = B35/S23
3o2$2b2o$2b2o$2b2o2$2b2o$2b2o2$2b2o$2b2o2$2b2o$2b2o2$2b2o$2b2o2$2b2o$
2b2o2$2b2o$2b2o2$2b2o$2b2o2$2b2o$2b2o2$2b2o$2b2o2$2b2o$2b2o2$5b2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$5b2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obobo$66b2o!
|viewerconfig = #C [[ AUTOSTART ZOOM 8 HEIGHT 400 WIDTH 1000 GPS 6 T 0 PAUSE 2 LOOP 140 ]]
|position = center
|caption = The block fuse with a pre-beehive and blinker ignition
|style = width:300px;
}}

There also exist converters that convert clean to reburnable ignition and vice versa.<ref name="post169032" />

{{EmbedViewer
|rle = x = 0, y = 0, rule = B35/S23
36b2o$35bo2bo$35bo2bo46b2o$36b2o47bobo$86b2o$36b2o$36b2o48b2o$86b2o$36b
2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b
2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b
2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b
2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b
2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b
2o$36b2o48b2o$86b2o$36b2o$36b2o48b2o$86b2o$36b2o$37bo$34bo49b2o$34b2o
48b2o2$34b2o$2b3ob2ob2ob2ob2ob2ob2ob2ob2ob2obobo17b3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o5b2o$ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o18b3ob2ob2ob2ob2o
b2ob2ob2ob2ob2obobo3bobo$o84b2o3b2o$o!
|viewerconfig = #C [[ AUTOSTART ZOOM 5 HEIGHT 400 WIDTH 1000 GPS 6 T 0 PAUSE 2 LOOP 130 ]]
|position = center
|caption = Converters. The left one converts from clean to reburnable ignition, while the right one converts from reburnable to clean ignition.
|style = width:300px;
}}

==Change in frequency, stabilisation time and evolutionary sequences==
{{main|OCA:Grounded Life/List of common objects}}
From the same random starting conditions, Grounded Life usually settles into much fewer objects than in Life due to the fact that many life [[evolutionary sequence]]s are sparks in this rule. It also stabilises ten times faster than Life on average.

The [[honey farm]] sequence, which evolves into 4 [[blinker]]s in a [[traffic light]]-like formation with a [[tub]] inside, is much rarer in Grounded Life due to the fact that the only 7-cell predecessor that still works is the line of seven, which is much rarer than the other predecessors.

The traffic light sequence is considerably rarer in Grounded Life due to the T-tetromino's disappearance, so the next most common predecessor that works is the X-pentomino, which is rarer.

The [[Bakery]], [[Teardrop]], [[Butterfly]], [[R-pentomino]], [[Blonk-tie]] and [[Procrastinator]] die out. While the fully formed [[Fleet]] is stable, its predecessors die out, making it much rarer as it can only form by chance.

==Universality==
On August 3, 2023, AlbertArmStain published a {{rl|Rule 110}} unit stripe based on the aforementioned beehive/block reburnable fuse, proving the rule's [[Universal computer|Turing-completeness]]. <ref name="post164523" />

== Soup search ==
{{related|Catagolue|Tutorials/Contributing to Catagolue}}

Soup search was performed using a modified version of [[apgsearch]], yielding uncommon objects such as the c/3o spaceship (Glider 4793) as early as 2014.<ref name="post13161" />

On October 12, 2022, the {{cata|census/b35s23/C1|b35s23/C1}} census on [[Catagolue]] reached a total of one trillion objects,<ref group=c name="C1_1e12" /> making Grounded Life one of several [[Life-like rule]]s with hauls [[Catagolue#Haul verification|subject to statistical verification and peer review]] before being committed.

The b35s23/C1 census accumulated 375 million objects in April 2015,<ref group=c>[https://web.archive.org/web/20150422135228/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2015-04-22)</ref>
169 billion objects in October 2017,<ref group=c>[https://web.archive.org/web/20171029134053/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2017-10-29)</ref>
519 billion objects in July 2021,<ref group=c>[https://web.archive.org/web/20210716224801/http://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2021-07-16)</ref>
561 billion objects in October 2021,<ref group=c>[https://web.archive.org/web/20211030140403/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2021-10-30)</ref>
1.69 trillion objects in February 2023,<ref group=c>[https://web.archive.org/web/20230221163702/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2023-02-21)</ref>
and 1.72 trillion objects in August 2023.<ref group=c>[https://web.archive.org/web/20230806111857/https://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2023-08-06)</ref>

==See also==
* [[OCA:Grounded Life/List of common objects]]
* {{rl|Pseudo Life}}, a rule where many patterns from this rule also work, although with generally more chaotic evolution.
* {{rl|B35/S236}}, an exploding rule one outer-totalistic condition away from Grounded Life

==References==
<references>
<ref name="post5304">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 5304
|title = Re: B35/S23
|author = LumpsOfMuck
|date = October 14, 2011
}}</ref>
<ref name="post12942">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 12942
|title = Re: B35/S23
|author = Lewis
|date = August 19, 2014
}}</ref>
<ref name="post13161">{{LinkForumThread
|format = ref
|f = 7
|t = 1443
|p = 13161
|title = Re: apgsearch: a high-performance soup searcher
|author = Lewis
|date = September 10, 2014
}}</ref>
<ref name="post17286">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 17286
|title = Re: B35/S23
|author = praosylen
|date = February 27, 2015
}}</ref>
<ref name="post135647">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 135647
|title = Re: B35/S23
|author = FWKnightship
|date = September 10, 2021
}}</ref>
<ref name="post35738" >{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 35738
|title = Re: B35/S23
|author = Hdjensofjfnen
|date = September 15, 2016
}}</ref>
<ref name="post160876" >{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 160876
|title = Re: B35/S23
|author = Haycat Durnak
|date = April 26, 2023
}}</ref>
<ref name="post164488">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 164488
|title = Re: B35/S23
|author = Layz Boi
|date = August 3, 2023
}}</ref>
<ref name="post164523">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 164523
|title = Re: B35/S23
|author = AlbertArmStain
|date = August 4, 2023
}}</ref>
<ref name="post165772">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 165772
|title = Re: B35/S23
|author = Confocaloid
|date = August 26, 2023
}}</ref>
<ref name="post166070" >{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 166070
|title = Re: B35/S23
|author = MEisSCAMMER
|date = August 31, 2023
}}</ref>
<ref name="post169032" >{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 169032
|title = Re: B35/S23
|author = MEisSCAMMER
|date = April 26, 2023
}}</ref>
</references>

; Catagolue
<references group=c>
<ref name="C1_1e12">[https://web.archive.org/web/20221013093222/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1], [https://web.archive.org/web/20221013093138/https://catagolue.hatsya.com/haul/b35s23/C1 /haul/b35s23/C1] (archived copies as of 2022-10-13)</ref>
</references>

==External links==
* {{LinkCatagolueRule|b35s23}}
* {{LinkForumThread|t=757|title=B35/S23}}

[[Category:Life-like cellular automata]]

Alain Noels

2023-10-29T15:59:45Z

MEisSCAMMER: the template appears to have broken the redirect

#REDIRECT [[Garden of Eden#Records]]
{{proposeddeletion|[[LifeWiki:Tiki bar#Proposed deletion of redirects from personal names to pages about a different subject]]}}

User talk:Not a pun

2023-10-28T22:22:13Z

MEisSCAMMER: new section

===Re: your userpage===
You wanted a way to embed RLEs on the wiki; the template you want is [[Template:EmbedViewer|EmbedViewer]]. [[User:MEisSCAMMER|MEisSCAMMER]] ([[User talk:MEisSCAMMER|talk]]) 22:22, 28 October 2023 (UTC)

User:H. H. P. M. P. Cole/OCA:Factorio

2023-10-09T00:26:30Z

MEisSCAMMER: grammar

'''Factorio''' is a [[Larger than Life]] rule.

I am its discoverer and as of 8/10/23, its main contributor apart from a few hauls from wildmyron.

{{Rule
|name = Factorio
|imgname = factorio
|char = Chaotic
|r = 3
|b = 3
|s = 2
|c = 2
|n = +
}}

=General properties=

Factorio is a range-3 cross rule. This means that one cell is affected by its orthogonal neighbours one to three cells from it. Here is a neighbourhood of a cell.

{{LV:Viewer|x = 7, y = 7, rule = B/S012345678History
3.A$3.A$3.A$3AC3A$3.A$3.A$3.A!
}}

The rules are thus:

- If there are three cells in the neigbourhood and the cell's state is off, then the cell turns on.

- If there are two cells in the neigbourhood and the cell's state is on, then the cell remains on.

- Otherwise, the cell turns or remains off.

Due to it being a R3 Cross rule, there are some unique properties to the rule unheard of or impossible in isotropic non-totalistic automata.

- All patterns that are 1-by-n remain 1-by-n.

- All patterns that are 2-by-n remain 2-by-n.

- Cells two spaces apart emulate B3/S2V. Some small p1 and p2 objects which use the emulation are in the pattern collection above (found using rlifesrc and converted by hand).

=Prime forms and expansions=

Notice that the collection above does not contain every still-life and oscillator. The reason is because the oscillator collection would be quite repetitive if we included every one of them! Hence trivial variants are omitted.

The mechanisms of oscillators with greater bounding boxes can be encapsulated by defining a specific one called a prime form, which has the smallest bounding box with the same mechanism. Any oscillator in this set can be achieved by expansion or contraction of rows or columns. For example, the right is a valid expansion of the left:
{{LV:Viewer|x = 13, y = 3, rule = R3,C2,S2,B3,N+
10b2o$b2o$o2bo5bo2bo!}}

Here, the right is not a valid expansion of the left, as the left oscillator is period-6 and the right one is period-2 (actually two period-2 oscillators).
{{LV:Viewer|x = 12, y = 7, rule = R3,C2,S2,B3,N+
9b2o$b2o5bo2bo$o2bo3$obo5bobo$bobo5bobo!}}

Here, the right is a valid expansion of the left as the oscillators have the same mechanics. This shows that expansions may involve partial columns.
{{LV:Viewer|x = 17, y = 12, rule = R3,C2,S2,B3,N+
3bo10bo$3b2o9bobo$4bo11bo3$obo8bobo$3o8b3o3$3bo10bo$3b2o9b2o$4bo10bo!}}

=SLs=

TBC

=Oscs=

Known periods are 2, 3, 4, 5, 6, 8, 9, and 12.

=Spaceships=

The top left pattern, and the characteristic pattern of Factorio, is the factorial, or factorialship (symbol F).

Known speeds are c/1o, 2c/2o, c/2o, and c/3d.

=Other interesting stuff=

TBC

=Appendix=

All 4-cell oscs and still-lifes:
{{LV:Viewer|x = 191, y = 25, rule = R3,C2,S2,B3,N+
b2o11b2o13b2o12bobo15bobo15b2o15b2o8bobo9b2o12b2o8bobo11b2o13bobo13bo
2bo$o2bo9bo3bo9bo4bo9bo3bo13bobo14b2o16bobo7bo2bo7bo2bo11b2o8b2o13b2o
13bobo13bo2bo9$b2o11b2o13b2o12bobo15bobo15b2o15b2o8bobo9b2o12b2o8bobo
26bobo13bo2bo2$o2bo9bo3bo9bo4bo9bo3bo13bobo14b2o16bobo7bo2bo7bo2bo11b
2o8b2o28bobo13bo2bo9$b2o11b2o13b2o12bobo15bobo15b2o15b2o8bobo9b2o12b2o
8bobo42bo2bo3$o2bo9bo3bo9bo4bo9bo3bo13bobo14b2o16bobo7bo2bo7bo2bo11b2o
8b2o44bo2bo!}}

Pattern Collection:

{{LV:Viewer|
x = 441, y = 389, rule = R3,C2,S2,B3,N+
191bo12bo12bo10bo$191bo12bo12bo10bo$171bo19bo12bo12bo10bo15bobobo$171b
o$65bo11bo8bo15bo7bo9bo8bo41b2o14bo12bo12bo10bo23bo$65bo11bo8bo15bo7b
o9bo8bo57bo3bo8bo3bo8bo3bo6bo3bo67bobobo53bobobo$41bobobo19bo11bo8bo15b
2o6b2o8b2o7b2o22bo18bo14b2o11b2o11b2o9b2o18bobobo2bobobo$153bo18bo2bo
10bo12bo96bo23bo33bo$17b3o21bo61bo7bo9bo8bo22bo17bo3bo68bo6bo68bo$17b
obo45bo11bo8bo16bo7bo9bo8bo18bo37bo12bo12bo10bo71bobobo53bobobo6bo$17b
3o21bobobo56bo7bo9bo8bo19bo49bo25bo18bobobo2bobobo13bo6bo42b3o43bo$134b
o14bo3bo115bo6bo42bobo41b3o$76bo8bo17bo7bo9bo8bo3bo15bo116bobo6bo17b9o
15bo3bo29b9o2bobo7b2o$39b9o28bo8bo47b2o105b18o12bo49bo42b3o8bobo$76b2o
7b2o48bo13bo118bo105bo2bo$77bo5bo2bobo23bo9bo87bo11bo9bo34bo8bo43bo$112b
o9bo52bo3bo6bo3bo6bo3bo8bo11bo9bo63bobobo53bobobo17b3o$43bo67b2o8b2o40b
o7bo3bo3bo6bo3bo6bo3bo8bo11bo9bo14bobobo18bo6bo100bo$111bo7bobo2bo38b
o7bo3bo3bo6bo3bo6bo3bo75bo22bo19bo37bo$41bobo21bo12bo13bo70bo7bo43bo11b
o23bo25bo42bo$65bo12bo13bo52bo7bo5bo50bo4bo6bo4bo4bo63bobobo53bobobo$
43bo21bo12bo13bo52bo7bo5bo15bo3bo6bo3bo6bo3bo10bo2bo8bo2bo2bo16bobobo
25bo$145bo7bo5bo3bo7bo4bo10bo11bo14bo11bobo67bo61bo$43bo17bo12bo13bo60b
o15bo8bo72bo$61bo3bo8bo3bo9bo3bo56bo16bo129bobobo53bobobo$41bobobo15b
2o11b2o12b2o13bo7bo9bo8bo14bo3bo3bo5bo5bo81bobobo$60bo12bo13bo15bo7bo
9bo8bo17bobo11bo3bo$79bo13bo8b2o6b2o8b2o7b2o$79bo13bo55bo$78b2o12b2o8b
o7bo9bo8bo$78bo11bobo2bo6bo7bo9bo8bo54bo$103bo7bo9bo8bo53bo$184bo2bo$
102bo7bo9bo8bo4bo$103bo7bo9bo8bo3bo52bo$133b2o52bo$135bo48bo$112bo9bo
$112bo9bo64bo$111b2o8b2o$111bo7bobo2bo2$344bo3b2o2$345bo3$345bo$345bo
$328b3o19b3o21b3o2$277bobobo$330bo21bo21bo$142bobobo6b2o7bobo7b2o7b2o
7b2o89bo48bo21bo21bo$152bo2bo5bobo6b2o8bobo6b2o139bo21bo21bo$146bo132b
obo$313b2o20b2o20b2o20b2o11b3o12b3o13b3o12b3o$2bo10b2o127bobobo134bo$
13b2o280b2o15bo2bo18bo2bo18bo2bo18bo2bo56b3o$obo139bo134bobobo14b2o13b
o4bo16bo4bo16bo4bo16bo4bo11bo14bo13bo$309bo8bo12bo8bo12bo8bo12bo8bo9b
o14bo13bo$2bo139bobobo5b2obo5bob2o5b2obo135bo8bo12bo8bo12bo8bo12bo8bo
9bo14bo6bo6bo6bo7b3o$153b2o7bobo7b2o122b2o13bo4bo16bo4bo16bo4bo16bo4b
o33bo13bo$2bo28bo263b2o15bo2bo18bo2bo18bo2bo18bo2bo14b3o2bo9b3o2bo8b3o
2bo7b3o$13b2o7b2o6bob2o5bobo2bo356bo$obobo8bobo7b2o6bo7bo2bobo268b2o20b
2o20b2o20b2o20bo$14b2o6bobo6bo3$152bo8bo9bo8bo8bo9bo6bo8bo$153bo8bo7b
o8bo10bo7bo6b2o8bobo$152bobo6bo2bo6bobo6b2o6b2o7b2o8b2o5bobo108bo13bo
27bo13bo$153bobo6b2o6bobo6bo2bo7b2o7b2o6bo8bo89b3o2bo7b3o2bo8b2o2bo10b
3o2bo7b3o2bo8b2o2bo10b3o2bo$13b2o7b2o7bobo6bo2bo5bo2bo6bobo6bobo228b2o
10bo13bo27bo13bo27bo$13bobo6bo2bo5b2o7b2o7bobo6bo2bo5b2o242bo13bo27bo
13bo27bo$14bobo6b2o8b2o7b2o6bobo6b2o8b2o227bo2bo16bo6bo13bo20bo6bo13b
o$15b2o7b2o6bobo6b2o7b2o6bobo6bobo227bo4bo15bo20bo6bo13bo20bo6bo$295b
o8bo27bo13bo27bo13bo$153bo10bo6bo10bo6bo8bo96bo8bo27bo13bo27bo13bo$155b
o6bo10bo6bo8bobo5b2o98bo4bo9b2o2bo10b3o2bo7b3o2bo8b2o2bo10b3o2bo7b3o2b
o$152b2o7b2o7bo2bo5bo2bo7bo8bo98bo2bo16bo27bo13bo27bo$154b2o7b2o6b2o7b
2o6bobo8b2o$299b2o$13bo2bo5bobo6b2o9b2o6bobo7b2o$14bobo6bobo5bo2bo5b2o
7bobo7b2o$14b2o7b2o8b2o5bo2bo5bo2bo5b2o$13bobo6bo2bo6b2o7b2o7b2o6bo2b
o278b3o$152bo8bo10bo6bo$152b2o7bo2bo7b2o7b2o$154bo8bo6bo10bo158bo$154b
2o6b2o6b2o7b2o159bo$340bo2$14b2o6bobo6bobo6b2o8b2o7bobo5bo2bo261bob3o
$13bo2bo5bobo7bobo5b2o8b2o6bobo7b2o263bo$13bo2bo6bobo5bobo8b2o5bo2bo5b
obo7b2o$14b2o7bobo6bobo7b2o5bo2bo6bobo5bo2bo84bo5bo11bo5bo$152bo11bo7b
2o7b2o150bo$154b2o7b2o5b2o7b2o152bo$152b2o7b2o7bo11bo150bo$325bo3b2o2$
326bo$14b3o8b2o2b2o25b2o7bob2o7bob2o13b3o7b2o3b2o$13bo3bo7bo4bo8b3o24b
o10bo13b2o3b2o7b3o$13bo3bo19b2o3b2o22bo10bo13b2o3b2o5b2o3b2o42bo8bo164b
o$13bo3bo38b2o8bo10bo74b2o7bobo162bo$14b3o8bo4bo6b2o3b2o9bo101bo8bo154b
3o$25b2o2b2o8b3o11bo100b2o6bobo$53bo$49b2o15bo10bo241bo$66bo10bo13bob
obobo221bo$66bo10bo13b2o3b2o221bo$49b2o14bob2o6b2obo13bobobo$152b2o7b
obo147bob3o$13b2o9b2o126bo8bo150bo$13b2o9b2o129bo8bo$15b2o9b2o126b2o6b
obo$15b2o9b2o284bo$17b2o9b2o282bo$17b2o9b2o282bo$30b2o272bo3b2o$30b2o
$305bo$64bob2o11bob2o8b2o2b2o7bobo7b2o2b2o$65bo14bo22bo3bo$65bo14bo23b
obo6bo2b2o2bo184bo$65bo14bo10bo4bo6bo3bo5b2o4b2o31bobo2bo5bo3b2o8b2o3b
o122bo$103bo3bo44bobo2bo6b2o3bo6bo2bobo116b3o$54b3o$38b3o11b2o3bo33bo
4bo7bobo8bo2bo$36b2o3bo15bo7bo14bo217bo$36b2o3bo10b2o3bo7bo14bo217bo$
18b2o5bobo6b2o5bo12bobo8bo14bo10b2o2b2o7bobo8bo2bo132bo4bo41bo$34b2o3b
2o7bobo3bobo194b2o2b2o$33bo5b2o7bobo138bobo5bobo8b2o7b2o2bo7bobobo7bo
2b2o7bo49b2o$18b2o5bobo5bo3b2o8bo3b2o100bobo6bobo6b2o6b2o$15bo10bo6bo
3b2o8bo17bo14bo73bo8bo9bo7bo5bo114bo2bo$15bo10bo7b3o10bo3b2o12bo14bo71b
o3bo6bo6bo3bo6bo6bo2bo4bobobo5b2o2bo8bo10bo11bo58bo4bo$15bo10bo21b3o14b
o14bo73bo6bo3bo7bo4bo3bo4bo111bo8bo$64bob2o10b2obo72bo8bo9bo7bo5bo111b
o8bo$197bobo8b2o7b2o2bo7bobobo7bo2b2o7bo47bo4bo$251bo4bo45bo2bo$15bo10b
o224b2o2b2o$15bo10bo276b2o$15bo10bo$13b2obo7b2obo3$153bobo5b2o8bo2bo$
153bo8bo8b2obo$152bob2o5bob2o6bob2o$152b2o8bobo6bo2bo$91b3o3b3o12bob2o
$90bo9bo12bo$90bo9bo12bo$19bo2bo2bo10bo2bo2bo2bo12bo2bo2bo25bo9bo12bo
252b2o5b2o$237bo94bobo9b2obo3bob2o$200bobo11bo2bo7bo2bo6bo61b2o8b2o9b
3o8bobo13bo2bobo2bo12b2o5b2o$19bo5bo10bo8bo12bo5bo2bo107bobo10b2o45bo
41bo3bo15b2o8b2o9bo2bo42bo3bo3bo3bo$90bo9bo12bo39bobo6b2o157bo7bobo$90b
o9bo12bo9bo28bo3bo4bo3bo8bo2bo8bo2bo10b2o12b2o9bobo9bo39bo3bo38b2o10b
obo29bo3bo3bo3bo$19bo2bo2bo10bo8bo12bo2bo5bo22bo9bo12bo9bo30bo9bo8bo11b
o11bo13bo10bo13bo60bo10bo$91b3o3b3o14b3o3b3o31bo9bo8bo11bo11bo13bo10b
o13bo40bobobo$123bo30bo9bo8bo11bo11bo13bo10bo13bo60bo10bo$36bo2bo2bo2b
o15bo2bo2bo213bo2$281bo15b2o9b2o8b3o$154bo9bo8bo11bo11bo13bo10bo13bo60b
2o9b2o10b2o25bo2bo$154bo9bo8bo11bo11bo13bo10bo13bo84bo9bo2bo12bo2bo$154b
o9bo8bo11bo11bo13bo10bo13bo81bo2bo7bo2bo12b2o4b2o13b2o5b2o$152b2obo6b
2obo5b2obo8b2obo8b2obo10b2obo7b2obo10b2obo$329bo2bo31bo3bo3bo3bo$331b
o2bo10b2o4b2o13b2o5b2o$347bo2bo$17bo2bo2bo2bo2bo6bo2bo2bo2bo2bo298bo2b
o13bo3bo3bo3bo3$17bo11bo6bo11bo$152bo51bo11bo11bo$157b2o10b3o6b3o7b3o
13bobo9b2o10b2o9b2o3bo5b2o$17bo11bo6bo11bo10b2o2b2o2b2o83bo2bo3bo12bo
5b3o10bo14bo10bo11bo10b2o5bo3b2o$59bo8bo83bo16b3o9bo9bo$117b2o3b2o48b
o8bo6b3o105bo2b2o6bobobo6bo2b2o6bobobo12bo2bo33bo3bo$17bo2bo2bo2bo2bo
6bo11bo68b2o3b2o78b2o9bobo9b2o69bobobo6bo2b2o17bo3bo31bo2bobo2bo$59bo
8bo50bobo79b3o9b3o9b3o91bo12bo13bo2bo$59b2o2b2o2b2o228bo10bo9bobobo8b
o52b2o3bo$36bo2bo2bo2bo2bo70bobo117bobo2bo5b2o44bo2b2o6bobobo6bo2b2o6b
obobo30b2obo3bob2o$117b2o3b2o80bo11bo11bo11b2o5bo2bobo96bo2bobo$117b2o
3b2o80b2o10b2o10b2o157b2o$205bo11bo11bo135bo2bobo2bo$352bobo2$297b2o10b
2o9b2o$296bo2b2o17bo3bo$18b2o2b2o2b2o9b2o2b2o2b2o2b2o8b2o2b2o2b2o2b2o
223bobobo6bo2b2o6bo2b2o$18bo8bo9bo12bo8bo12bo165bo2bo4bobo58b2o2bo8bo
$163bob2o7bo5bo5bo12bo2b2o5bo2b2o5bobobo5bobobo6b2obob2o50b2o10b2o9b2o
$89bo2bo59bo12b3o6b3ob3o6bob2o10bo8bo11bo7bo102bo7bo7bo7bo7bo7b2o6bo9b
o9bo7bo9bo$18bo8bo9bo12bo8bo12bo79bobo2bo29bob2o143bobo6b2o6b2o5bobo5b
2o14b2o7b2o2bobo2b2o$18bo8bo9bo12bo8bo12bo101b3ob3o6bob2o145bo7bo22bo
7b2o5bo26b2o2bobo2b2o$89bo2bo22bo2bo4bo2bo25bobo2bo7b3o6bo5bo10bo7bo2b
2o5bo2b2o5bobobo5bobobo118bo7bo13b2o16bo7bo9bo7bo$118b2o2b2o33bo5bob2o
33b2o8b2o8bobo7bobo102b2o5bobo5bobo6b2o6b2o13bobo$18bo8bo9bo12bo8bo12b
o11bo2bo27bo10bo111bobo5bobo86b2o5bobo5bobo6b2o6b2o13bobo$18b2o2b2o2b
2o9b2o2b2o2b2o2b2o8bo12bo20bobo143bobobob2o105bo7bo13b2o16bo7bo9bo7bo
$115bo10bo209bo7bo22bo7b2o5bo26b2o2bobo2b2o$84bo2bo5bobo22b2o2b2o210b
obo6b2o6b2o5bobo5b2o14b2o7b2o2bobo2b2o$59bo12bo17bobo5bo2bo13bo2bo4bo
2bo206bo7bo7bo7bo7bo7b2o6bo9bo9bo7bo9bo$59b2o2b2o2b2o2b2o$90bobo64bo2b
o5bo5bo2bo14bo2bo2bo5bo2bo2bo$98bo2bo2$93bo2bo60bo2bo2bo5bo2bo2bo14bo
8bo8bo2$297bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$93bo2bo63bo11bo17bo2bo
2bo5bo2bo2bo2$296b2o101b2o$157bo2bo2bo5bo2bo2bo14bo8bo8bo$296b2o101b2o
2$18bo2bo2bo51bo2bo2bo74bo2bo5bo5bo2bo14bo2bo2bo5bo2bo2bo3$18bo5bo51b
o5bo110bo11bo2$23bobobobobobobobobobobobobobobobobobobobobobobobobobo
bobo219b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$18bo2bo2bo51bo2bo2bo107bo2bo
2bo5bo2bo2bo$23bo53bo$294bo2bo100bo2bo$23bo53bo112bo2bo5bo5bo2bo$294b
o2bo100bo2bo$23bo53bo2$23bo53bo2$23bo53bo78bo2bo2bo2bo5bo2bo2bo10bo2b
o2bo5bo2bo2bo11bo2bo2bo5bo2bo2bo$18bo2bo2bo51bo2bo2bo$23bobobobobobob
obobobobobobobobobobobobobobobobobobobobobo$156bo8bo2bo2bo5bo10bo5bo2b
o2bo5bo11bo5bo2bo2bo5bo99b3o2b2o$18bo5bo51bo5bo259bo$334bo$156bo8bo5b
o2bo2bo10bo2bo2bo5bo2bo2bo11bo2bo2bo5bo2bo2bo97bo$18bo2bo2bo51bo2bo2b
o251bo7bo$342bo$156bo2bo2bo2bo8bo16bo11bo17bo11bo108bo$277bobobo52bo$
289bo8bo12b3o2b2o10b3o2b2o9b3o2b2o$168bo2bo2bo2bo10bo2bo2bo2bo2bo2bo2b
o11bo2bo2bo5bo2bo2bo40bo39bo32bo$289bob6obo10bo16bo$277bobobo7bob6obo
10bo16bo$168bo8bo10bo17bo11bo5bo2bo2bo5bo72bo7bo8bo23bo$281bo10bo2bo21b
o32bo$18bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo196bo32bo$168bo8bo10bo17bo
11bo2bo2bo5bo2bo2bo40bobobo27bo16bo$309b2o2b3o10b2o2b3o9b2o2b3o$18bo101b
o221bo$168bo2bo2bo2bo10bo2bo2bo2bo2bo2bo2bo127bo$334bo$18bo101bo213bo
7bo$342bo$342bo$18bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo213bo$334b2o2b3o3$
153b2o3bo4bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo4bo3b2o$154b2o5bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3b
o3bo3bo3bo3bo3bo3bo3bo3bo5b2o4$18b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
$18bo104bo2$153b2o3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo
3b2o17bobobo9b2o3bo$18bo104bo30b2o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5b
o5bo5bo5bo5bo5b2o37bo$18b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o153bo11b
o3bo2bo2$277bobobo2$277bo3bo2$18bo99bo34b2o3b2ob2o3b2ob2o3b2ob2o3b2ob
2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2o
13bobobo35bobo6b2o13b2o8b2o8bobo6bobo10b2o9b2o$19b3o3b3o3b3o3b3o3b3o3b
3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o172b2o9bo2bo76bo3bo6bo3b
o$18bo99bo170bo2bo9b2o$18bo99bo35bo107bo53bo2bo5bobo12b2o8bobo7bo2bo7b
2o$382bobo8b2o$289bobo9bobo79bobo9b2o$153bo109bo26bobo9bobo13b2o7b2o13b
2o7bobo6b2o7b2o$153b2o107b2o$154bo107bo$316b2o7b2o14b2o8b2o7bobo6bobo
3$16bobo107bobo161b2o9bo2bo$18bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o162bo2bo9b2o78bobo8bobo$16bo111bo252bo3bo6bo3bo$260bo80b2o7b2o7b2o$16b
o111bo26bo103b2o28b2o10b2o13bo2bo5bobo$18bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo29bo102bo31b2o10b2o78b2o8b2o$16bobo107bobo27bo183bobo6b2o
8b2o21bo2bo9b2o$317bobo6b2o$155bo104bo$340bobo6b2o7bobo$318b2o7b2o$154b
2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bo
bob2o2bobob2o2bobob2o2bobob2o2bobob2o31b2o8b2o$289b2o12b2o35b2o7bobo6b
2o$86bo2bo2bo2bo220b2o7b2o$154bo104bo$262bo26bobo9bobo$83bo2bo8bo2bo191b
obo9bobo$154bo107bo$259bo$80bo2bo14bo$154bo2$77bo2bo17bo160bo$154bo107b
o2$74bo2bo17bo2bo163bo$154bo104bo$289b2o7b2o$71bo2bo17bo2bo194bobo3bo
bo$154b2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bob
ob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2$68bo2bo17bo2bo197bobo3b
obo$155bo104bo28b2o7b2o2$65bo2bo17bo2bo66bo$156bo102bo$155bo103b2o$62b
o2bo17bo2bo173bo3$59bo2bo17bo2bo3$56bo2bo17bo2bo3$53bo2bo17bo2bo3$50b
o2bo17bo2bo2$277bobobo$47bo2bo17bo2bo218bobo$277bo3bo7b2o3bo$294bo$44b
o2bo17bo2bo208bobobo15bo$297bo3b2o$277bo3bo17bobo$41bo2bo17bo2bo$277b
obobo2$41bo17bo2bo3$41bo14bo2bo2$277bobobo7bobo$41bo2bo8bo2bo232b2o$277b
o3bo10bo$292bo$44bo2bo2bo2bo223bobobo$290bo$281bo8bo$292b2o$277bobobo
9bobo8$291bo8bo6bo2bo8bo8bo6bo2bo$272bo4bobobo$289b2o7b2o7bobo7b2o7b2o
7bobo$270bobo8bo7b2o7b2o7bobo7b2o7b2o7bobo2$272bo4bobobo7bo8bo8bo9bo8b
o8bo$317bo8bo8bo$272bo4bo11bo8bo8bo9bo8bo8bo2$270bobobo2bobobo7b2o7b2o
7bobo7b2o7b2o7bobo$289b2o7b2o7bobo7b2o7b2o7bobo$298bobo25bobo$291bo15b
o2bo8bo15bo2bo!
}}

Catagolue: https://catagolue.hatsya.com/census/xfactorio

5blink

2023-10-03T21:44:17Z

MEisSCAMMER: encyclopedic tone

{{Oscillator
|name = 5blink
|pname = 5blink
|c = 28
|bx = 14
|by = 9
|p = 5
|m = 5
|h = 19.2
|v = 0.76
|discoverer = Scot Ellison
|discoveryear = 2011
|rulemin = B3/S23
|rulemax = B38/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S2-n3-k
|isorulemax = B34tw5aejny6ei7c8/S234cetwy5ceiy6-n78
|animated = true
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 3 GPS 2 ZOOM 24 HEIGHT 300 WIDTH 600 ]]
|apgcode = xp5_6a8w7zwor3sn52z04a511
}}
'''5blink''' is a small {{period|5}} [[oscillator]] found by [[Scot Ellison]] in July {{year|2011}}. It contains a blinker that is rephased repeatedly.

Its [[stator]] includes a [[tub]] acting as a [[rock]]. This can be replaced with a [[boat]], [[beehive]], [[loaf]], [[mango]], [[small lake]] and most other still lifes with a similarly placed cell.

It give out a [[dot]] [[spark]] which can be useful for, e.g, p90+40n variations of the [[p50 glider shuttle]].

==See also==
* [[Smallest period 5 oscillators]]

==External links==
{{LinkCatagolue|xp5_6a8w7zwor3sn52z04a511}}

{{Sparker|p=5|type=dot|strength=moderate}}

OCA:Grounded Life

2023-09-25T21:42:42Z

MEisSCAMMER: /* Universality */ it doesn't actually work in B35/S238, so removed it (behaves similarly, but not all of the circuitry works properly, and it ends up failing to simulate anything)

OCA:Grounded Life

2023-09-25T21:37:30Z

MEisSCAMMER: /* Beehive/block fuse */ spelling

OCA:Grounded Life

2023-09-25T21:36:34Z

MEisSCAMMER: /* Spaceships */ this reads better

Template:Rule

2023-09-25T21:35:39Z

MEisSCAMMER: 'debate' is the wrong word here

<includeonly><table class="infobox">
<tr>
<td colspan="2" class="infobox_head">{{#if:{{{name|}}} | {{{name|}}} | {{#if: {{{r|}}} | R{{{r|}}},C{{{c|{{{g|}}}}}},S{{{s|}}},B{{{b|}}},N{{{n|}}} | {{#if: {{{f|}}} | B{{{b|}}}/S{{{s|}}}/F{{{f|}}}/K{{{k|}}}/L{{{l|}}} | {{#if:{{{g|{{{c|}}}}}} | {{{s|}}}/{{{b|}}}/{{{g|{{{c|}}}}}} | B{{{b|}}}/S{{{s|}}} }} }} }} }}</td>
</tr>
{{#if: {{{hideimg|}}} || <tr><td colspan="2" class="infobox_img">{{EmbedViewerRule|r={{{r|}}}|c={{{c|{{{g|}}}}}}|n={{{n|}}}|f={{{f|}}}|k={{{k|}}}|l={{{l|}}}|b={{{b|}}}|s={{{s|}}}}}</td></tr> }}
{{#if: {{{imgname|}}} | <tr><td colspan="2" class="infobox_animlink">[[Media:{{{imgname|}}}.png|View static image]]</td></tr>}}{{#if: {{{animated|}}} | <tr><td colspan="2" class="infobox_animlink">[[Media:{{{imgname|}}}.gif|View animated image]]</td></tr>}}
<tr>
<th>[[Rulestring]]</th>
<td>{{#if: {{{r|}}} | R{{{r|}}},C{{{c|{{{g|}}}}}},S{{{s|}}},B{{{b|}}},N{{{n|}}} | {{#if: {{{f|}}} | B{{{b|}}}/S{{{s|}}}/F{{{f|}}}/K{{{k|}}}/L{{{l|}}} | {{{s|}}}/{{{b|}}}{{#if:{{{g|{{{c|}}}}}}|/{{{g|{{{c}}}}}}}} B{{{b|}}}/S{{{s|}}}{{#if:{{{g|{{{c|}}}}}}|/C{{{g|{{{c}}}}}}}}{{#if:{{{g|{{{c|}}}}}}| B{{{b|}}}/S{{{s|}}}/G{{{g|{{{c|}}}}}}}} }} }}</td>
</tr>
{{#if: {{{ruleinteger|}}} | <tr>
<th> [[Rule integer]] </th>
<td> {{{ruleinteger|}}} </td>
</tr>
}}
<tr>
<th> Character </th>
<td> {{#if: {{{char|}}} | {{{char|}}} | Miscellaneous }} </td>
</tr>
{{#if: {{{reversal|}}} |
<tr>
<th> [[Black/white reversal]] </th>
<td> {{{reversal|}}} </td>
</tr>
}}
{{#if: {{{strobing|}}} |
<tr>
<th> [[Strobing dual]] </th>
<td> {{{strobing|}}} </td>
</tr>
}}
{{#if: {{{checkerboard|}}} |
<tr>
<th> [[Checkerboard dual]] </th>
<td> {{{checkerboard|}}} </td>
</tr>
}}
</table></includeonly><noinclude>{{ambox|text=The current OCA infobox infrastructure is under discussion; see forum thread https://conwaylife.com/forums/viewtopic.php?p=166744#p166744 for related discussion of what could/should be done with infoboxes}}
{{Rule
|name = Maze
|imgname = maze
|b = 3
|s = 12345
|char = Explosive
|ruleinteger = 31752
|reversal = B0128/S01234678
|animated = true
}}
The rule template is an infobox template for rules for [[cellular automata]]. It takes the following parameters:

* <tt>name</tt>: (optional) the name of the rule. If not specified, the infobox head will be a rulestring.
* <tt>imgname</tt>: (optional) the name of the image (of a typical pattern) to link in the infobox; <tt>.png</tt> and <tt>.gif</tt> are appended automatically for the still and animated versions. Should be set if an image (static or animated) for this rule has been uploaded. The <tt>File:</tt> prefix should not be specified.
* <tt>animated</tt>: (optional) should be set to <tt>true</tt> if an animated image for this rule has been uploaded.
* <tt>hideimg</tt> (optional): setting this to <tt>true</tt> disables and hides the looped animation of an evolving random soup.<ref group=note>See also [[LifeWiki:Tiki bar#Suggested deprecation of EmbedViewerRule]] for the discussion related to the current implementation of the random-soup animation in {{tl|EmbedViewerRule}} and possible alternatives.</ref>
* <tt>b</tt>: the rule's birth (B) conditions.
* <tt>s</tt>: the rule's survival (S) conditions.
** Note the use of comma in Higher-range outer-totalistic cellular automata.
* <tt>f</tt>: for [[BSFKL]] rules, the rule's forcing (F) conditions.
* <tt>k</tt>: for [[BSFKL]] rules, the rule's killing (K) conditions.
* <tt>l</tt>: for [[BSFKL]] rules, the rule's living (L) conditions.
* <tt>c</tt>: for [[Generations]] rules and [[Higher-range outer-totalistic cellular automata]], the total number of cell states. The parameter may also be specified as <tt>g</tt>.
* <tt>r</tt>: for [[Higher-range outer-totalistic cellular automata]], the range.
* <tt>n</tt>: for [[Higher-range outer-totalistic cellular automata]] and weighted rules, the neighbourhood type. It should be one of ABCDFGHLMNWX23*+#@.
** <tt>NM</tt> for Moore neighbourhood.
** <tt>NN</tt> for von Neumann neighbourhood.
** <tt>NC</tt> for Circular neighborhood.
** <tt>N2</tt> for L2/Euclidean neighborhood.
** <tt>NB</tt> for Checkerboard neighborhood.
** <tt>N#</tt> for Hash neighborhood.
** <tt>N+</tt> for Cross neighborhood.
** <tt>NX</tt> for Saltire neighborhood.
** <tt>N*</tt> for Star neighborhood.
** <tt>NH</tt> for Hexagonal neighborhood.
** <tt>NA</tt> for Asterisk neighborhood.
** <tt>N3</tt> for Tripod neighborhood.
** <tt>NL</tt> for Triangular neighborhood.
** <tt>ND</tt> for Aligned Checkerboard neighborhood.
** <tt>NF</tt> for Far Corners/Edges neighborhood. Optionally, override <tt>r</tt> by specifying C<number> and/or E<number>.
** <tt>N@</tt> for custom neighborhood. @ is followed by hexadecimal digits that defines neighborhood.
** <tt>NW</tt> for custom weighted neighborhood. W is followed by hexadecimal digits that defines neighborhood.
** <tt>NG</tt> for Gaussian-weighted neighborhood.
* <tt>char</tt>: the rule's character/behaviour in sufficiently large [[soup]]s with ~0.5 [[density]]. Like [[Wolfram's classification]], the description is not strict. Suggested options:
** <tt>Stable</tt>: rules in which patterns tend to stabilize quickly and show little activity.
** <tt>Chaotic</tt>: rules in which patterns tend to show complex behavior, but do not generally explode.
** <tt>Explosive</tt>: rules in which patterns tend to grow without bound.
* <tt>ruleinteger</tt>: the rule's [[rule integer]] (if any).
*Duals:
:* <tt>reversal</tt>: (optional) the rule's [[black/white reversal]].
::The following should only be specified for [[self-complementary]] rules. (For others, they are an alternating pair of rules, switching over time and space respectively.)
::* <tt>strobing</tt>: the rule's [[strobing dual]]. (Should additionally only be specified for those with S8 and not B0.)
::* <tt>checkerboard</tt>: The rule's [[checkerboard dual]].

==Example==
An example can been seen to the right; it was generated with the following invocation:

<nowiki>{{</nowiki>Rule
|name = Maze
|imgname = maze
|b = 3
|s = 12345
|char = Explosive
|ruleinteger = 31752
|reversal = B0128/S01234678
|animated = true
<nowiki>}}</nowiki>

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

[[Category:Infobox templates]]
</noinclude><includeonly>{{#ifeq:{{NAMESPACE}}|User||{{#ifeq:{{NAMESPACE}}|Template||{{#ifeq:b{{{b|}}}s{{{s|}}}|b3s23||[[Category:Alien rules]]}}{{#if:{{{g|{{{c|}}}}}}|{{#if:{{{r|}}}|[[Category:Higher-range outer-totalistic cellular automata]]|[[Category:Generations]]}}|}}}}}}</includeonly>

Template:Rule

2023-09-24T19:09:49Z

MEisSCAMMER: neutrality

<includeonly><table class="infobox">
<tr>
<td colspan="2" class="infobox_head">{{#if:{{{name|}}} | {{{name|}}} | {{#if: {{{r|}}} | R{{{r|}}},C{{{c|{{{g|}}}}}},S{{{s|}}},B{{{b|}}},N{{{n|}}} | {{#if: {{{f|}}} | B{{{b|}}}/S{{{s|}}}/F{{{f|}}}/K{{{k|}}}/L{{{l|}}} | {{#if:{{{g|{{{c|}}}}}} | {{{s|}}}/{{{b|}}}/{{{g|{{{c|}}}}}} | B{{{b|}}}/S{{{s|}}} }} }} }} }}</td>
</tr>
{{#if: {{{hideimg|}}} || <tr><td colspan="2" class="infobox_img">{{EmbedViewerRule|r={{{r|}}}|c={{{c|{{{g|}}}}}}|n={{{n|}}}|f={{{f|}}}|k={{{k|}}}|l={{{l|}}}|b={{{b|}}}|s={{{s|}}}}}</td></tr> }}
{{#if: {{{imgname|}}} | <tr><td colspan="2" class="infobox_animlink">[[Media:{{{imgname|}}}.png|View static image]]</td></tr>}}{{#if: {{{animated|}}} | <tr><td colspan="2" class="infobox_animlink">[[Media:{{{imgname|}}}.gif|View animated image]]</td></tr>}}
<tr>
<th>[[Rulestring]]</th>
<td>{{#if: {{{r|}}} | R{{{r|}}},C{{{c|{{{g|}}}}}},S{{{s|}}},B{{{b|}}},N{{{n|}}} | {{#if: {{{f|}}} | B{{{b|}}}/S{{{s|}}}/F{{{f|}}}/K{{{k|}}}/L{{{l|}}} | {{{s|}}}/{{{b|}}}{{#if:{{{g|{{{c|}}}}}}|/{{{g|{{{c}}}}}}}} B{{{b|}}}/S{{{s|}}}{{#if:{{{g|{{{c|}}}}}}|/C{{{g|{{{c}}}}}}}}{{#if:{{{g|{{{c|}}}}}}| B{{{b|}}}/S{{{s|}}}/G{{{g|{{{c|}}}}}}}} }} }}</td>
</tr>
{{#if: {{{ruleinteger|}}} | <tr>
<th> [[Rule integer]] </th>
<td> {{{ruleinteger|}}} </td>
</tr>
}}
<tr>
<th> Character </th>
<td> {{#if: {{{char|}}} | {{{char|}}} | Miscellaneous }} </td>
</tr>
{{#if: {{{reversal|}}} |
<tr>
<th> [[Black/white reversal]] </th>
<td> {{{reversal|}}} </td>
</tr>
}}
{{#if: {{{strobing|}}} |
<tr>
<th> [[Strobing dual]] </th>
<td> {{{strobing|}}} </td>
</tr>
}}
{{#if: {{{checkerboard|}}} |
<tr>
<th> [[Checkerboard dual]] </th>
<td> {{{checkerboard|}}} </td>
</tr>
}}
</table></includeonly><noinclude>{{ambox|text=The current OCA infobox infrastructure is under debate; see forum thread https://conwaylife.com/forums/viewtopic.php?p=166744#p166744 for related discussion of what could/should be done with infoboxes}}
{{Rule
|name = Maze
|imgname = maze
|b = 3
|s = 12345
|char = Explosive
|ruleinteger = 31752
|reversal = B0128/S01234678
|animated = true
}}
The rule template is an infobox template for rules for [[cellular automata]]. It takes the following parameters:

* <tt>name</tt>: (optional) the name of the rule. If not specified, the infobox head will be a rulestring.
* <tt>imgname</tt>: (optional) the name of the image (of a typical pattern) to link in the infobox; <tt>.png</tt> and <tt>.gif</tt> are appended automatically for the still and animated versions. Should be set if an image (static or animated) for this rule has been uploaded. The <tt>File:</tt> prefix should not be specified.
* <tt>animated</tt>: (optional) should be set to <tt>true</tt> if an animated image for this rule has been uploaded.
* <tt>hideimg</tt> (optional): setting this to <tt>true</tt> disables and hides the looped animation of an evolving random soup.<ref group=note>See also [[LifeWiki:Tiki bar#Suggested deprecation of EmbedViewerRule]] for the discussion related to the current implementation of the random-soup animation in {{tl|EmbedViewerRule}} and possible alternatives.</ref>
* <tt>b</tt>: the rule's birth (B) conditions.
* <tt>s</tt>: the rule's survival (S) conditions.
** Note the use of comma in Higher-range outer-totalistic cellular automata.
* <tt>f</tt>: for [[BSFKL]] rules, the rule's forcing (F) conditions.
* <tt>k</tt>: for [[BSFKL]] rules, the rule's killing (K) conditions.
* <tt>l</tt>: for [[BSFKL]] rules, the rule's living (L) conditions.
* <tt>c</tt>: for [[Generations]] rules and [[Higher-range outer-totalistic cellular automata]], the total number of cell states. The parameter may also be specified as <tt>g</tt>.
* <tt>r</tt>: for [[Higher-range outer-totalistic cellular automata]], the range.
* <tt>n</tt>: for [[Higher-range outer-totalistic cellular automata]] and weighted rules, the neighbourhood type. It should be one of ABCDFGHLMNWX23*+#@.
** <tt>NM</tt> for Moore neighbourhood.
** <tt>NN</tt> for von Neumann neighbourhood.
** <tt>NC</tt> for Circular neighborhood.
** <tt>N2</tt> for L2/Euclidean neighborhood.
** <tt>NB</tt> for Checkerboard neighborhood.
** <tt>N#</tt> for Hash neighborhood.
** <tt>N+</tt> for Cross neighborhood.
** <tt>NX</tt> for Saltire neighborhood.
** <tt>N*</tt> for Star neighborhood.
** <tt>NH</tt> for Hexagonal neighborhood.
** <tt>NA</tt> for Asterisk neighborhood.
** <tt>N3</tt> for Tripod neighborhood.
** <tt>NL</tt> for Triangular neighborhood.
** <tt>ND</tt> for Aligned Checkerboard neighborhood.
** <tt>NF</tt> for Far Corners/Edges neighborhood. Optionally, override <tt>r</tt> by specifying C<number> and/or E<number>.
** <tt>N@</tt> for custom neighborhood. @ is followed by hexadecimal digits that defines neighborhood.
** <tt>NW</tt> for custom weighted neighborhood. W is followed by hexadecimal digits that defines neighborhood.
** <tt>NG</tt> for Gaussian-weighted neighborhood.
* <tt>char</tt>: the rule's character/behaviour in sufficiently large [[soup]]s with ~0.5 [[density]]. Like [[Wolfram's classification]], the description is not strict. Suggested options:
** <tt>Stable</tt>: rules in which patterns tend to stabilize quickly and show little activity.
** <tt>Chaotic</tt>: rules in which patterns tend to show complex behavior, but do not generally explode.
** <tt>Explosive</tt>: rules in which patterns tend to grow without bound.
* <tt>ruleinteger</tt>: the rule's [[rule integer]] (if any).
*Duals:
:* <tt>reversal</tt>: (optional) the rule's [[black/white reversal]].
::The following should only be specified for [[self-complementary]] rules. (For others, they are an alternating pair of rules, switching over time and space respectively.)
::* <tt>strobing</tt>: the rule's [[strobing dual]]. (Should additionally only be specified for those with S8 and not B0.)
::* <tt>checkerboard</tt>: The rule's [[checkerboard dual]].

==Example==
An example can been seen to the right; it was generated with the following invocation:

<nowiki>{{</nowiki>Rule
|name = Maze
|imgname = maze
|b = 3
|s = 12345
|char = Explosive
|ruleinteger = 31752
|reversal = B0128/S01234678
|animated = true
<nowiki>}}</nowiki>

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

[[Category:Infobox templates]]
</noinclude><includeonly>{{#ifeq:{{NAMESPACE}}|User||{{#ifeq:{{NAMESPACE}}|Template||{{#ifeq:b{{{b|}}}s{{{s|}}}|b3s23||[[Category:Alien rules]]}}{{#if:{{{g|{{{c|}}}}}}|{{#if:{{{r|}}}|[[Category:Higher-range outer-totalistic cellular automata]]|[[Category:Generations]]}}|}}}}}}</includeonly>

User:MEisSCAMMER

2023-08-30T23:40:43Z

MEisSCAMMER:

Hi! This is my userpage (currently small; I only created it because the redlink was bothering me).

Currently the only thing of substance I have done in this wiki is the page on [[OCA:Grounded Life|Grounded Life]].

Wire

2023-08-30T23:39:17Z

MEisSCAMMER: /* 2c/3 wire */ tone

{{Glossary}}
A '''wire''' is a repeating pattern that a [[signal]] can travel along without making any permanent change to the pattern.<ref>{{citeCGoLMC|section=Section 4.5.1}}</ref> If instead the pattern is destroyed by the travelling signal (i.e. it [[burn]]s from one end) it is a [[fuse]].<ref>{{citeCGoLMC|section=Section 4.5.2|page=103}}</ref>

The first documented wire was discovered by [[Dean Hickerson]] in March {{year|1997}} while studying some period-3 [[oscillator]]s found by [[Achim Flammenkamp]]. It transmits signals that travel through the wire diagonally at two-thirds of the [[speed of light]]. This was the inspiration for Hickerson's [[drifter]] [[search program]], which led to the discovery of a 5c/9 wire a month later.

Hickerson also used his program to search for a wire signal elbow, hoping to use it to construct a fast signal loop and solve the [[omniperiodicity]] problem; this effort was unsuccessful for [[Life]], with the closest match being a 2c/3 [[signal elbow]] found in July {{year|1997}} that turned a single signal into a reflected double signal.

Signals on wires are hard to manipulate as compared to signals in a vacuum, especially in the form of [[glider]]s, for which there is a rich and growing [[toolkit]].<ref>{{citeCGoLMC|section=Section 4.7}}</ref>

==2c/3 wire==

'''2c/3 wire''' was discovered by Dean Hickerson in {{year|1997}}. It can be found in the ''misc'' section of [[jslife]] under the name ''signals 2c3d''.<ref name="jslife">{{CiteSummersPattern|name=jslife|accessdate=June 6, 2022}}</ref>

{{EmbedViewer
|position = center
|pname = 2c3wire
|caption = Diagonal 2c/3 wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 600 WIDTH 600 X 8 Y 4 ZOOM 8 GPS 10 LOOP 128 PAUSE 2 ]]
|style = width:300px;
}}

Each signal is made up of two half-signals that can be separated from each other by an arbitrary number of [[ticks]].

Considerable effort has been spent on finding a way to turn a [[2c/3]] signal 90 or 180 degrees, since this would have been one way to prove that Life was omniperiodic. There is a known 2c/3 [[converter]] shown under [[signal elbow]], which converts a standard 2c/3 signal into a double-length signal. This is usable in some situations, but unfortunately it fails when its input is a double-length signal, so it cannot be used to complete two or more consecutive turns. It could only produce zigzag wires in any case rather than completing a loop, since the wire coming out of the elbow is a mirror image of the input wire.

In February {{year|2004}}, [[Noam Elkies]] discovered a [[glider synthesis]] of a reaction that can repeatably insert a signal into the upper end of a 2c/3 wire. See [[stable pseudo-Heisenburp]] for details. On September 11, {{year|2017}}, [[Martin Grant]] reduced the input reaction to five gliders or three gliders plus a [[Herschel]].<ref name="post50807" /> With the Herschel option the [[recovery time]] is 152 ticks.

Devices that extract a signal from a 2c/3 wire have also been built; currently the lowest repeat time of a standard 2c/3 signal receiver is 964 ticks,<ref name="post135690" /> and that of a double-length signal is 970 ticks,<ref name="post137526" /> both of which were achieved by [[Goldtiger997]] in {{year|2021}} by using complex [[staged recovery]] systems.

==5c/9 wire==

'''5c/9 wire''' was discovered by Dean Hickerson in 1997.

{{EmbedViewer
|position = center
|pname = 5c9wire
|caption = Diagonal 5c/9 wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 600 WIDTH 600 X 8 Y 4 ZOOM 6 GPS 10 LOOP 180 PAUSE 2 ]]
|style = width:300px;
}}

Oscillators have been found that inject signals of various periods including 9, 10, 11, and [[p47 lumps of muck hassler|47]] into a 5c/9 wire.<ref>{{cite web|url=https://conwaylife.com/ref/DRH/sig.inj.html|title=Dean Hickerson's signal-injector collection}}</ref>

It is possible to convert a 2c/3 wire signal into a 5c/9 signal; the viewer above shows the aforementioned five-glider input reaction for a 2c/3 signal and its subsequent conversion to 5c/9 signal. Another elementary 5c/9 signal injector involves a [[lumps of muck]] reaction,<ref name="post54568" /> which can be made from the synchronized [[2-glider collision]] at a repeat time of 62 ticks<ref name="post54617" />, a single Herschel with a much higher repeat time<ref name="post101243" />, or a fixed-period lumps of muck hassler that uses a specific catalyst (such as the p47).

However, no converter has yet been found for 5c/9 to 2c/3–or any other viable signal type, for that matter.

==c/2 wire==

'''c/2 wire''' was discovered by [[Hartmut Holzwart]] in {{year|2003}}.

{{EmbedViewer
|position = center
|pname = c2wire
|caption = Diagonal c/2 wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 440 ZOOM 8 GPS 10 LOOP 50 PAUSE 2 ]]
|style = width:300px;
}}

Both halves of the signal (the non-uniform portion of the pattern) are needed, since the wire is offset by one cell between the two half signals.

It is technically possible to use [https://conwaylife.com/forums/viewtopic.php?f=2&t=3507 Extrementhusiast's construction and detection mechanisms from 2018] to complete a c/2 diagonal [[telegraph]] pattern that can send one bit of information every few thousand ticks. Or a somewhat higher transmission rate can be arranged with a mechanism similar to the one used in Louis-François Handfield's [[high-bandwidth telegraph]]. No complete c/2 diagonal telegraph has been built to date.

==Lightspeed wire==

The [[zebra stripes]] [[agar]] can be used to form a wire. Below are several signals which can travel through such a wire at [[lightspeed]] (one cell to the right per generation).

{{EmbedViewer
|position = center
|pname = zebrawiresignals
|caption = Several lightspeed signals travel through a zebra stripes wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 360 WIDTH 800 GPS 10 LOOP 138 ZOOM 6 ]]
|style = width:300px;
}}

This wire must extend infinitely at the leading edge to avoid destruction, limiting its practical usefulness.

==References==
<references>
<ref name="post50807">{{LinkForumThread
|format = ref
|title = Re: Stable signal converters
|p = 50807
|author = Martin Grant
|date = September 11, 2017
}}</ref>
<ref name="post135690">{{LinkForumThread
|format = ref
|title = Re: Faster 2c/3 Wires
|p = 135690
|author = Goldtiger997
|date = September 12, 2021
}}</ref>
<ref name="post137526">{{LinkForumThread
|format = ref
|title = Re: Faster 2c/3 Wires
|p = 137526
|author = Goldtiger997
|date = November 11, 2021
}}</ref>
<ref name="post54568">{{LinkForumThread
|format = ref
|title = Re: Interacting with LoM
|p = 54568
|author = Adam P. Goucher
|date = January 2, 2018
}}</ref>
<ref name="post54617">{{LinkForumThread
|format = ref
|title = Re: Interacting with LoM
|p = 54617
|author = Chris Cain
|date = January 3, 2018
}}</ref>
<ref name="post101243">{{LinkForumThread
|format = ref
|title = Re: The Hunting of the Elementary Conduits
|p = 101243
|author = Sphenocorona
|date = July 28, 2020
}}</ref>
</references>

==External links==
* {{LinkGoLNews|2005/02/stable_2c3_signal_receiver.html|archivedate=20100523082242|title=Stable 2c/3 signal receiver|date=February 7, 2005|author=Dave Greene}}
* {{LinkLexicon|lex_w.htm#wire|name=Wire}}
* {{LinkLexicon|lex_1.htm#a-2c3wire|name=2c/3 wire}}
* {{LinkLexicon|lex_1.htm#a-5c9wire|name=5c/9 wire}}
* {{LinkLexicon|lex_l.htm#lightspeedwire|name=Lightspeed wire}}

__NOTOC__

OCA:Glider 3736

2023-08-30T15:23:49Z

MEisSCAMMER: named rules

The '''glider 3736''' is a small [[alien]] 2c/5 orthogonal [[spaceship]], discovered by [[Robert Wainwright]] in {{year|1994}}.<ref name="glider_dot_db" />
The spaceship works in multiple [[Cellular automaton|rules]], including {{rl|Grounded Life}} (B35/S23), {{rl|Pseudo Life}} (B357/S238) and {{rl|B35/S236}}.
The name comes from the [[glider.db|online Fano database]] of gliders in Life-like cellular automata.<ref name="fano_b35s23" /><ref name="fano_b3578s23" />

The spaceship [[Evolution|evolves]] in the same way in all [[Life-like rule]]s from {{nowrap|B35/S23}} to {{nowrap|B3578/S02368}} and all [[isotropic non-totalistic rule]]s from {{nowrap|B3aeijr5aikn/S23-ck}} to {{nowrap|B2i34ceijqry56-ac78/S0234-akw5aejk67c8}}.

Common predecessors depend on the rule. In particular, there are multiple known ways how a [[T-tetromino]] can evolve into a glider 3736.<ref name="post154878" />

There are known diagonal [[SMOS]]es that are right-angle [[collision]]s between two copies of this spaceship, with simplified speeds ranging from c/70d to c/5d and periods ranging from 5 to 345.<ref name="post154886" />

==Gallery==
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 4, y = 7, rule = B35/S23
2o$obo$o2bo$bobo$o2bo$obo$2o!
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 36 GPS 2 AUTOSTART TRACKLOOP 5 1/5 0/5 ]]
|position = center
|caption = Glider 3736
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 3, y = 2, rule = B2i3-cknq4j5acikn6ik7c/S23-k4jqy5j6aci
3o$bo!
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 24 GPS 15 AUTOSTART T 0 PAUSE 3 T 79 PAUSE 1 LOOP 80 ]]
|position = center
|caption = T-tetromino evolves into a glider 3736<ref name="post154878" /> ({{nowrap|B2i3-cknq4j5acikn6ik7c/S23-k4jqy5j6aci}})
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 18, y = 18, rule = B2i3aeijr4cijq5-cj6in7c8/S23-c4jnqz5ej6aen
11b3ob3o$11bo2bo2bo$12bo3bo$13b3o8$2o$obo$o2bo$bobo$o2bo$obo$2o!
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 18 GPS 40 GRID OFF AUTOSTART TRACKLOOP 345 5/345 5/345 ]]
|position = center
|caption = [[Endemic]] 5c/345 diagonal [[SMOS]] made up of glider 3736s<ref name="post154886" />
|style = width:100px;
|apgcode = xq345_f5fl8x1z8/b2i3aeijr4cijq5-cj6in7c8s23-c4jnqz5ej6aen
}}}}
{{gallery bottom}}

== References ==
<references>
<ref name="fano_b35s23">{{cite web
|url = https://web.archive.org/web/20150422140136/http://fano.ics.uci.edu/ca/rules/b35s23/
|title = B35/S23
|work = Fano Experimental Web Server
}}</ref>
<ref name="fano_b3578s23">{{cite web
|url = https://web.archive.org/web/20160310000605/http://fano.ics.uci.edu/ca/rules/b3578s23/
|title = B3578/S23
|work = Fano Experimental Web Server
}}</ref>
<ref name="glider_dot_db">{{cite web
|url = https://www.ics.uci.edu/~eppstein/ca/glider.db
|title = {{filename|glider.db}}
|archiveurl = https://web.archive.org/web/20221104201052/https://www.ics.uci.edu/~eppstein/ca/glider.db
|archivedate = 2022-11-04
}}</ref>
<ref name="post154878">{{LinkForumThread
|format = ref
|f = 11
|t = 5886
|p = 154878
|title = Re: Glider 3736
|author = LaundryPizza03
|date = December 14, 2022
}}</ref>
<ref name="post154886">{{LinkForumThread
|format = ref
|f = 11
|t = 5886
|p = 154886
|title = Re: Glider 3736
|author = FWKnightship
|date = December 15, 2022
}}</ref>
</references>

== External links ==
* {{LinkCatagolue|xq5_359a953|rule=b35s23}}
* Dedicated forum threads for specific rules supporting this glider: [https://conwaylife.com/forums/viewtopic.php?f=11&t=757 B35/S23], [https://conwaylife.com/forums/viewtopic.php?f=11&t=1921 B35/S236], [https://conwaylife.com/forums/viewtopic.php?f=11&t=2205 B3578/S23], [https://conwaylife.com/forums/viewtopic.php?f=11&t=3284 B357/S23], [https://conwaylife.com/forums/viewtopic.php?f=11&t=5836 B35/S238], [https://conwaylife.com/forums/viewtopic.php?f=11&t=5879 B357/S238]

[[Category:Alien patterns]]
[[Category:Alien spaceships]]
__NOTOC__

OCA:Grounded Life

2023-08-29T16:59:03Z

MEisSCAMMER: infobox

OCA:Grounded Life

2023-08-16T17:03:26Z

MEisSCAMMER: /* Oscillators */ more grammar

{{Rule
|b = 35
|s = 23
|char = Chaotic
|ruleinteger = 6184
|reversal = B0123478/S0124678
}}
'''B35/S23''' (also known as '''Grounded Life''') is a [[Life-like cellular automaton]] in which a [[cell]] survives from one generation to the next if it has 2 or 3 [[Neighbourhood|neighbors]], and is born if it has 3 or 5 neighbors. Under this rule, patterns tend to stabilize more quickly than in standard [[Life]],<ref name="post5304" /> which is one of the reasons for its alternate name.

==Patterns==
The two most common objects in B35/S23 are the [[block]] and the [[blinker]].

Some patterns work as they do in life, but many instead die off completely, such as the [[beehive]], [[boat]], [[T-tetromino]], [[pi-heptomino]], and [[stairstep hexomino]].

===Still lifes===

Because B35/S23 adds one birth transition from Life, all still lives in B35/S23 are still lives in Conway's Game of Life, but the reverse is not true. For example, the [[boat]] fails in B35/S23.

Many small still lifes under the standard Life rules have dead cells with five alive neighbours, so the list of still lifes for the two rules are extremely different for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in B35/S23 are boat (with 5 cells), beehive (with 6 cells) and [[Loaf]], [[Long boat]] and [[Eater 1]] (with 7 cells) Also, any pattern using a [[House]] or a [[Bun]] as an induction coil that is a still life under the standard rules, or any extended forms of the [[ship]] or [[Boat]] are not still lifes in B35/S23.

All still lifes up to 10 bits have occurred naturally. Almost all still lifes with 11 bits have occured naturally, with the only exception being [[Hook line tub]]. Notably, [[tub]] and [[barge]] are significantly more common than they're in Life.

===Oscillators===

Naturally occurring objects in this rule include oscillators of periods 2, 3, 4, 5, 8 and 26. There are also seminatural oscillators of periods 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 18, 21, 24, 26, 29, 33, 46, 82, and 142. Alien oscillators are also much more common than in similar rules, especially 8P8 (a mirrored [[short table]]) and 8P4 (a [[pre-pulsar]] predecessor in Life).

Notably, the [[washing machine]] is much more common in this rule, even in asymmetric soups.
It is the 56th most common object in asymmetric soups and the 21st most common object in D4_x4 soups. [[Toad]]s are also much more common.

Many alien oscillators exist in this rule, several of which are shown below:
{{EmbedViewer
|rle = x = 0, y = 0, rule = B35/S23History
94F$F24.F17.F20.F28.F$F24.F17.F20.F28.F$F2.2D13.2A.2A2.F2.2D6.A6.F4.D
15.F28.F$F.D2.D5.2A4.A2.2A.A.F.D2.D3.3A.A.A2.F3.2D3.3A9.F28.F$F4.D3.3A
2.A2.A4.2A.F4.D8.2A2.F2.D.D4.A4.4A2.F28.F$F3.D4.A2.3A3.A3.A2.F2.2D6.A
.3A2.F.D2.D9.4A2.F28.F$F2.D7.2A4.2A4.A.F4.D4.2A.A4.F.5D3.A4.4A2.F11.6A
11.F$F.D14.A.2A2.A.F.D2.D4.A7.F4.D3.3A3.4A2.F28.F$F.4D12.2A.2A2.F2.2D
5.A7.F4.D15.F9.A8.A9.F$F24.F17.F20.F8.A.A6.A.A8.F$F24.F17.F20.F7.A.A8.
A.A7.F$65F6.A.A10.A.A6.F$F21.F41.F7.A12.A7.F$F2.2D4.A6.A5.F9.2D30.F4.
A7.D3.D6.A4.F$F.D2.D3.2A4.2A5.F8.D2.D29.F4.A6.2D2.2D6.A4.F$F.D6.2A4.2A
5.F8.D2.D4.6A6.2A.2A8.F4.A5.D.D.D.D6.A4.F$F.3D5.A4.A6.F9.2D4.A.4A.A6.
A.A9.F4.A7.D3.D6.A4.F$F.D2.D16.F8.D2.D4.6A6.2A.2A8.F4.A7.D3.D6.A4.F$F
.D2.D4.A4.A6.F8.D2.D4.A4.A19.F4.A7.D3.D6.A4.F$F2.2D6.A2.A7.F9.2D30.F7.
A4.D3.D3.A7.F$F10.4A7.F41.F6.A.A10.A.A6.F$F10.A2.A7.43F7.A.A8.A.A7.F$
F10.A2.A7.F41.F8.A.A6.A.A8.F$F10.A2.A7.F2.2D4.D32.F9.A8.A9.F$F10.4A7.
F.D2.D2.2D7.2A15.2A6.F28.F$F10.A2.A7.F4.D.D.D7.2A15.2A6.F11.6A11.F$F9.
A4.A6.F3.D4.D32.F28.F$F21.F2.D5.D32.F28.F$F9.A4.A6.F.D6.D32.F28.F$F8.
2A4.2A5.F.4D3.D12.2A5.2A11.F28.F$F8.2A4.2A5.F17.A4.A5.A4.A7.F28.F$F8.
A6.A5.F16.3A3.A5.A3.3A6.F28.F$F21.F16.A.A2.A7.A2.A.A6.30F$31F33.F28.F
$F29.F33.F28.F$F29.F8.A.A2.A7.A2.A.A6.F28.F$F20.2D3.2D2.F8.3A3.A5.A3.
3A6.F28.F$F19.D2.D.D2.D.F9.A4.A5.A4.A7.F28.F$F22.D4.D.F13.2A5.2A11.F28.
F$F20.2D3.2D2.F33.F21.2A5.F$F22.D4.D.F33.F5.2A9.2A3.A.A4.F$F19.D2.D.D
2.D.F33.F4.A.A9.A.A2.3A4.F$F20.2D3.2D2.F8.2A15.2A6.F4.3A9.2A10.F$F3.3A
6.3A14.F8.2A15.2A6.F28.F$F4.A8.A15.F33.F28.F$F18.46F6.A21.F$F6.2A2.2A
6.F44.F5.A.A4.D3.2D10.F$F6.2A2.2A6.F44.F5.3A3.2D2.D2.D9.F$F18.F44.F10.
D.D2.D12.F$F18.F44.F9.D2.D2.3D10.F$F18.F37.2A5.F9.5D.D2.D9.F$F6.2A2.2A
6.F10.3A24.2A5.F12.D2.D2.D2.3A4.F$F6.2A2.2A6.F10.2A7.2D3.2D3.3A5.2A5.
F12.D3.2D3.A.A4.F$F18.F10.3A5.D2.D.D2.D2.3A12.F22.A5.F$F4.A8.A4.F12.2A
7.D.D20.F28.F$F3.3A6.3A3.F6.2A4.2A6.D2.3D18.F28.F$F18.F6.2A11.D3.D2.D
17.F11.2A9.3A3.F$F18.F7.3A8.D4.D2.D17.F5.3A2.A.A9.A.A3.F$F18.F8.2A8.4D
2.2D12.3A3.F5.A.A3.2A9.2A4.F$F18.F7.3A21.2A5.3A3.F6.2A20.F$F18.F31.2A
11.F28.F$F18.F31.2A11.F28.F$F18.F44.F28.F$F18.F44.F28.F$F18.F44.F28.F
$94F$F36.F55.F$F36.F55.F$F36.F55.F$F36.F13.2A21.2A17.F$F36.F13.A.A19.
A.A17.F$F36.F14.2A19.2A18.F$F36.F22.2A3.2A26.F$F36.F21.A.A3.A.A25.F$F
36.F21.3A3.3A25.F$F36.F22.A5.A26.F$F16.3A7.3A7.F6.2A35.2A10.F$F2.2D3.
2D7.A2.A5.A2.A7.F6.A.A33.A.A10.F$F.D2.D.D2.D6.A.A7.A.A7.F7.2A33.2A11.
F$F.D2.D4.D7.2A7.2A8.F55.F$F2.2D4.D27.F55.F$F.D2.D2.D9.2A7.2A8.F55.F$
F.D2.D.D9.A.A7.A.A7.F55.F$F2.2D2.4D6.A2.A5.A2.A7.F55.F$F16.3A7.3A7.F10.
2A27.2A14.F$F36.F9.A.2A25.2A.A13.F$F36.F9.3A27.3A13.F$F36.F55.F$F36.F
55.F$F36.F55.F$F36.F9.3A27.3A13.F$F36.F9.A.2A25.2A.A13.F$F36.F10.2A27.
2A14.F$F36.F55.F$38F55.F$F92.F$F92.F$F92.F$F44.2A33.2A11.F$F11.D4.D3.
2D21.A.A33.A.A10.F$F10.2D3.2D2.D2.D20.2A35.2A10.F$F9.D.D2.D.D5.D36.A5.
A26.F$F11.D.D2.D4.D36.3A3.3A25.F$F11.D.5D2.D37.A.A3.A.A25.F$F11.D4.D2.
D39.2A3.2A26.F$F11.D4.D2.4D28.2A19.2A18.F$F50.A.A19.A.A17.F$F50.2A21.
2A17.F$F92.F$F92.F$F92.F$94F!
|viewerconfig = #C [[ HEIGHT 950 WIDTH 800 ZOOM 8 GRID OFF THEME LifeHistory ]]
|position = center
|caption = A [[stamp collection]] of oscillators. From left to right, top to bottom, they are:
12P2 and [[Washing machine]] (rare examples of [[billiard table]]s in B35/S23),
14P3 (a natural oscillator resembling the [[caterer]]),
8P4 (a [[pre-pulsar]] predecessor in Life, which resembles 8P8),
12P4 (dependent on the B5a transition; the pattern dies in Life due to the lack of it),
56P11 (resemblant of [[Achim's p11]]),
46P6,
14P8 (extensible, although only in discrete lengths or with proper [[induction coil]]s),
8P8 (a mirrored [[short table]]),
32P33 (four [[block]]s hassling four [[T-tetromino]]s),
18P26 (the highest-period oscillator to have appeared naturally),
24P26 (an oscillator composed of interacting beehive sparks; appears in 1250 C4_4 soups),
48P46 (a [[shuttle]] of [[loaf]] and [[beehive]] sparks),
36P82,
and 104P142 (the highest period oscillator to have appeared semi-naturally).
  
|style = width:300px;
}}

===Spaceships===

Of particular note is the fact that neither the [[glider]] nor any of the [[xWSS]]es work in B35/S23 (all of them die off), giving the rule its alternate name. The most common spaceship according to [[Catagolue]] is the [[OCA:Glider 3736|glider 3736]].

Known [[spaceship]] speeds are c/2o, c/3o, c/4o, c/5o, c/6o, 2c/5o, c/4d and c/5d.

The three smallest spaceships in {{rl|Pseudo Life}} work:
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
2b3o$bo3bo$o2bo2bo$3ob3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -4 THEME Book STARTFROM 10 ]]
|position = center
|caption = 13P5H2V0 (glider 3736) (Robert Wainwright, 1994)
|style = width:100px;
|apgcode = xq5_359a953/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
2bo$b3o$o3bo$bo2bo$3b2obo$6bo$4bobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 6 ]]
|position = center
|caption = 14P3H1V0 (glider 4793) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq3_0oogheez17/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
3bo$b2ob2o$o2bo2bo$obobobo$3bo$bo3bo$bobobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 18P2H1V0 (glider 4716) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq2_4urhru4zw202/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
o3b2o6bo$2ob4o5bo$o5b2o2b5o$3bo3b3obo$3bob2ob2obo$5b3o$6b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 27P4H1V0
|style = width:100px;
}}}}
{{gallery bottom}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
17b2o2$15b2o$14bobo$13b2o$11b4o2bo4bo$11bobo3bo2bobo$10b3obo2bobo2bo$6bo6b2ob
2ob2o$4bobo3b3o3bo$2b3o6bo4b2o$bo5b2o7b2o$5o2b2o2b2obo2bo$b4o4bo2b2o$2b3o5bo
2bo$3bo7b3o$11bob2o$12b2o$9bo3bo$7b3o3bo$8b2o$9b4o$10b2o$11bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 600 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 90P4H1V1
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
11bo$10bobo$8b2o$6bo$6bo3bo3bo$5bob4o2bo$3b2obo2bo2b3o$5bo2b2obob3o$2b
o2bob3o3bo2bo$2bo2b5obo3bo$bo2b2o9b2o$o6bobo3bob4o$bo4bo7b2o$5b4o2bo3b
o$4bob2o4bo4b3o$7bob5o$8bob2o$11bo2bo$11bo2bo$14bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 600 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 78P5H1V1
|style = width:100px;
}}}}
{{gallery bottom}}

=== Puffers ===

There is a naturally occurring orthogonal c/2 [[puffer]] with period 136, leaving three [[blinker]]s and two [[block]]s every 68 ticks. Combining two or more puffers can give other puffers and spaceships.<ref name="post12942" /><ref name="post17286" /> The puffer engine also works in B357/S238 (where it becomes a p248 puffer).
On September 10, 2021, FWKnightship posted a 24c/48 siderake emitting 2c/5 spaceships.<ref name="post135647" />

{{EmbedViewer
|rle = x = 81, y = 16, rule = B35/S23
16b2o$16b2o2$57bo$57bo$57b2o14b3o$12b2o39bo18b4o$3o3b3o3b2o33bo3b3o2b
2ob2o10b4o3b2o$25bo11b3o7bo4b2o4b3o11b2o5b2o$4bo20b2o10bobo7bo4bo4bob
2o14b2ob2o$4bo18b4o10b3o12bo3bo4bo13b4o$4bo18b2o25b3o7b4o12bo$17bo42b
o$17bo2bo19b2o18bobo$16bo3bo19b2o$17bobo!
|viewerconfig = #C [[ HEIGHT 360 WIDTH 900 THUMBSIZE 2 ZOOM 10 GPS 12 AUTOSTART TRACKLOOP 136 1/2 0/2 ]]
|position = center
|caption = A period-136 orthogonal c/2 puffer<ref name="post12942" />
|style = width:300px;
|apgcode = yl68_1_17_f843afff9c5c3cef7d244e5948674525/b35s23
}}

===Beehive/block fuse===
One of the most useful reactions is the following, in which a beehive spark interacts with a chain of blocks, moving it further down the chain:

{{EmbedViewer
|rle = x = 30, y = 4, rule = B35/S23
bo$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$bo!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 140 ]]
|position = center
|caption = The beehive/block fuse
|style = width:300px;
}}

Once the beehive reaches the end, it will reverse the direction while shortening the chain, and will eventually annihilate it given enough time. This can be stopped with a [[pond]]:

{{EmbedViewer
|rle = x = 32, y = 4, rule = B35/S23
bo27b2o$obob2ob2ob2ob2ob2ob2ob2ob2obo2bo$obob2ob2ob2ob2ob2ob2ob2ob2ob
o2bo$bo27b2o!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 45 ]]
|position = center
}}

{{EmbedViewer
|rle = x = 95, y = 79, rule = B35/S23
53b2o$53b2o$12b2o$11bobo2b2o35b2o17b2o$11b2o3bo36bobo16bobo$17bo36b2o
17b2o$3bo12b2o$2bobob2ob2ob2obo5b2ob2ob2ob2ob2ob2o$2bobob2ob2ob2obo5b
2ob2ob2ob2ob2obobo2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob
2o$3bo12b2o19b2o2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob2o
$17bo$11b2o3bo20b2o$11bobo2b2o19b2o15b2o17b2o$12b2o39bobo16bobo12b2o$
37b2o14b2o17b2o13b2o$37b2o$53b2o32b2o$37b2o14b2o32b2o$37b2o$87b2o$37b
2o48b2o$37b2o$87b2o$37b2o48b2o$37b2o$33b2o6b2o39b2o3b2o$32bobo6bobo38b
2o3b2o$32b2o3b2o3b2o$37b2o43b2o3b2o$81bobo3bobo$37b2o42b2o5b2o$37b2o$
88b2o$37b2o50bo$18b2o17b2o49bo$17bo2bob2o64b2o$17bo2bob2o13b2o$18b2o17b
2o49b2o$88b2o$37b2o$5b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2bobo49b2o$4bobob2o
b2ob2ob2ob2ob2ob2ob2ob2o2b2o50b2o$4b2o61b2o$67b2o19b2o$18b2o68b2o$4b2o
11bo2bob2o$4b2o11bo2bob2o23b2o22b2ob2ob2ob2ob2o3b2o$18b2o27bo23b2ob2o
b2ob2ob2o3b2o$4b2o42bo$4b2o43bobob2ob2ob2ob2ob2o21b2o$50b2ob2ob2ob2ob
2ob2o21b2o$4b2o64b2o$4b2o22b2ob2ob2ob2ob2ob2ob2o22bobo15b2o$27bobob2o
b2ob2ob2ob2ob2o23b2o15b2o$4b2o21b2o$4b2o46b2o12b2o$2o6b2o17b2o23bobo11b
2o$2o6b2o17b2o24b2o2$27b2o$b2o4b2o18b2o$obo4bobo$2o6b2o17b2o$4b2o21b2o
$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o20bo2bo$4b2o
20bo2bo$27b2o$4b2o$3bo2bo$3bo2bo$4b2o!
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 WIDTH 1000 ZOOM 5 GPS 6 LOOP 300 ]]
|position = center
|caption = A collection of beehive/block fuse reactions
|style = width:300px;
}}

These chains can interact in different ways to form logic gates.

==Change in frequency, stabilisation time and evolutionary sequences==
From the same random starting conditions, B35/S23 usually settles into much fewer objects than in Life due to the fact that many life [[evolutionary sequence]]s are sparks in this rule. It also stabilises ten times faster than life on average.

The honey farm sequence, which evolves into 4 [[blinker]]s in a [[traffic light]]-like formation with a [[tub]] inside, is much rarer in B35/S23 due to the fact that the only 7-cell predecessor that still works is the line of seven, which is much rarer than the other predecessors.

The traffic light sequence is considerably rarer in B35/S23 due to the T-tetromino's disappearance, so the next most common predecessor that works is the X-pentomino, which is rarer.

The [[Bakery]], [[Teardrop]], [[Butterfly]] and [[Fleet]] die out.

==Universality==
On August 3, 2023, AlbertArmStain published a {{rl|Rule 110}} unit stripe based on the aforementioned beehive/block fuse, proving the rule's [[Universal computer|Turing-completeness]].<ref name="post164523" />

== Soup search ==
{{related|Catagolue|Tutorials/Contributing to Catagolue}}

Soup search was performed using a modified version of [[apgsearch]], yielding uncommon objects such as the c/3o spaceship (Glider 4793) as early as 2014.<ref name="post13161" />

On October 12, 2022, the {{cata|census/b35s23/C1|b35s23/C1}} census on [[Catagolue]] reached a total of one trillion objects,<ref group=c name="C1_1e12" /> making B35/S23 one of several [[Life-like rule]]s with hauls [[Catagolue#Haul verification|subject to statistical verification and peer review]] before being committed.

The b35s23/C1 census accumulated 375 million objects in April 2015,<ref group=c>[https://web.archive.org/web/20150422135228/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2015-04-22)</ref>
169 billion objects in October 2017,<ref group=c>[https://web.archive.org/web/20171029134053/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2017-10-29)</ref>
519 billion objects in July 2021,<ref group=c>[https://web.archive.org/web/20210716224801/http://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2021-07-16)</ref>
561 billion objects in October 2021,<ref group=c>[https://web.archive.org/web/20211030140403/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2021-10-30)</ref>
1690 billion objects in February 2023,<ref group=c>[https://web.archive.org/web/20230221163702/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2023-02-21)</ref>
1722 billion objects in August 2023.<ref group=c>[https://web.archive.org/web/20230806111857/https://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2023-08-06)</ref>

==See also==
* {{rl|Pseudo Life}}, a rule where many patterns from this rule also work, although with generally more chaotic evolution.

==References==
<references>
<ref name="post5304">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 5304
|title = Re: B35/S23
|author = LumpsOfMuck
|date = October 14, 2011
}}</ref>
<ref name="post12942">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 12942
|title = Re: B35/S23
|author = Lewis
|date = August 19, 2014
}}</ref>
<ref name="post13161">{{LinkForumThread
|format = ref
|f = 7
|t = 1443
|p = 13161
|title = Re: apgsearch: a high-performance soup searcher
|author = Lewis
|date = September 10, 2014
}}</ref>
<ref name="post17286">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 17286
|title = Re: B35/S23
|author = praosylen
|date = February 27, 2015
}}</ref>
<ref name="post135647">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 135647
|title = Re: B35/S23
|author = FWKnightship
|date = September 10, 2021
}}</ref>
<ref name="post164523">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 164523
|title = Re: B35/S23
|author = AlbertArmStain
|date = August 3, 2023
}}</ref>
</references>

; Catagolue
<references group=c>
<ref name="C1_1e12">[https://web.archive.org/web/20221013093222/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1], [https://web.archive.org/web/20221013093138/https://catagolue.hatsya.com/haul/b35s23/C1 /haul/b35s23/C1] (archived copies as of 2022-10-13)</ref>
</references>

==External links==
* {{LinkCatagolueRule|b35s23}}

[[Category:Life-like cellular automata]]

OCA talk:Grounded Life

2023-08-16T17:02:00Z

MEisSCAMMER: /* Stamp collection */ edited title; didn't notice that it was the same as another above it

== Stamp collection ==

Well, I think there is no single best common standard for how to format galleries. The stamp collection looks nice, and might be a reasonable choice in this case. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 11:07, 9 August 2023 (UTC)

So be it lah!

== Stamp collection 2 ==

I'm not sure if a caption is the right place for the description of the stamp collection. It's getting a bit too long, and I think a better place for it might just be in a paragraph below it. [[User:MEisSCAMMER|MEisSCAMMER]] ([[User talk:MEisSCAMMER|talk]]) 17:01, 16 August 2023 (UTC)

OCA talk:Grounded Life

2023-08-16T17:01:33Z

MEisSCAMMER: /* Stamp collection */ new section

== Stamp collection ==

Well, I think there is no single best common standard for how to format galleries. The stamp collection looks nice, and might be a reasonable choice in this case. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 11:07, 9 August 2023 (UTC)

So be it lah!

== Stamp collection ==

I'm not sure if a caption is the right place for the description of the stamp collection. It's getting a bit too long, and I think a better place for it might just be in a paragraph below it. [[User:MEisSCAMMER|MEisSCAMMER]] ([[User talk:MEisSCAMMER|talk]]) 17:01, 16 August 2023 (UTC)

OCA:Grounded Life

2023-08-16T17:00:24Z

MEisSCAMMER: /* Oscillators */ grammar and tightening up of the stamp collection caption, as well as removing line breaks which didn't really go well with the width of the template. Also see the talk page

{{Rule
|b = 35
|s = 23
|char = Chaotic
|ruleinteger = 6184
|reversal = B0123478/S0124678
}}
'''B35/S23''' (also known as '''Grounded Life''') is a [[Life-like cellular automaton]] in which a [[cell]] survives from one generation to the next if it has 2 or 3 [[Neighbourhood|neighbors]], and is born if it has 3 or 5 neighbors. Under this rule, patterns tend to stabilize more quickly than in standard [[Life]],<ref name="post5304" /> which is one of the reasons for its alternate name.

==Patterns==
The two most common objects in B35/S23 are the [[block]] and the [[blinker]].

Some patterns work as they do in life, but many instead die off completely, such as the [[beehive]], [[boat]], [[T-tetromino]], [[pi-heptomino]], and [[stairstep hexomino]].

===Still lifes===

Because B35/S23 adds one birth transition from Life, all still lives in B35/S23 are still lives in Conway's Game of Life, but the reverse is not true. For example, the [[boat]] fails in B35/S23.

Many small still lifes under the standard Life rules have dead cells with five alive neighbours, so the list of still lifes for the two rules are extremely different for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in B35/S23 are boat (with 5 cells), beehive (with 6 cells) and [[Loaf]], [[Long boat]] and [[Eater 1]] (with 7 cells) Also, any pattern using a [[House]] or a [[Bun]] as an induction coil that is a still life under the standard rules, or any extended forms of the [[ship]] or [[Boat]] are not still lifes in B35/S23.

All still lifes up to 10 bits have occurred naturally. Almost all still lifes with 11 bits have occured naturally, with the only exception being [[Hook line tub]]. Notably, [[tub]] and [[barge]] are significantly more common than they're in Life.

===Oscillators===

Naturally occurring objects in this rule include oscillators of periods 2, 3, 4, 5, 8 and 26. There are also seminatural oscillators of periods 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 18, 21, 24, 26, 29, 33, 46, 82, and 142. Alien oscillators are also much more common than in similar rules, especially 8P8 ( Mirrored [[Short table]] ) and 8P4 ( A [[Pre-pulsar]] predecessor in Life).

Notably, [[Washing machine]] is much more common in this rule, even in asymmetric soups.
It is the 56th most common object in asymmetric soups and the 21st most common object in D4_x4 soups. [[Toad]]s are also much more common.

Many alien oscillators exist in this rule, several of which are shown below:
{{EmbedViewer
|rle = x = 0, y = 0, rule = B35/S23History
94F$F24.F17.F20.F28.F$F24.F17.F20.F28.F$F2.2D13.2A.2A2.F2.2D6.A6.F4.D
15.F28.F$F.D2.D5.2A4.A2.2A.A.F.D2.D3.3A.A.A2.F3.2D3.3A9.F28.F$F4.D3.3A
2.A2.A4.2A.F4.D8.2A2.F2.D.D4.A4.4A2.F28.F$F3.D4.A2.3A3.A3.A2.F2.2D6.A
.3A2.F.D2.D9.4A2.F28.F$F2.D7.2A4.2A4.A.F4.D4.2A.A4.F.5D3.A4.4A2.F11.6A
11.F$F.D14.A.2A2.A.F.D2.D4.A7.F4.D3.3A3.4A2.F28.F$F.4D12.2A.2A2.F2.2D
5.A7.F4.D15.F9.A8.A9.F$F24.F17.F20.F8.A.A6.A.A8.F$F24.F17.F20.F7.A.A8.
A.A7.F$65F6.A.A10.A.A6.F$F21.F41.F7.A12.A7.F$F2.2D4.A6.A5.F9.2D30.F4.
A7.D3.D6.A4.F$F.D2.D3.2A4.2A5.F8.D2.D29.F4.A6.2D2.2D6.A4.F$F.D6.2A4.2A
5.F8.D2.D4.6A6.2A.2A8.F4.A5.D.D.D.D6.A4.F$F.3D5.A4.A6.F9.2D4.A.4A.A6.
A.A9.F4.A7.D3.D6.A4.F$F.D2.D16.F8.D2.D4.6A6.2A.2A8.F4.A7.D3.D6.A4.F$F
.D2.D4.A4.A6.F8.D2.D4.A4.A19.F4.A7.D3.D6.A4.F$F2.2D6.A2.A7.F9.2D30.F7.
A4.D3.D3.A7.F$F10.4A7.F41.F6.A.A10.A.A6.F$F10.A2.A7.43F7.A.A8.A.A7.F$
F10.A2.A7.F41.F8.A.A6.A.A8.F$F10.A2.A7.F2.2D4.D32.F9.A8.A9.F$F10.4A7.
F.D2.D2.2D7.2A15.2A6.F28.F$F10.A2.A7.F4.D.D.D7.2A15.2A6.F11.6A11.F$F9.
A4.A6.F3.D4.D32.F28.F$F21.F2.D5.D32.F28.F$F9.A4.A6.F.D6.D32.F28.F$F8.
2A4.2A5.F.4D3.D12.2A5.2A11.F28.F$F8.2A4.2A5.F17.A4.A5.A4.A7.F28.F$F8.
A6.A5.F16.3A3.A5.A3.3A6.F28.F$F21.F16.A.A2.A7.A2.A.A6.30F$31F33.F28.F
$F29.F33.F28.F$F29.F8.A.A2.A7.A2.A.A6.F28.F$F20.2D3.2D2.F8.3A3.A5.A3.
3A6.F28.F$F19.D2.D.D2.D.F9.A4.A5.A4.A7.F28.F$F22.D4.D.F13.2A5.2A11.F28.
F$F20.2D3.2D2.F33.F21.2A5.F$F22.D4.D.F33.F5.2A9.2A3.A.A4.F$F19.D2.D.D
2.D.F33.F4.A.A9.A.A2.3A4.F$F20.2D3.2D2.F8.2A15.2A6.F4.3A9.2A10.F$F3.3A
6.3A14.F8.2A15.2A6.F28.F$F4.A8.A15.F33.F28.F$F18.46F6.A21.F$F6.2A2.2A
6.F44.F5.A.A4.D3.2D10.F$F6.2A2.2A6.F44.F5.3A3.2D2.D2.D9.F$F18.F44.F10.
D.D2.D12.F$F18.F44.F9.D2.D2.3D10.F$F18.F37.2A5.F9.5D.D2.D9.F$F6.2A2.2A
6.F10.3A24.2A5.F12.D2.D2.D2.3A4.F$F6.2A2.2A6.F10.2A7.2D3.2D3.3A5.2A5.
F12.D3.2D3.A.A4.F$F18.F10.3A5.D2.D.D2.D2.3A12.F22.A5.F$F4.A8.A4.F12.2A
7.D.D20.F28.F$F3.3A6.3A3.F6.2A4.2A6.D2.3D18.F28.F$F18.F6.2A11.D3.D2.D
17.F11.2A9.3A3.F$F18.F7.3A8.D4.D2.D17.F5.3A2.A.A9.A.A3.F$F18.F8.2A8.4D
2.2D12.3A3.F5.A.A3.2A9.2A4.F$F18.F7.3A21.2A5.3A3.F6.2A20.F$F18.F31.2A
11.F28.F$F18.F31.2A11.F28.F$F18.F44.F28.F$F18.F44.F28.F$F18.F44.F28.F
$94F$F36.F55.F$F36.F55.F$F36.F55.F$F36.F13.2A21.2A17.F$F36.F13.A.A19.
A.A17.F$F36.F14.2A19.2A18.F$F36.F22.2A3.2A26.F$F36.F21.A.A3.A.A25.F$F
36.F21.3A3.3A25.F$F36.F22.A5.A26.F$F16.3A7.3A7.F6.2A35.2A10.F$F2.2D3.
2D7.A2.A5.A2.A7.F6.A.A33.A.A10.F$F.D2.D.D2.D6.A.A7.A.A7.F7.2A33.2A11.
F$F.D2.D4.D7.2A7.2A8.F55.F$F2.2D4.D27.F55.F$F.D2.D2.D9.2A7.2A8.F55.F$
F.D2.D.D9.A.A7.A.A7.F55.F$F2.2D2.4D6.A2.A5.A2.A7.F55.F$F16.3A7.3A7.F10.
2A27.2A14.F$F36.F9.A.2A25.2A.A13.F$F36.F9.3A27.3A13.F$F36.F55.F$F36.F
55.F$F36.F55.F$F36.F9.3A27.3A13.F$F36.F9.A.2A25.2A.A13.F$F36.F10.2A27.
2A14.F$F36.F55.F$38F55.F$F92.F$F92.F$F92.F$F44.2A33.2A11.F$F11.D4.D3.
2D21.A.A33.A.A10.F$F10.2D3.2D2.D2.D20.2A35.2A10.F$F9.D.D2.D.D5.D36.A5.
A26.F$F11.D.D2.D4.D36.3A3.3A25.F$F11.D.5D2.D37.A.A3.A.A25.F$F11.D4.D2.
D39.2A3.2A26.F$F11.D4.D2.4D28.2A19.2A18.F$F50.A.A19.A.A17.F$F50.2A21.
2A17.F$F92.F$F92.F$F92.F$94F!
|viewerconfig = #C [[ HEIGHT 950 WIDTH 800 ZOOM 8 GRID OFF THEME LifeHistory ]]
|position = center
|caption = A [[stamp collection]] of oscillators. From left to right, top to bottom, they are:
12P2 and [[Washing machine]] (rare examples of [[billiard table]]s in B35/S23),
14P3 (a natural oscillator resembling the [[caterer]]),
8P4 (a [[pre-pulsar]] predecessor in Life, which resembles 8P8),
12P4 (dependent on the B5a transition; the pattern dies in Life due to the lack of it),
56P11 (resemblant of [[Achim's p11]]),
46P6,
14P8 (extensible, although only in discrete lengths or with proper [[induction coil]]s),
8P8 (the mirrored [[short table]]),
32P33 (four [[block]]s hassling four [[T-tetromino]]s),
18P26 (the highest-period oscillator to have appeared naturally),
24P26 (an oscillator composed of interacting beehive sparks; appears in 1250 C4_4 soups),
48P46 (a [[shuttle]] of [[loaf]] and [[beehive]] sparks),
36P82,
and 104P142 (the highest period oscillator to have appeared semi-naturally).
  
|style = width:300px;
}}

===Spaceships===

Of particular note is the fact that neither the [[glider]] nor any of the [[xWSS]]es work in B35/S23 (all of them die off), giving the rule its alternate name. The most common spaceship according to [[Catagolue]] is the [[OCA:Glider 3736|glider 3736]].

Known [[spaceship]] speeds are c/2o, c/3o, c/4o, c/5o, c/6o, 2c/5o, c/4d and c/5d.

The three smallest spaceships in {{rl|Pseudo Life}} work:
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
2b3o$bo3bo$o2bo2bo$3ob3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -4 THEME Book STARTFROM 10 ]]
|position = center
|caption = 13P5H2V0 (glider 3736) (Robert Wainwright, 1994)
|style = width:100px;
|apgcode = xq5_359a953/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
2bo$b3o$o3bo$bo2bo$3b2obo$6bo$4bobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 6 ]]
|position = center
|caption = 14P3H1V0 (glider 4793) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq3_0oogheez17/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
3bo$b2ob2o$o2bo2bo$obobobo$3bo$bo3bo$bobobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 18P2H1V0 (glider 4716) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq2_4urhru4zw202/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
o3b2o6bo$2ob4o5bo$o5b2o2b5o$3bo3b3obo$3bob2ob2obo$5b3o$6b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 27P4H1V0
|style = width:100px;
}}}}
{{gallery bottom}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
17b2o2$15b2o$14bobo$13b2o$11b4o2bo4bo$11bobo3bo2bobo$10b3obo2bobo2bo$6bo6b2ob
2ob2o$4bobo3b3o3bo$2b3o6bo4b2o$bo5b2o7b2o$5o2b2o2b2obo2bo$b4o4bo2b2o$2b3o5bo
2bo$3bo7b3o$11bob2o$12b2o$9bo3bo$7b3o3bo$8b2o$9b4o$10b2o$11bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 600 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 90P4H1V1
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
11bo$10bobo$8b2o$6bo$6bo3bo3bo$5bob4o2bo$3b2obo2bo2b3o$5bo2b2obob3o$2b
o2bob3o3bo2bo$2bo2b5obo3bo$bo2b2o9b2o$o6bobo3bob4o$bo4bo7b2o$5b4o2bo3b
o$4bob2o4bo4b3o$7bob5o$8bob2o$11bo2bo$11bo2bo$14bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 600 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 78P5H1V1
|style = width:100px;
}}}}
{{gallery bottom}}

=== Puffers ===

There is a naturally occurring orthogonal c/2 [[puffer]] with period 136, leaving three [[blinker]]s and two [[block]]s every 68 ticks. Combining two or more puffers can give other puffers and spaceships.<ref name="post12942" /><ref name="post17286" /> The puffer engine also works in B357/S238 (where it becomes a p248 puffer).
On September 10, 2021, FWKnightship posted a 24c/48 siderake emitting 2c/5 spaceships.<ref name="post135647" />

{{EmbedViewer
|rle = x = 81, y = 16, rule = B35/S23
16b2o$16b2o2$57bo$57bo$57b2o14b3o$12b2o39bo18b4o$3o3b3o3b2o33bo3b3o2b
2ob2o10b4o3b2o$25bo11b3o7bo4b2o4b3o11b2o5b2o$4bo20b2o10bobo7bo4bo4bob
2o14b2ob2o$4bo18b4o10b3o12bo3bo4bo13b4o$4bo18b2o25b3o7b4o12bo$17bo42b
o$17bo2bo19b2o18bobo$16bo3bo19b2o$17bobo!
|viewerconfig = #C [[ HEIGHT 360 WIDTH 900 THUMBSIZE 2 ZOOM 10 GPS 12 AUTOSTART TRACKLOOP 136 1/2 0/2 ]]
|position = center
|caption = A period-136 orthogonal c/2 puffer<ref name="post12942" />
|style = width:300px;
|apgcode = yl68_1_17_f843afff9c5c3cef7d244e5948674525/b35s23
}}

===Beehive/block fuse===
One of the most useful reactions is the following, in which a beehive spark interacts with a chain of blocks, moving it further down the chain:

{{EmbedViewer
|rle = x = 30, y = 4, rule = B35/S23
bo$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$bo!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 140 ]]
|position = center
|caption = The beehive/block fuse
|style = width:300px;
}}

Once the beehive reaches the end, it will reverse the direction while shortening the chain, and will eventually annihilate it given enough time. This can be stopped with a [[pond]]:

{{EmbedViewer
|rle = x = 32, y = 4, rule = B35/S23
bo27b2o$obob2ob2ob2ob2ob2ob2ob2ob2obo2bo$obob2ob2ob2ob2ob2ob2ob2ob2ob
o2bo$bo27b2o!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 45 ]]
|position = center
}}

{{EmbedViewer
|rle = x = 95, y = 79, rule = B35/S23
53b2o$53b2o$12b2o$11bobo2b2o35b2o17b2o$11b2o3bo36bobo16bobo$17bo36b2o
17b2o$3bo12b2o$2bobob2ob2ob2obo5b2ob2ob2ob2ob2ob2o$2bobob2ob2ob2obo5b
2ob2ob2ob2ob2obobo2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob
2o$3bo12b2o19b2o2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob2o
$17bo$11b2o3bo20b2o$11bobo2b2o19b2o15b2o17b2o$12b2o39bobo16bobo12b2o$
37b2o14b2o17b2o13b2o$37b2o$53b2o32b2o$37b2o14b2o32b2o$37b2o$87b2o$37b
2o48b2o$37b2o$87b2o$37b2o48b2o$37b2o$33b2o6b2o39b2o3b2o$32bobo6bobo38b
2o3b2o$32b2o3b2o3b2o$37b2o43b2o3b2o$81bobo3bobo$37b2o42b2o5b2o$37b2o$
88b2o$37b2o50bo$18b2o17b2o49bo$17bo2bob2o64b2o$17bo2bob2o13b2o$18b2o17b
2o49b2o$88b2o$37b2o$5b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2bobo49b2o$4bobob2o
b2ob2ob2ob2ob2ob2ob2ob2o2b2o50b2o$4b2o61b2o$67b2o19b2o$18b2o68b2o$4b2o
11bo2bob2o$4b2o11bo2bob2o23b2o22b2ob2ob2ob2ob2o3b2o$18b2o27bo23b2ob2o
b2ob2ob2o3b2o$4b2o42bo$4b2o43bobob2ob2ob2ob2ob2o21b2o$50b2ob2ob2ob2ob
2ob2o21b2o$4b2o64b2o$4b2o22b2ob2ob2ob2ob2ob2ob2o22bobo15b2o$27bobob2o
b2ob2ob2ob2ob2o23b2o15b2o$4b2o21b2o$4b2o46b2o12b2o$2o6b2o17b2o23bobo11b
2o$2o6b2o17b2o24b2o2$27b2o$b2o4b2o18b2o$obo4bobo$2o6b2o17b2o$4b2o21b2o
$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o20bo2bo$4b2o
20bo2bo$27b2o$4b2o$3bo2bo$3bo2bo$4b2o!
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 WIDTH 1000 ZOOM 5 GPS 6 LOOP 300 ]]
|position = center
|caption = A collection of beehive/block fuse reactions
|style = width:300px;
}}

These chains can interact in different ways to form logic gates.

==Change in frequency, stabilisation time and evolutionary sequences==
From the same random starting conditions, B35/S23 usually settles into much fewer objects than in Life due to the fact that many life [[evolutionary sequence]]s are sparks in this rule. It also stabilises ten times faster than life on average.

The honey farm sequence, which evolves into 4 [[blinker]]s in a [[traffic light]]-like formation with a [[tub]] inside, is much rarer in B35/S23 due to the fact that the only 7-cell predecessor that still works is the line of seven, which is much rarer than the other predecessors.

The traffic light sequence is considerably rarer in B35/S23 due to the T-tetromino's disappearance, so the next most common predecessor that works is the X-pentomino, which is rarer.

The [[Bakery]], [[Teardrop]], [[Butterfly]] and [[Fleet]] die out.

==Universality==
On August 3, 2023, AlbertArmStain published a {{rl|Rule 110}} unit stripe based on the aforementioned beehive/block fuse, proving the rule's [[Universal computer|Turing-completeness]].<ref name="post164523" />

== Soup search ==
{{related|Catagolue|Tutorials/Contributing to Catagolue}}

Soup search was performed using a modified version of [[apgsearch]], yielding uncommon objects such as the c/3o spaceship (Glider 4793) as early as 2014.<ref name="post13161" />

On October 12, 2022, the {{cata|census/b35s23/C1|b35s23/C1}} census on [[Catagolue]] reached a total of one trillion objects,<ref group=c name="C1_1e12" /> making B35/S23 one of several [[Life-like rule]]s with hauls [[Catagolue#Haul verification|subject to statistical verification and peer review]] before being committed.

The b35s23/C1 census accumulated 375 million objects in April 2015,<ref group=c>[https://web.archive.org/web/20150422135228/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2015-04-22)</ref>
169 billion objects in October 2017,<ref group=c>[https://web.archive.org/web/20171029134053/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2017-10-29)</ref>
519 billion objects in July 2021,<ref group=c>[https://web.archive.org/web/20210716224801/http://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2021-07-16)</ref>
561 billion objects in October 2021,<ref group=c>[https://web.archive.org/web/20211030140403/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2021-10-30)</ref>
1690 billion objects in February 2023,<ref group=c>[https://web.archive.org/web/20230221163702/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2023-02-21)</ref>
1722 billion objects in August 2023.<ref group=c>[https://web.archive.org/web/20230806111857/https://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2023-08-06)</ref>

==See also==
* {{rl|Pseudo Life}}, a rule where many patterns from this rule also work, although with generally more chaotic evolution.

==References==
<references>
<ref name="post5304">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 5304
|title = Re: B35/S23
|author = LumpsOfMuck
|date = October 14, 2011
}}</ref>
<ref name="post12942">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 12942
|title = Re: B35/S23
|author = Lewis
|date = August 19, 2014
}}</ref>
<ref name="post13161">{{LinkForumThread
|format = ref
|f = 7
|t = 1443
|p = 13161
|title = Re: apgsearch: a high-performance soup searcher
|author = Lewis
|date = September 10, 2014
}}</ref>
<ref name="post17286">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 17286
|title = Re: B35/S23
|author = praosylen
|date = February 27, 2015
}}</ref>
<ref name="post135647">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 135647
|title = Re: B35/S23
|author = FWKnightship
|date = September 10, 2021
}}</ref>
<ref name="post164523">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 164523
|title = Re: B35/S23
|author = AlbertArmStain
|date = August 3, 2023
}}</ref>
</references>

; Catagolue
<references group=c>
<ref name="C1_1e12">[https://web.archive.org/web/20221013093222/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1], [https://web.archive.org/web/20221013093138/https://catagolue.hatsya.com/haul/b35s23/C1 /haul/b35s23/C1] (archived copies as of 2022-10-13)</ref>
</references>

==External links==
* {{LinkCatagolueRule|b35s23}}

[[Category:Life-like cellular automata]]

Two-glider octomino

2023-08-13T16:27:28Z

MEisSCAMMER: /* Use in conduits */ deleted duplicated section

{{Methuselah
|name = Two-glider octomino
|pname = 2glideroctomino
|c = 8
|bx = 4
|by = 4
|l = 386
|f = 48
|mcps = 8
|discoveryear = 1971 
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B3/S23
|synthesis = 2
|synthesisRLE = true
|plaintext = true
|rle = true
}}
The '''two-glider octomino'''{{refn|group=n|Sometimes simply called the octomino despite this being an ambiguous term due to the existence of 368 other [[octominoes]].}} is a fairly common [[methuselah]] that stabilizes into four [[beehive]]s and two [[traffic light]]s after 386 generations. It is so named because it can be formed by a particular [[2-glider collision]], shown below.

{{EmbedViewer
|rle = x = 11, y = 10, rule = B3/S23
8bo$8bobo$8b2o5$3o$2bo$bo!
|viewerconfig = #C [[ THUMBSIZE 3 ZOOM 24 HEIGHT 450 THEME Book GPS 5 AUTOSTART T 0 PAUSE 3 T 11 PAUSE 2 LOOP 12 ]]
|position = center
|caption = The 2G [[collision]] that makes the two-glider octomino<ref name="niemiec" />
|style = width:300px;
}}

==Predecessors==
{|style="margin:auto;width:300px;"
|{{EmbedViewer
|pname = 2glideroctominofromblockandt
|viewerconfig = #C [[ X -1 Y -1 AUTOSTART GPS 6 LOOP 15 T 0 PAUSE 1 T 14 PAUSE 1 ]]
|position = center
}}
|-
|{{EmbedViewer
|pname = 2glideroctomino6cellpredecessors
|viewerconfig = #C [[ AUTOSTART GPS 3 LOOP 4 T 0 PAUSE 1 T 2 PAUSE 1 T 3 PAUSE 0.7 ]]
|position = center
}}
|}
Shown are an easily edgeshootable six-cell pattern whose great-grandchild is the two-glider octomino and three six-cell patterns that are uncles of the two-glider octomino (i.e. their grandchild is the same as the two-glider octomino's child). The latter six-cell pattern can be created through a [[T-tetromino]] or other traffic light predecessor interacting with a block.

==Evolution==
<gallery widths="240px">
Image:Two-glider octomino ash.png|The ash of a two-glider octomino,<ref group=n>[[Ash]] on {{LinkCatagolue|style=brief|xp2_yj2552z696ycezy0888y41110s0111zw70ggg07yh696zzybg8gzyb121}}</ref> consisting of two traffic lights and four beehives.
</gallery>

After initially expanding downwards and then in various directions, the octomino drops a toad at generation 21. Meanwhile, the region on the other side has become a traffic light predecessor. The region that dropped the toad starts moving in the opposite direction, drops a [[block]] predecessor, then starts interacting with the traffic light. The resulting region continues moving, edgeshoots a block, then heads downwards. This lasts until generation 69, by which point the second block has been destroyed. c/2 downards movement resumes at generation 99, and at generation 106, a traffic light predecessor is edgeshot. The c/2 forwards movement ends at generation 110.

At generation 114, one group of chaos starts to move towards the block and toad. At generation 124, it destroys the block. This temporarily halts its movement, but it resumes around generation 139 and destroys the toad at generation 153, by which point half of the traffic light has been destroyed. From generation 166 to generation 183, three traffic light predecessors form and are destroyed. At generation 203, the first object that survives to the end, a beehive, is formed on the side from the region that destroyed the toad.

At generation 276, a pond is formed from the remaining half of the traffic light from generation 117. At generation 283, the second surviving object, another beehive, is formed. At generation 285, a block, a toad, and a [[honey farm]] predecessor form. Three-quarters of the honey farm are destroyed upon hitting the block and toad, but the last beehive survives some time longer, until generation 331, at which point it is destroyed. One generation later, a traffic light predecessor that was created at generation 320 finishes developing, which will survive to the end. Another traffic light also forms at the same time, but starting at generation 337, it is destroyed by various chaos. The resulting mess spawns the third surviving beehive at generation 350. Meanwhile, at generation 354, an R-pentomino starts interacting with the mess, causing it to form a traffic light at generation 385 and a beehive at generation 386, at which point the pattern stabilizes.

==Hasslers==
See [[Two-glider octomino hasslers]] for a list of oscillators that hassle the object.

==Use in conduits==
The Two-glider octomino is a recognized [[conduit]] object, represented by the letter '''O'''.

==Eaters==
[[File:Two-glider octomino eater.png|200px|thumb|right|a two-glider octomino about to be eaten by a fishhook]]
The two-glider octomino can be eaten using a variety of methods. One of the simplest and quickest requires a single [[fishhook]], which finishes eating the two-glider octomino after only nine-generations.

==Trivia==
As noted by [[Emerson J. Perkins]] in {{year|2011}}, the octomino appears to move diagonally at the speed of c/39 on an {{times|11|11}} [[torus]].<ref name="post4819" />

==Notes==
<references group=n />

==See also==
* [[Octomino II]]
* [[70P26]], which hassles two of them

==References==
<references>
<ref name="niemiec">{{LinkNiemiec|meth.htm#g2-meth|The 5 methuselahs buildable from 2 gliders|rle=0/7oo.rle|nobullet=nobullet}}</ref>
<ref name="post4819">{{LinkForumThread
|format = ref
|p = 4819
|title = Re: New ideas for pattern types
|author = Emerson J. Perkins
|date = July 4, 2011
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_o.htm#octomino}}

[[Category:Gliderless methuselahs]]
[[Category:Polyominoes]]
[[Category:Collisions]]
__NOTOC__

OCA:Tlife

2023-08-13T01:57:35Z

MEisSCAMMER: /* Oscillators */ grammar ('it' to 'one')

{{Rule
|name = tlife
|char = Chaotic
|b = 3
|s = 2-i34q
|hideimg = true
}}
'''tlife''' is a [[non-totalistic cellular automaton]] devised by [[M. I. Wright]] on September 6, 2015. It is very closely related to the much more commonly known rule [[Conway's Game of Life]], differing by only two transitions. It is likely one of the best-studied non-totalistic rules in existence.

== Rules ==
tlife is identical to Life in all transitions, save for two:

* cells with two adjacent cells in a straight orthogonal line (as in [[blinker]]) will die (-S2i), and
* cells with four adjacent cells (as in the dense phase of [[beacon]]) will survive (+S4q).

The two differing transitions, illustrated:

000 110
111 -> 0 110 -> 1
000 001

== Patterns ==
Although many patterns from Conway Life still function identically in tlife, some do not; for example, the [[blinker]] dies in tlife, and the [[beacon]] (depending on the phase) is or evolves into an 8-cell still life. Conversely, some patterns from tlife work in normal Life, but some do not.

{|style="float:right;margin-left:16px;margin-bottom:8px;width:100px;"
|{{EmbedViewer
|rle = x = 3, y = 2, rule = B3/S2-i34q
3o$bo!
|viewerconfig = #C [[ HEIGHT 600 WIDTH 800 THUMBSIZE 3 ZOOM 60 Y -1 AUTOSTART GPS 2 TRACKLOOP 5 0 1/5 ]]
|position = center
|caption = The [[T-tetromino]] spaceship
|apgcode = xq5_27/b3s2-i34q
}}
|-
|{{EmbedViewer
|rle = x = 7, y = 7, rule = B3/S2-i34q
4b2o$3bo2bo$2bob2o$bo2bo$ob2o$obo$bo!
|viewerconfig = #C [[ HEIGHT 600 WIDTH 800 THUMBSIZE 3 ZOOM 36 AUTOSTART GPS 2 ]]
|position = center
|caption = "Gate Kid" (named after its apgcode), or "honeyloaf p5" (its original name), a period 5 oscillator which works in both tlife and tdrylife
|apgcode = xp5_g8kid52z121/b3s2-i34q
}}
|}

=== Spaceships ===
{{for|other uses of "Ant"|ants}}
The [[glider]] exists in tlife, and there are two other basic elementary spaceships: a slightly bigger [[c/4 diagonal]] called ''ant'' and a [[non-monotonic]] [[c/5 orthogonal]] (the [[T-tetromino]], usually called simply ''T'' or ''T-ship'').<ref name="tmain" />

Alongside these, other elementary spaceships have been discovered. One such spaceship, which travels at [[c/2 orthogonal]] (period 4), is dubbed the ''disemiMWSS'', referencing the fact it looks like two [[middleweight spaceship]]s interacting with each other; there is also a skewed variant. There is also another c/2 orthogonal spaceship that evolves from a phase of the [[queen bee]], which has several minor variants. Other important spaceships include chains of interacting Ts, a small 2c/6 orthogonal ship, a small-to-medium [[c/4 orthogonal]] ship, and a large 8c/282 orthogonal ship consisting of many copies of a puffer of the same speed.<ref name="ships1" /><ref name="hypership" /> There are [[eater]]s for the glider, T, and ant, as well as for the queen bee ship and its variants.<ref name="tmain"/>

In all, c/2, [[2c/5 orthogonal|2c/5]], 2c/4, 4c/8, [[c/3 orthogonal|c/3]], 2c/6, c/4, c/5, and 8c/282 orthogonal, as well as c/4 diagonal, spaceships are known to exist, discounting higher-period c/2 technology.<ref name="ships1"/>

The only named spaceship other than the glider known to function in both CGoL and tlife is the [[crab]]; however, several other, unnamed c/4 diagonal spaceships work in both rules.<ref name="crab">{{LinkForumThread|f=11|t=1831|p=23029|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=September 27, 2015|format=ref}}</ref><ref name="lifeships">{{LinkForumThread|p=39575|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=January 20, 2017|format=ref}}</ref> All known spaceships that function in both B3/S23 and B3/S2-i34q travel at a velocity of (1,1)c/4.

=== Oscillators ===

There is a common unloopable (non-classical) period-160 [[reflectorless rotating oscillator]] that often evolves from (what would, in normal Life, be) a [[loaf]] predecessor or a [[honey farm]] predecessor. Multiple copies of this oscillator can be combined to form interesting patterns such as guns, higher-period oscillators, and glider or T duplicators. A single copy can also reflect a glider or T, or convert one into the other.<ref name="tmain"/> There is also a somewhat similar period 33,<ref>{{LinkForumThread|p=30352|title=Re: tlife (B3/S2-i34q)|author=Nico Brown (glider_rider)|date=April 23, 2016|format=ref}}</ref> several p20s based on a failed replicator, a p14 shuttle, a variety of p2 oscillators, small rule-specific period 3, 4, 5, 6, and 8 oscillators,<ref name="tmain"/><ref>{{LinkForumThread|p=24323|title=Re: tlife (B3/S2-i34q)|author=Sphenocorona|date=October 29, 2015|format=ref}}</ref> larger billiard tables of all periods up to 10,<ref name="billiards1">{{LinkForumThread|p=54077|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 14, 2017|format=ref}}</ref><ref>{{LinkForumThread|p=53676|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 22, 2017|format=ref}}</ref> and an infinitely extensible family of oscillators consisting of replicating signals traveling up and down two diagonal lines of connected blocks.<ref>{{LinkForumThread|p=27818|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=February 28, 2016|format=ref}}</ref> p4, p6, and p8 [[sparker]]s have also been found, allowing p16 T-hassling oscillators and p6N glider loops for certain N > 4 (exactly which N is unexplored, but it is likely to be all N), as well as p96+40N T shuttles for all N.<ref name="billiards1"/><ref>{{LinkForumThread|p=53787|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 16, 2017|format=ref}}</ref><ref>{{LinkForumThread|p=44057|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=June 4, 2017|format=ref}}</ref> Combinations of lower-period oscillators may lead to p12s and p15s; however, no examples have been explicitly constructed.

=== Infinite growth ===
As mentioned above, multiple copies of the period 160 oscillator can interact to form guns. There exist many guns for the glider and the T consisting of only two copies, as well as two double-barreled T guns.<ref>{{LinkForumThread|p=35966|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=September 20, 2016|format=ref}}</ref> There is also a gun for the ant consisting of 3 interacting p160 oscillators.<ref name="tmain"/> By combining multiple basic guns, larger guns have been formed for the c/2, 2c/6, disemiMWSS and skewed variants, as well as pairs of interacting T's. A period 231 T gun is also known, using an [[over-unity reaction]] supported by reflectors formed from the p33 oscillator.<ref>{{LinkForumThread|p=30990|title=Re: tlife (B3/S2-i34q)|author=Luka Okanishi (AbhpzTa)|date=May 14, 2016|format=ref}}</ref>

Several puffers are known. Most known puffers travel at c/2 orthogonal and use one of three engines: one or more [[B-heptomino]]es escorted by at least two disemiMWSSs, a [[Schick engine]]-like tagalong to a pair of disemiMWSSs, or a p8 engine derived from a 4c/8 ship.<ref>{{LinkForumThread|p=23553|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=October 9, 2015|format=ref}}</ref><ref name="puffer2" /><ref name="ships1"/> These engines can be perturbed by still more disemiMWSSs to form rakes for the glider and the T, as well as presumably for other spaceships.<ref name="puffer2"/><ref>{{LinkForumThread|p=23559|title=Re: tlife (B3/S2-i34q)|author=EricG|date=October 9, 2015|format=ref}}</ref> There is also an 8c/282 (mod 141) puffer made up of an ant bouncing between two [[boat]]s, displacing each in a forward direction while creating a block and a forward T, discovered by [[dani]]; [[Luka Okanishi]] used this to construct a large 8c/282 ship.<ref>{{LinkForumThread|p=63228|title=Re: tlife (B3/S2-i34q)|author=dani|date=August 29, 2018|format=ref}}</ref><ref name="hypership"/>

A [[sawtooth]] has been constructed, Sawtooth 1761.<ref>{{LinkForumThread|p=24988|title=Re: tlife (B3/S2-i34q)|author=EricG|date=November 12, 2015|format=ref}}</ref>

There is a breeder consisting of four Schick puffer-based glider rakes repeatedly synthesizing double-barreled T guns.<ref>{{LinkForumThread|p=23565|title=Re: tlife (B3/S2-i34q)|author=EricG|date=October 9, 2015|format=ref}}</ref>

No wickstretchers or spacefillers are known.

== Similar rules ==

Various rules similar to tlife have been constructed, such as B36/S2-i34q (tHighlife), B37/S2-i34q (tDrylife), and B367/S2-i34q (SilverLife).

=== B36/S2-i34q ===
{{split|OCA:tHighLife}}
{{Rule
|name = tHighLife
|char = Chaotic
|b = 36
|s = 2-i34q
|hideimg = true
}}
This rule is commonly known as "tHighLife" or "Thigh Life", due to it sharing a B6 transition with {{rl|HighLife}}.

Very interestingly, it has a simple orthogonal [[replicator]] which replicates at 4c/11 orthogonal, very similarly to HighLife's own replicator. [[Luka Okanishi]] used this to construct a 4c/11 orthogonal spaceship.
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 5, rule = B36/S2-i34q
2b3o$bo3bo$o5bo$bo3bo$2b3o!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 10 GPS 8 AUTOSTART T 0 PAUSE 2 T 44 PAUSE 1 LOOP 45 ]]
|position = center
|imgname = thighlifereplicator
|caption = The replicator
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 72, y = 27, rule = B36/S2-i34q
8b2o$8b6o19b5o3b5o$2o4b4ob3o19b5o3b5o$bo3bo5b3o19b5o3b5o$bo3b3o3bo$2b
4o$2b2o2bo$2b3obo$3b2obo$5bo16bo$3b2o2bo12bob2o$19b2ob2o$18bobo14b5o27b
5o$17b3o15b5o27b5o$35b5o27b5o$10b2o4b3o24bo$9b2obo4b2o26bo$8b3obo$8bo
2bo10b3o$24b2o2bo$21bo2b2o2bo8b3o5b3o$22bo3b2o8bo3bo3bo3bo$21bobo11bo
5bobo5bo$21bo2b2o10bo3bo3bo3bo$20bo16b3o5b3o$21bo2bo$22b3o!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 ]]
|position = center
|imgname = thighlife4c11spaceship
|caption = The 4c/11 spaceship
|style = width:300px;
}}}}
{{gallery bottom}}

=== B37/S2-i34q ===
{{split|OCA:tDryLife}}
{{Rule
|name = tDryLife
|char = Chaotic
|b = 37
|s = 2-i34q
|hideimg = true
}}
This rule is commonly known as "tdrylife", taking its B7 from {{rl|DryLife}}.

Unlike DryLife, it is not explosive, and has a lot of very interesting patterns. The only two relatively common oscillators are the [[cap]] and the [[toad]], neither with a usable spark, resulting in no guns having been discovered so far (as opposed to the well-known rakes).

Many interesting spaceships have been constructed in this rule. For example, there is a naturally occurring 2c/23 orthogonal spaceship involving the T trying to escape a [[pre-beehive]]. [[Luka Okanishi]] used this spaceship to create other patterns moving at this speed. A T forward rake was also built using known reflections for gliders and Ts when colliding with the 2c/23 spaceship.

{{EmbedViewer
|rle = x = 8, y = 4, rule = B37/S2-i34q
bobo$o2bo2b2o$bobo2b2o$6b2o!
|position = center
|imgname = tdrylife2c23spaceship
|caption = The 2c/23 ship
|apgcode = xq23_2507wee/b37s2-i34q
}}

A c/2 orthogonal spaceship based on 2 [[B-heptomino]]es has been seen to occur naturally.

{{EmbedViewer
|rle = x = 13, y = 17, rule = B37/S2-i34q
5b2o$2b5o$b2obo$b2o3$bo4bo3bo$bo5bo2bo$2bo8bo$8bo2b2o$2b2o4bob3o$bobo
8bo$bo2b2o$o3bo$bo2bo3b2obo$b3o5b3o$10bo!
|position = center
|imgname = tdrylifec2spaceship
|caption = The c/2 ship
|apgcode = xq20_0si2jkg8ozx1w11pgz27dwoo5421/b37s2-i34q
}}

It has a 11c/776 diagonal glide symmetric [[pond]] [[puffer]], which is actually the [[century]]. It parallels the [[R-pentomino]] based 9c/28 orthogonal pond puffer from DryLife. In June 2017, [[Luka Okanishi]] managed to build a 22c/1552 diagonal spaceship using pond puffer interactions.<ref>{{LinkForumThread|f=11|t=2266|p=44806|title=Re: tDryLife|author=Luka Okanishi (AbhpzTa)|date=June 21, 2017|format=ref}}</ref>

{{EmbedViewer
|rle = x = 61, y = 45, rule = B37/S2-i34q
41b2o$40bo2bo$40bo2bo$41b2o3$58b2o$57bo2bo$57bo2bo$58b2o2$30b2o$29bo2b
o$29bo2bo$30b2o3$47b2o$46bo2bo$46bo2bo$47b2o2$19b2o$18bo2bo$18bo2bo$
19b2o2$3o$obo33b2o$o2bo31bo2bo$2o3bo29bo2bo$bo4bo29b2o$5bobo3bo$4b3o4b
2o$12bo$11bo$7b2o2bo$b2o7b2o$b2o4b2o2bo$7bo3bo$8bo3b2o$8bo5bo2$10bob2o
$11b2o!
|position = center
|imgname = tdrylifepondpuffer
|caption = The pond puffer
|apgcode = yl388_1_8_0b4a1c894d6d85ab2d963168dd29a040/b37s2-i34q
}}

Most interestingly, there is a (2,6)c/21 ([[:category:spaceships with slope 3|slope 3]]) [[ship]] [[puffer]]. This can be stabilised into various interesting patterns, such as a two-engine knightship. [[Alexey Nigin]] has created a [[quadratic growth]] pattern which uses oblique spaceships to create pond puffers, based on a reaction discovered by [[Rhombic]]. A much slower quadratic growth pattern was discovered later by Rhombic, based on the synthesis of pond puffers with a T and a pond.

{{EmbedViewer
|rle = x = 56, y = 24, rule = B37/S2-i34q
53bo$48bo2b4o$49b2o4bo$52bobo$42bo8bobo$36b3o3b2ob2o$42b2ob2o3$35bobo$
36bobo$37b2o2$24b2o$24bobo$25b2o2$12b2o$12bobo$13b2o2$2o$obo$b2o!
|position = center
|imgname = tdrylifeshippuffer
|caption = The (12, 4)c/42 ship puffer
|apgcode = yl42_1_6_665e25ae9102cb33b169409d57f1f243/b37s2-i34q
}}

=== B367/S2-i34q ===
{{split|OCA:SilverLife}}
{{Rule
|name = SilverLife
|char = Chaotic
|b = 367
|s = 2-i34q
|hideimg = true
}}
This rule is commonly known as "SilverLife", it combines B6 and B7.

It is rich in exotic speeds, including a p91 flamingoship.

{{EmbedViewer
|rle = x = 7, y = 9, rule = B367/S2-i34q
3b3o$2b2ob2o$bobob2o$4b2o$bo2bo$3bo$2o$o$o!
|position = center
|caption = The (6, 1)c/91 flamingoship
|apgcode = xq91_0k27pf6ze201/b367s2-i34q
}}

There's also a 7c/55 diagonal pond puffer.
{{EmbedViewer
|rle = x = 8, y = 8, rule = B367/S2-i34q
6bo$4bo2bo$3b2o$2b3o$b3o2$o$bo!
|position = center
|caption = 7c/55 diagonal pond puffer
|apgcode = yl55_1_16_849ee0a7ef7869a03bd075211a55ded6/b367s2-i34q
}}

== References ==
<references>

<ref name="tmain">{{LinkForumThread
|p = 22549
|title = tlife (B3/S2-i34q)
|author = M. I. Wright
|date = September 13, 2015
|format = ref
}}</ref>

<ref name="ships1">{{LinkForumThread
|p = 23546
|title = Re: tlife (B3/S2-i34q)
|author = Arie Paap (wildmyron)
|date = November 29, 2016
|format = ref
}}</ref>

<ref name="hypership">{{LinkForumThread
|p = 63228
|title = Re: tlife (B3/S2-i34q)
|author = Luka Okanishi (AbhpzTa)
|date = September 1, 2018
|format = ref
}}</ref>

<ref name="puffer2">{{LinkForumThread
|p = 23563
|title = Re: tlife (B3/S2-i34q)
|author = Sphenocorona
|date = October 9, 2015
|format = ref
}}</ref>

</references>

== External links ==
* {{LinkForumThread|f=11|t=1831|title=tlife}}
* {{LinkForumThread|f=11|t=2265|title=thighlife}}
* {{LinkForumThread|f=11|t=2266|title=tdrylife}}
* {{LinkForumThread|f=11|t=3027|title=SilverLife}}
* {{LinkCatagolueRule|b3s2-i34q|rulename=tlife}}
* {{LinkCatagolueRule|b36s2-i34q|rulename=thighlife}}
* {{LinkCatagolueRule|b37s2-i34q|rulename=tdrylife}}
* {{LinkCatagolueRule|b367s2-i34q|rulename=SilverLife}}

{{DISPLAYTITLE:OCA:tlife}}
[[Category:Isotropic non-totalistic rules]]

Wire

2023-08-12T19:48:22Z

MEisSCAMMER: /* Lightspeed wire */ I changed the pattern to make it a torus, so making some changes in the viewerconfig to make it flow nicer

{{Glossary}}
A '''wire''' is a repeating pattern that a [[signal]] can travel along without making any permanent change to the pattern.<ref>{{citeCGoLMC|section=Section 4.5.1}}</ref> If instead the pattern is destroyed by the travelling signal (i.e. it [[burn]]s from one end) it is a [[fuse]].<ref>{{citeCGoLMC|section=Section 4.5.2|page=103}}</ref>

The first documented wire was discovered by [[Dean Hickerson]] in March {{year|1997}} while studying some period-3 [[oscillator]]s found by [[Achim Flammenkamp]]. It transmits signals that travel through the wire diagonally at two-thirds of the [[speed of light]]. This was the inspiration for Hickerson's [[drifter]] [[search program]], which led to the discovery of a 5c/9 wire a month later.

Hickerson also used his program to search for a wire signal elbow, hoping to use it to construct a fast signal loop and solve the [[omniperiodicity]] problem; this effort was unsuccessful for [[Life]], with the closest match being a 2c/3 [[signal elbow]] found in July {{year|1997}} that turned a single signal into a reflected double signal.

Signals on wires are hard to manipulate as compared to signals in a vacuum, especially in the form of [[glider]]s, for which there is a rich and growing [[toolkit]].<ref>{{citeCGoLMC|section=Section 4.7}}</ref>

==2c/3 wire==

'''2c/3 wire''' was discovered by Dean Hickerson in {{year|1997}}. It can be found in the ''misc'' section of [[jslife]] under the name ''signals 2c3d''.<ref name="jslife">{{CiteSummersPattern|name=jslife|accessdate=June 6, 2022}}</ref>

{{EmbedViewer
|position = center
|pname = 2c3wire
|caption = Diagonal 2c/3 wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 600 WIDTH 600 X 8 Y 4 ZOOM 8 GPS 10 LOOP 128 PAUSE 2 ]]
|style = width:300px;
}}

Each signal is made up of two half-signals that can be separated from each other by an arbitrary number of [[ticks]].

Considerable effort has been spent on finding a way to turn a [[2c/3]] signal 90 or 180 degrees, since this would be one way to prove Life to be omniperiodic. There is a known 2c/3 [[converter]] shown under [[signal elbow]], which converts a standard 2c/3 signal into a double-length signal. This is usable in some situations, but unfortunately it fails when its input is a double-length signal, so it cannot be used to complete two or more consecutive turns. It could only produce zigzag wires in any case rather than completing a loop, since the wire coming out of the elbow is a mirror image of the input wire.

In February {{year|2004}}, [[Noam Elkies]] discovered a [[glider synthesis]] of a reaction that can repeatably insert a signal into the upper end of a 2c/3 wire. See [[stable pseudo-Heisenburp]] for details. On September 11, {{year|2017}}, [[Martin Grant]] reduced the input reaction to five gliders or three gliders plus a [[Herschel]].<ref name="post50807" /> With the Herschel option the [[recovery time]] is 152 ticks.

Devices that extract a signal from a 2c/3 wire have also been built; currently the lowest repeat time of a standard 2c/3 signal receiver is 964 ticks,<ref name="post135690" /> and that of a double-length signal is 970 ticks,<ref name="post137526" /> both of which were achieved by [[Goldtiger997]] in {{year|2021}} by using complex [[staged recovery]] systems.

==5c/9 wire==

'''5c/9 wire''' was discovered by Dean Hickerson in 1997.

{{EmbedViewer
|position = center
|pname = 5c9wire
|caption = Diagonal 5c/9 wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 600 WIDTH 600 X 8 Y 4 ZOOM 6 GPS 10 LOOP 180 PAUSE 2 ]]
|style = width:300px;
}}

Oscillators have been found that inject signals of various periods including 9, 10, 11, and [[p47 lumps of muck hassler|47]] into a 5c/9 wire.<ref>{{cite web|url=https://conwaylife.com/ref/DRH/sig.inj.html|title=Dean Hickerson's signal-injector collection}}</ref>

It is possible to convert a 2c/3 wire signal into a 5c/9 signal; the viewer above shows the aforementioned five-glider input reaction for a 2c/3 signal and its subsequent conversion to 5c/9 signal. Another elementary 5c/9 signal injector involves a [[lumps of muck]] reaction,<ref name="post54568" /> which can be made from the synchronized [[2-glider collision]] at a repeat time of 62 ticks<ref name="post54617" />, a single Herschel with a much higher repeat time<ref name="post101243" />, or a fixed-period lumps of muck hassler that uses a specific catalyst (such as the p47).

However, no converter has yet been found for 5c/9 to 2c/3–or any other viable signal type, for that matter.

==c/2 wire==

'''c/2 wire''' was discovered by [[Hartmut Holzwart]] in 2003.

{{EmbedViewer
|position = center
|pname = c2wire
|caption = Diagonal c/2 wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 440 ZOOM 8 GPS 10 LOOP 50 PAUSE 2 ]]
|style = width:300px;
}}

Both halves of the signal (the non-uniform portion of the pattern) are needed, since the wire is offset by one cell between the two half signals.

It is technically possible to use [https://conwaylife.com/forums/viewtopic.php?f=2&t=3507 Extrementhusiast's construction and detection mechanisms from 2018] to complete a c/2 diagonal [[telegraph]] pattern that can send one bit of information every few thousand ticks. Or a somewhat higher transmission rate can be arranged with a mechanism similar to the one used in Louis-François Handfield's [[high-bandwidth telegraph]]. No complete c/2 diagonal telegraph has been built to date.

==Lightspeed wire==

The [[zebra stripes]] [[agar]] can be used to form a wire. Below are several signals which can travel through such a wire at [[lightspeed]] (one cell to the right per generation).

{{EmbedViewer
|position = center
|pname = zebrawiresignals
|caption = Several lightspeed signals travel through a zebra stripes wire
|viewerconfig = #C [[ AUTOSTART THUMBSIZE 2 HEIGHT 360 WIDTH 800 GPS 10 LOOP 138 ZOOM 6 ]]
|style = width:300px;
}}

This wire must extend infinitely at the leading edge to avoid destruction, limiting its practical usefulness.

==References==
<references>
<ref name="post50807">{{LinkForumThread
|format = ref
|title = Re: Stable signal converters
|p = 50807
|author = Martin Grant
|date = September 11, 2017
}}</ref>
<ref name="post135690">{{LinkForumThread
|format = ref
|title = Re: Faster 2c/3 Wires
|p = 135690
|author = Goldtiger997
|date = September 12, 2021
}}</ref>
<ref name="post137526">{{LinkForumThread
|format = ref
|title = Re: Faster 2c/3 Wires
|p = 137526
|author = Goldtiger997
|date = November 11, 2021
}}</ref>
<ref name="post54568">{{LinkForumThread
|format = ref
|title = Re: Interacting with LoM
|p = 54568
|author = Adam P. Goucher
|date = January 2, 2018
}}</ref>
<ref name="post54617">{{LinkForumThread
|format = ref
|title = Re: Interacting with LoM
|p = 54617
|author = Chris Cain
|date = January 3, 2018
}}</ref>
<ref name="post101243">{{LinkForumThread
|format = ref
|title = Re: The Hunting of the Elementary Conduits
|p = 101243
|author = Sphenocorona
|date = July 28, 2020
}}</ref>
</references>

==External links==
* {{LinkGoLNews|2005/02/stable_2c3_signal_receiver.html|archivedate=20100523082242|title=Stable 2c/3 signal receiver|date=February 7, 2005|author=Dave Greene}}
* {{LinkLexicon|lex_w.htm#wire|name=Wire}}
* {{LinkLexicon|lex_1.htm#a-2c3wire|name=2c/3 wire}}
* {{LinkLexicon|lex_1.htm#a-5c9wire|name=5c/9 wire}}
* {{LinkLexicon|lex_l.htm#lightspeedwire|name=Lightspeed wire}}

__NOTOC__

RLE:Zebrawiresignals

2023-08-12T19:45:45Z

MEisSCAMMER: changed to torus, so it doesn't explode anymore

x = 150, y = 13, rule = B3/S23: T138
bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo$b148o2$b14o2b10o2b120o$o13b2o10b2o40bo13bo13bo12bo39bo$b13o
3b9o3b12o2b24o4b11o4b10o3b10o4b14o2b20o$40b2o11bo12bo14bo15bo10bo2bo
10bo3b2o$b13o3b11o3b10o2b9o4b11o4b11o4b10o3b10o4b9o5bo3b18o$o13b2o12b
2o22bo14bo14bo13bo12bo13bo2b2o21bo$b14o2b12o2b96o2b20o2$b148o$bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo!

User:MEisSCAMMER

2023-08-08T21:54:13Z

MEisSCAMMER: created userpage

Hi! This is my userpage (currently small; I only created it because the redlink was bothering me).

Currently the only thing of substance I have done in this wiki is [[OCA:B35/S23]].

OCA:Grounded Life

2023-08-08T21:50:07Z

MEisSCAMMER: /* Oscillators */ replacing gallery with a single collection, because it's much nicer this way

{{Rule
|b = 35
|s = 23
|char = Chaotic
|ruleinteger = 6184
|reversal = B0123478/S0124678
}}
'''B35/S23''' (also known as '''Grounded Life''') is a [[Life-like cellular automaton]] in which a [[cell]] survives from one generation to the next if it has 2 or 3 [[Neighbourhood|neighbors]], and is born if it has 3 or 5 neighbors. Under this rule, patterns tend to stabilize more quickly than in standard [[Life]],<ref name="post5304" /> which is one of the reasons for its alternate name.

==Patterns==
The two most common objects in B35/S23 are the [[block]] and the [[blinker]].

Some patterns work as they do in life, but many instead die off completely, such as the [[beehive]], [[boat]], [[T-tetromino]], [[pi-heptomino]], and [[stairstep hexomino]].

===Still lifes===

Because B35/S23 adds one birth transition from Life, all still lives in B35/S23 are still lives in Conway's Game of Life, but the reverse is not true. For example, the [[boat]] fails in B35/S23.
All still lifes up to 10 bits have occurred naturally. Almost all still lifes with 11 bits have occured naturally, with the only exception being [[Hook line tub]]. Notably, [[tub]] and [[barge]] are significantly more common than they're in Life.

===Oscillators===

Naturally occurring objects in this rule include oscillators of periods 2, 3, 4, 5, 8 and 26. There are also seminatural oscillators of periods 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 18, 21, 24, 26, 29, 33, 46, 82, and 142.

Notably, [[Washing machine]] is much more common in this rule, even in asymmetric soups.
It is the 56th most common object in asymmetric soups and the 21st most common object in D4_x4 soups. [[Toad]]s are also much more common.

Many alien oscillators exist in this rule, several of which are shown below:
{{EmbedViewer|
rle=x = 0, y = 0, rule = B35/S23History
$.94F$.F24.F17.F20.F28.F$.F24.F17.F20.F28.F$.F2.2D13.2A.2A2.F2.2D6.A6.
F4.D15.F28.F$.F.D2.D5.2A4.A2.2A.A.F.D2.D3.3A.A.A2.F3.2D3.3A9.F28.F$.F
4.D3.3A2.A2.A4.2A.F4.D8.2A2.F2.D.D4.A4.4A2.F28.F$.F3.D4.A2.3A3.A3.A2.
F2.2D6.A.3A2.F.D2.D9.4A2.F28.F$.F2.D7.2A4.2A4.A.F4.D4.2A.A4.F.5D3.A4.
4A2.F11.6A11.F$.F.D14.A.2A2.A.F.D2.D4.A7.F4.D3.3A3.4A2.F28.F$.F.4D12.
2A.2A2.F2.2D5.A7.F4.D15.F9.A8.A9.F$.F24.F17.F20.F8.A.A6.A.A8.F$.F24.F
17.F20.F7.A.A8.A.A7.F$.65F6.A.A10.A.A6.F$.F21.F41.F7.A12.A7.F$.F2.2D4.
A6.A5.F9.2D30.F4.A7.D3.D6.A4.F$.F.D2.D3.2A4.2A5.F8.D2.D29.F4.A6.2D2.2D
6.A4.F$.F.D6.2A4.2A5.F8.D2.D4.6A6.2A.2A8.F4.A5.D.D.D.D6.A4.F$.F.3D5.A
4.A6.F9.2D4.A.4A.A6.A.A9.F4.A7.D3.D6.A4.F$.F.D2.D16.F8.D2.D4.6A6.2A.2A
8.F4.A7.D3.D6.A4.F$.F.D2.D4.A4.A6.F8.D2.D4.A4.A19.F4.A7.D3.D6.A4.F$.F
2.2D6.A2.A7.F9.2D30.F7.A4.D3.D3.A7.F$.F10.4A7.F41.F6.A.A10.A.A6.F$.F10.
A2.A7.43F7.A.A8.A.A7.F$.F10.A2.A7.F41.F8.A.A6.A.A8.F$.F10.A2.A7.F2.2D
4.D32.F9.A8.A9.F$.F10.4A7.F.D2.D2.2D7.2A15.2A6.F28.F$.F10.A2.A7.F4.D.
D.D7.2A15.2A6.F11.6A11.F$.F9.A4.A6.F3.D4.D32.F28.F$.F21.F2.D5.D32.F28.
F$.F9.A4.A6.F.D6.D32.F28.F$.F8.2A4.2A5.F.4D3.D12.2A5.2A11.F28.F$.F8.2A
4.2A5.F17.A4.A5.A4.A7.F28.F$.F8.A6.A5.F16.3A3.A5.A3.3A6.F28.F$.F21.F16.
A.A2.A7.A2.A.A6.30F$.31F33.F28.F$.F29.F33.F28.F$.F29.F8.A.A2.A7.A2.A.
A6.F28.F$.F20.2D3.2D2.F8.3A3.A5.A3.3A6.F28.F$.F19.D2.D.D2.D.F9.A4.A5.
A4.A7.F28.F$.F22.D4.D.F13.2A5.2A11.F28.F$.F20.2D3.2D2.F33.F21.2A5.F$.
F22.D4.D.F33.F5.2A9.2A3.A.A4.F$.F19.D2.D.D2.D.F33.F4.A.A9.A.A2.3A4.F$
.F20.2D3.2D2.F8.2A15.2A6.F4.3A9.2A10.F$.F4.3A6.3A13.F8.2A15.2A6.F28.F
$.F5.A8.A14.F33.F28.F$.F24.40F6.A21.F$.F7.2A2.2A11.F44.A.A3.2D3.2D10.
F$.F7.2A2.2A11.F44.3A2.D2.D.D2.D9.F$.F24.F52.D.D12.F$.F24.F51.D2.3D10.
F$.F24.F31.2A17.D3.D2.D9.F$.F7.2A2.2A11.F10.3A18.2A16.D4.D2.D2.3A4.F$
.F7.2A2.2A11.F10.2A11.3A5.2A16.4D2.2D3.A.A4.F$.F24.F10.3A10.3A35.A5.F
$.F5.A8.A9.F12.2A53.F$.F4.3A6.3A8.F6.2A4.2A53.F$.F24.F6.2A42.2A9.3A3.
F$.F24.F7.3A34.3A2.A.A9.A.A3.F$.F24.F8.2A22.3A9.A.A3.2A9.2A4.F$.F24.F
7.3A15.2A5.3A10.2A20.F$.F24.F25.2A40.F$.F24.F25.2A40.F$.F24.F67.F$.F24.
F67.F$.F24.F67.F$.94F$.F36.F55.F$.F36.F55.F$.F36.F55.F$.F36.F13.2A21.
2A17.F$.F36.F13.A.A19.A.A17.F$.F36.F14.2A19.2A18.F$.F36.F22.2A3.2A26.
F$.F36.F21.A.A3.A.A25.F$.F36.F21.3A3.3A25.F$.F36.F22.A5.A26.F$.F16.3A
7.3A7.F6.2A35.2A10.F$.F2.2D3.2D7.A2.A5.A2.A7.F6.A.A33.A.A10.F$.F.D2.D
.D2.D6.A.A7.A.A7.F7.2A33.2A11.F$.F.D2.D4.D7.2A7.2A8.F55.F$.F2.2D4.D27.
F55.F$.F.D2.D2.D9.2A7.2A8.F55.F$.F.D2.D.D9.A.A7.A.A7.F55.F$.F2.2D2.4D
6.A2.A5.A2.A7.F55.F$.F16.3A7.3A7.F10.2A27.2A14.F$.F36.F9.A.2A25.2A.A13.
F$.F36.F9.3A27.3A13.F$.F36.F55.F$.F36.F55.F$.F36.F55.F$.F36.F9.3A27.3A
13.F$.F36.F9.A.2A25.2A.A13.F$.F36.F10.2A27.2A14.F$.F36.F55.F$.38F55.F
$.F92.F$.F92.F$.F92.F$.F44.2A33.2A11.F$.F11.D4.D3.2D21.A.A33.A.A10.F$
.F10.2D3.2D2.D2.D20.2A35.2A10.F$.F9.D.D2.D.D5.D36.A5.A26.F$.F11.D.D2.
D4.D36.3A3.3A25.F$.F11.D.5D2.D37.A.A3.A.A25.F$.F11.D4.D2.D39.2A3.2A26.
F$.F11.D4.D2.4D28.2A19.2A18.F$.F50.A.A19.A.A17.F$.F50.2A21.2A17.F$.F92.
F$.F92.F$.F92.F$.94F!
| viewerconfig= #C [[ ZOOM 5 HEIGHT 600 THEME LifeHistory ]]
| position=center
}}

===Spaceships===

Of particular note is the fact that neither the [[glider]] nor any of the [[xWSS]]es work in B35/S23 (all of them die off), giving the rule its alternate name. The most common spaceship according to [[Catagolue]] is glider 3736.

Known [[spaceship]] speeds are c/2o, c/3o, c/4o, c/5o, c/6o, 2c/5o, and c/4d.

The three smallest spaceships in {{rl|Pseudo Life}} work:
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
2b3o$bo3bo$o2bo2bo$3ob3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -4 THEME Book STARTFROM 10 ]]
|position = center
|caption = 13P5H2V0 (glider 3736) (Robert Wainwright, 1994)
|style = width:100px;
|apgcode = xq5_359a953/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
2bo$b3o$o3bo$bo2bo$3b2obo$6bo$4bobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 6 ]]
|position = center
|caption = 14P3H1V0 (glider 4793) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq3_0oogheez17/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
3bo$b2ob2o$o2bo2bo$obobobo$3bo$bo3bo$bobobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 18P2H1V0 (glider 4716) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq2_4urhru4zw202/b35s23
}}}}
{{gallery bottom}}

=== Puffers ===

There is a naturally occurring orthogonal c/2 [[puffer]] with period 136, leaving three [[blinker]]s and two [[block]]s every 68 ticks. Combining two or more puffers can give other puffers and spaceships.<ref name="post12942" /><ref name="post17286" /> The puffer engine also works in B357/S238 (where it becomes a p248 puffer).
On September 10, 2021, FWKnightship posted a 24c/48 siderake emitting 2c/5 spaceships.<ref name="post135647" />

{{EmbedViewer
|rle = x = 81, y = 16, rule = B35/S23
16b2o$16b2o2$57bo$57bo$57b2o14b3o$12b2o39bo18b4o$3o3b3o3b2o33bo3b3o2b
2ob2o10b4o3b2o$25bo11b3o7bo4b2o4b3o11b2o5b2o$4bo20b2o10bobo7bo4bo4bob
2o14b2ob2o$4bo18b4o10b3o12bo3bo4bo13b4o$4bo18b2o25b3o7b4o12bo$17bo42b
o$17bo2bo19b2o18bobo$16bo3bo19b2o$17bobo!
|viewerconfig = #C [[ HEIGHT 360 WIDTH 900 THUMBSIZE 2 ZOOM 10 GPS 12 AUTOSTART TRACKLOOP 136 1/2 0/2 ]]
|position = center
|caption = A period-136 orthogonal c/2 puffer<ref name="post12942" />
|style = width:300px;
|apgcode = yl68_1_17_f843afff9c5c3cef7d244e5948674525/b35s23
}}

===Beehive/block fuse===
One of the most useful reactions is the following, in which a beehive spark interacts with a chain of blocks, moving it further down the chain:

{{EmbedViewer
|rle = x = 30, y = 4, rule = B35/S23
bo$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$bo!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 140 ]]
|position = center
|caption = The beehive/block fuse
|style = width:300px;
}}

Once the beehive reaches the end, it will reverse the direction while shortening the chain, and will eventually annihilate it given enough time. This can be stopped with a [[pond]]:

{{EmbedViewer
|rle = x = 32, y = 4, rule = B35/S23
bo27b2o$obob2ob2ob2ob2ob2ob2ob2ob2obo2bo$obob2ob2ob2ob2ob2ob2ob2ob2ob
o2bo$bo27b2o!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 45 ]]
|position = center
}}

{{EmbedViewer
|rle = x = 95, y = 79, rule = B35/S23
53b2o$53b2o$12b2o$11bobo2b2o35b2o17b2o$11b2o3bo36bobo16bobo$17bo36b2o
17b2o$3bo12b2o$2bobob2ob2ob2obo5b2ob2ob2ob2ob2ob2o$2bobob2ob2ob2obo5b
2ob2ob2ob2ob2obobo2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob
2o$3bo12b2o19b2o2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob2o
$17bo$11b2o3bo20b2o$11bobo2b2o19b2o15b2o17b2o$12b2o39bobo16bobo12b2o$
37b2o14b2o17b2o13b2o$37b2o$53b2o32b2o$37b2o14b2o32b2o$37b2o$87b2o$37b
2o48b2o$37b2o$87b2o$37b2o48b2o$37b2o$33b2o6b2o39b2o3b2o$32bobo6bobo38b
2o3b2o$32b2o3b2o3b2o$37b2o43b2o3b2o$81bobo3bobo$37b2o42b2o5b2o$37b2o$
88b2o$37b2o50bo$18b2o17b2o49bo$17bo2bob2o64b2o$17bo2bob2o13b2o$18b2o17b
2o49b2o$88b2o$37b2o$5b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2bobo49b2o$4bobob2o
b2ob2ob2ob2ob2ob2ob2ob2o2b2o50b2o$4b2o61b2o$67b2o19b2o$18b2o68b2o$4b2o
11bo2bob2o$4b2o11bo2bob2o23b2o22b2ob2ob2ob2ob2o3b2o$18b2o27bo23b2ob2o
b2ob2ob2o3b2o$4b2o42bo$4b2o43bobob2ob2ob2ob2ob2o21b2o$50b2ob2ob2ob2ob
2ob2o21b2o$4b2o64b2o$4b2o22b2ob2ob2ob2ob2ob2ob2o22bobo15b2o$27bobob2o
b2ob2ob2ob2ob2o23b2o15b2o$4b2o21b2o$4b2o46b2o12b2o$2o6b2o17b2o23bobo11b
2o$2o6b2o17b2o24b2o2$27b2o$b2o4b2o18b2o$obo4bobo$2o6b2o17b2o$4b2o21b2o
$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o20bo2bo$4b2o
20bo2bo$27b2o$4b2o$3bo2bo$3bo2bo$4b2o!
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 WIDTH 1000 ZOOM 5 GPS 6 LOOP 300 ]]
|position = center
|caption = A collection of beehive/block fuse reactions
|style = width:300px;
}}

These chains can interact in different ways to form logic gates.

==Universality==
On August 3, 2023, AlbertArmStain published a {{rl|Rule 110}} unit stripe based on the aforementioned beehive/block fuse, proving the rule's [[Universal computer|Turing-completeness]].<ref name="post164523" />

== Soup search ==
{{related|Catagolue|Tutorials/Contributing to Catagolue}}

Soup search was performed using a modified version of [[apgsearch]], yielding uncommon objects such as the c/3o spaceship (Glider 4793) as early as 2014.<ref name="post13161" />

On October 12, 2022, the {{cata|census/b35s23/C1|b35s23/C1}} census on [[Catagolue]] reached a total of one trillion objects,<ref group=c name="C1_1e12" /> making B35/S23 one of several [[Life-like rule]]s with hauls [[Catagolue#Haul verification|subject to statistical verification and peer review]] before being committed.

The b35s23/C1 census accumulated 375 million objects in April 2015,<ref group=c>[https://web.archive.org/web/20150422135228/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2015-04-22)</ref>
169 billion objects in October 2017,<ref group=c>[https://web.archive.org/web/20171029134053/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2017-10-29)</ref>
519 billion objects in July 2021,<ref group=c>[https://web.archive.org/web/20210716224801/http://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2021-07-16)</ref>
561 billion objects in October 2021,<ref group=c>[https://web.archive.org/web/20211030140403/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2021-10-30)</ref>
1690 billion objects in February 2023,<ref group=c>[https://web.archive.org/web/20230221163702/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2023-02-21)</ref>
1722 billion objects in August 2023.<ref group=c>[https://web.archive.org/web/20230806111857/https://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2023-08-06)</ref>

==See also==
* {{rl|Pseudo Life}}, a rule where many patterns from this rule also work, although with generally more chaotic evolution.

==References==
<references>
<ref name="post5304">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 5304
|title = Re: B35/S23
|author = LumpsOfMuck
|date = October 14, 2011
}}</ref>
<ref name="post12942">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 12942
|title = Re: B35/S23
|author = Lewis
|date = August 19, 2014
}}</ref>
<ref name="post13161">{{LinkForumThread
|format = ref
|f = 7
|t = 1443
|p = 13161
|title = Re: apgsearch: a high-performance soup searcher
|author = Lewis
|date = September 10, 2014
}}</ref>
<ref name="post17286">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 17286
|title = Re: B35/S23
|author = praosylen
|date = February 27, 2015
}}</ref>
<ref name="post135647">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 135647
|title = Re: B35/S23
|author = FWKnightship
|date = September 10, 2021
}}</ref>
<ref name="post164523">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 164523
|title = Re: B35/S23
|author = AlbertArmStain
|date = August 3, 2023
}}</ref>
</references>

; Catagolue
<references group=c>
<ref name="C1_1e12">[https://web.archive.org/web/20221013093222/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1], [https://web.archive.org/web/20221013093138/https://catagolue.hatsya.com/haul/b35s23/C1 /haul/b35s23/C1] (archived copies as of 2022-10-13)</ref>
</references>

==External links==
* {{LinkCatagolueRule|b35s23}}

[[Category:Life-like cellular automata]]

OCA:Grounded Life

2023-08-08T02:39:33Z

MEisSCAMMER: /* Spaceships */ colon doesn't belong

{{Rule
|b = 35
|s = 23
|char = Chaotic
|ruleinteger = 6184
|reversal = B0123478/S0124678
}}
'''B35/S23''' (also known as '''Grounded Life''') is a [[Life-like cellular automaton]] in which a [[cell]] survives from one generation to the next if it has 2 or 3 [[Neighbourhood|neighbors]], and is born if it has 3 or 5 neighbors. Under this rule, patterns tend to stabilize more quickly than in standard [[Life]],<ref name="post5304" /> which is one of the reasons for its alternate name.

==Patterns==
The two most common objects in B35/S23 are the [[block]] and the [[blinker]].

Some patterns work as they do in life, but many instead die off completely, such as the [[beehive]], [[boat]], [[T-tetromino]], [[pi-heptomino]], and [[stairstep hexomino]].

===Oscillators===

Naturally occurring objects in this rule include oscillators of periods 2, 3, 4, 5, 8 and 26. There are also seminatural oscillators of periods 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 18, 21, 24, 26, 29, 33, 46, 82, and 142

{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
2b2o$3o2bo$o2b3o$2b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 12P2, One of very few [[Billiard table]] oscillators known in the rule
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
2bo$3obobo$5b2o$2bob3o$b2obo$bo$bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 14P3, A natural oscillator resembling the [[caterer]]
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
3o$bo2$bo$3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 8P4, An extremely common oscillator that is a predecessor of the [[pre-pulsar]] in life.
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
4o$4o$4o$4o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 12P4. This oscillator only depends on one isotropic transition different from Life: B5a. In Life, without this transition, the pattern dies.
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
o6bo$2o4b2o$2o4b2o$bo4bo2$bo4bo$2bo2bo$2b4o$2bo2bo$2bo2bo$2bo2bo$2b4o$2bo2bo$
bo4bo2$bo4bo$2o4b2o$2o4b2o$o6bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 46P6.
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
obo$3o2$3o$obo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 8P8. Extremely common and also known by its systematic name, mirrored [[Short table]]
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
b6o$ob4obo$b6o$bo4bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 14P8
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
7b6o2$5bo8bo$4bobo6bobo$3bobo8bobo$2bobo10bobo$3bo12bo$o18bo$o18bo$o18bo$o18b
o$o18bo$o18bo$3bo12bo$2bobo10bobo$3bobo8bobo$4bobo6bobo$5bo8bo2$7b6o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 10 HEIGHT 500 THEME Book ]]
|position = center
|caption = 56P11, an oscillator similar to [[Achim's p11]] in Life, just with the [[line-of-six spark]]s nearer to the outside of the oscillator. About 1 in 70000 D8_4 soups form one in the center.
|style = width:500px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
2o15b2o$2o15b2o4$5b2o5b2o$bo4bo5bo4bo$3o3bo5bo3b3o$obo2bo7bo2bobo3$obo2bo7bo
2bobo$3o3bo5bo3b3o$bo4bo5bo4bo$5b2o5b2o4$2o15b2o$2o15b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 500 THEME Book ]]
|position = center
|caption = 60P21
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
4b3o$4b2o$4b3o$6b2o$2o4b2o$2o$b3o$2b2o$b3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 500 THEME Book ]]
|position = center
|caption = 18P26, the highest-period oscillator to have appeared naturally. About 1 in 12000000 C2_2 soups form one in the center.
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 12, y = 12, rule = B35/S23
8b2o$8b2o$3o5b2o$3o5$9b3o$2b2o5b3o$2b2o$2b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 24P26, an oscillator composed purely out of interacting beehive sparks. About 1 in 1250 C4_4 soups form one in the center.
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
3o6b3o$bo8bo2$3b2o2b2o$3b2o2b2o4$3b2o2b2o$3b2o2b2o2$bo8bo$3o6b3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 32P33. About 14 in a billion D4_+2 soups form one in the center.
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
17b2o$b2o9b2o3bobo$obo9bobo2b3o$3o9b2o3$2bo$bobo$b3o4$17b3o$17bobo$18bo3$7b2o
9b3o$b3o2bobo9bobo$bobo3b2o9b2o$2b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 20 HEIGHT 500 THEME Book ]]
|position = center
|caption = 48P26
|style = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
3o7b3o$o2bo5bo2bo$obo7bobo$b2o7b2o2$b2o7b2o$obo7bobo$o2bo5bo2bo$3o7b3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 32 HEIGHT 500 THEME Book ]]
|position = center
|caption = 36P82.
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
7b2o21b2o$7bobo19bobo$8b2o19b2o$16b2o3b2o$15bobo3bobo$15b3o3b3o$16bo5bo$2o35b
2o$obo33bobo$b2o33b2o6$4b2o27b2o$3bob2o25b2obo$3b3o27b3o4$3b3o27b3o$3bob2o25b
2obo$4b2o27b2o6$b2o33b2o$obo33bobo$2o35b2o$16bo5bo$15b3o3b3o$15bobo3bobo$16b
2o3b2o$8b2o19b2o$7bobo19bobo$7b2o21b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 10 HEIGHT 500 THEME Book ]]
|position = center
|caption = 104P142, the highest period oscillator to have appeared semi-naturally in B35/S23.
|style = width:300px;
}}}}
{{gallery bottom}}

===Spaceships===

Of particular note is the fact that neither the [[glider]] nor any of the [[xWSS]]es work in B35/S23 (all of them die off), giving the rule its alternate name. The most common spaceship according to [[Catagolue]] is glider 3736.

Known [[spaceship]] speeds are c/2o, c/3o, c/4o, c/5o, c/6o, 2c/5o, and c/4d.

The three smallest spaceships in {{rl|Pseudo Life}} work:
{{gallery top}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
2b3o$bo3bo$o2bo2bo$3ob3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -4 THEME Book STARTFROM 10 ]]
|position = center
|caption = 13P5H2V0 (glider 3736) (Robert Wainwright, 1994)
|style = width:100px;
|apgcode = xq5_359a953/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
2bo$b3o$o3bo$bo2bo$3b2obo$6bo$4bobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 6 ]]
|position = center
|caption = 14P3H1V0 (glider 4793) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq3_0oogheez17/b35s23
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 7, y = 7, rule = B35/S23
3bo$b2ob2o$o2bo2bo$obobobo$3bo$bo3bo$bobobo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 4 ZOOM 24 HEIGHT 500 Y -2 THEME Book STARTFROM 4 ]]
|position = center
|caption = 18P2H1V0 (glider 4716) (Nathan Thompson, 1994)
|style = width:100px;
|apgcode = xq2_4urhru4zw202/b35s23
}}}}
{{gallery bottom}}

=== Puffers ===

There is a naturally occurring orthogonal c/2 [[puffer]] with period 136, leaving three [[blinker]]s and two [[block]]s every 68 ticks. Combining two or more puffers can give other puffers and spaceships.<ref name="post12942" /><ref name="post17286" /> The puffer engine also works in B357/S238 (where it becomes a p248 puffer).
On September 10, 2021, FWKnightship posted a 24c/48 siderake emitting 2c/5 spaceships.<ref name="post135647" />

{{EmbedViewer
|rle = x = 81, y = 16, rule = B35/S23
16b2o$16b2o2$57bo$57bo$57b2o14b3o$12b2o39bo18b4o$3o3b3o3b2o33bo3b3o2b
2ob2o10b4o3b2o$25bo11b3o7bo4b2o4b3o11b2o5b2o$4bo20b2o10bobo7bo4bo4bob
2o14b2ob2o$4bo18b4o10b3o12bo3bo4bo13b4o$4bo18b2o25b3o7b4o12bo$17bo42b
o$17bo2bo19b2o18bobo$16bo3bo19b2o$17bobo!
|viewerconfig = #C [[ HEIGHT 360 WIDTH 900 THUMBSIZE 2 ZOOM 10 GPS 12 AUTOSTART TRACKLOOP 136 1/2 0/2 ]]
|position = center
|caption = A period-136 orthogonal c/2 puffer<ref name="post12942" />
|style = width:300px;
|apgcode = yl68_1_17_f843afff9c5c3cef7d244e5948674525/b35s23
}}

===Beehive/block fuse===
One of the most useful reactions is the following, in which a beehive spark interacts with a chain of blocks, moving it further down the chain:

{{EmbedViewer
|rle = x = 30, y = 4, rule = B35/S23
bo$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$bo!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 140 ]]
|position = center
|caption = The beehive/block fuse
|style = width:300px;
}}

Once the beehive reaches the end, it will reverse the direction while shortening the chain, and will eventually annihilate it given enough time. This can be stopped with a [[pond]]:

{{EmbedViewer
|rle = x = 32, y = 4, rule = B35/S23
bo27b2o$obob2ob2ob2ob2ob2ob2ob2ob2obo2bo$obob2ob2ob2ob2ob2ob2ob2ob2ob
o2bo$bo27b2o!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 45 ]]
|position = center
}}

{{EmbedViewer
|rle = x = 95, y = 79, rule = B35/S23
53b2o$53b2o$12b2o$11bobo2b2o35b2o17b2o$11b2o3bo36bobo16bobo$17bo36b2o
17b2o$3bo12b2o$2bobob2ob2ob2obo5b2ob2ob2ob2ob2ob2o$2bobob2ob2ob2obo5b
2ob2ob2ob2ob2obobo2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob
2o$3bo12b2o19b2o2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o5b2ob2ob2ob2ob2ob2o
$17bo$11b2o3bo20b2o$11bobo2b2o19b2o15b2o17b2o$12b2o39bobo16bobo12b2o$
37b2o14b2o17b2o13b2o$37b2o$53b2o32b2o$37b2o14b2o32b2o$37b2o$87b2o$37b
2o48b2o$37b2o$87b2o$37b2o48b2o$37b2o$33b2o6b2o39b2o3b2o$32bobo6bobo38b
2o3b2o$32b2o3b2o3b2o$37b2o43b2o3b2o$81bobo3bobo$37b2o42b2o5b2o$37b2o$
88b2o$37b2o50bo$18b2o17b2o49bo$17bo2bob2o64b2o$17bo2bob2o13b2o$18b2o17b
2o49b2o$88b2o$37b2o$5b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2bobo49b2o$4bobob2o
b2ob2ob2ob2ob2ob2ob2ob2o2b2o50b2o$4b2o61b2o$67b2o19b2o$18b2o68b2o$4b2o
11bo2bob2o$4b2o11bo2bob2o23b2o22b2ob2ob2ob2ob2o3b2o$18b2o27bo23b2ob2o
b2ob2ob2o3b2o$4b2o42bo$4b2o43bobob2ob2ob2ob2ob2o21b2o$50b2ob2ob2ob2ob
2ob2o21b2o$4b2o64b2o$4b2o22b2ob2ob2ob2ob2ob2ob2o22bobo15b2o$27bobob2o
b2ob2ob2ob2ob2o23b2o15b2o$4b2o21b2o$4b2o46b2o12b2o$2o6b2o17b2o23bobo11b
2o$2o6b2o17b2o24b2o2$27b2o$b2o4b2o18b2o$obo4bobo$2o6b2o17b2o$4b2o21b2o
$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o21b2o$4b2o$27b2o$4b2o20bo2bo$4b2o
20bo2bo$27b2o$4b2o$3bo2bo$3bo2bo$4b2o!
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 600 WIDTH 1000 ZOOM 5 GPS 6 LOOP 300 ]]
|position = center
|caption = A collection of beehive/block fuse reactions
|style = width:300px;
}}

These chains can interact in different ways to form logic gates.

==Universality==
On August 3, 2023, AlbertArmStain published a {{rl|Rule 110}} unit stripe based on the aforementioned beehive/block fuse, proving the rule's [[Universal computer|Turing-completeness]].<ref name="post164523" />

== Soup search ==
{{related|Catagolue|Tutorials/Contributing to Catagolue}}

Soup search was performed using a modified version of [[apgsearch]], yielding uncommon objects such as the c/3o spaceship (Glider 4793) as early as 2014.<ref name="post13161" />

On October 12, 2022, the {{cata|census/b35s23/C1|b35s23/C1}} census on [[Catagolue]] reached a total of one trillion objects,<ref group=c name="C1_1e12" /> making B35/S23 one of several [[Life-like rule]]s with hauls [[Catagolue#Haul verification|subject to statistical verification and peer review]] before being committed.

The b35s23/C1 census accumulated 375 million objects in April 2015,<ref group=c>[https://web.archive.org/web/20150422135228/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2015-04-22)</ref>
169 billion objects in October 2017,<ref group=c>[https://web.archive.org/web/20171029134053/http://catagolue.appspot.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2017-10-29)</ref>
519 billion objects in July 2021,<ref group=c>[https://web.archive.org/web/20210716224801/http://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2021-07-16)</ref>
561 billion objects in October 2021,<ref group=c>[https://web.archive.org/web/20211030140403/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2021-10-30)</ref>
1690 billion objects in February 2023,<ref group=c>[https://web.archive.org/web/20230221163702/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1] (archived copy as of 2023-02-21)</ref>
1722 billion objects in August 2023.<ref group=c>[https://web.archive.org/web/20230806111857/https://catagolue.hatsya.com/census/b35s23 /census/b35s23] (archived copy as of 2023-08-06)</ref>

==References==
<references>
<ref name="post5304">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 5304
|title = Re: B35/S23
|author = LumpsOfMuck
|date = October 14, 2011
}}</ref>
<ref name="post12942">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 12942
|title = Re: B35/S23
|author = Lewis
|date = August 19, 2014
}}</ref>
<ref name="post13161">{{LinkForumThread
|format = ref
|f = 7
|t = 1443
|p = 13161
|title = Re: apgsearch: a high-performance soup searcher
|author = Lewis
|date = September 10, 2014
}}</ref>
<ref name="post17286">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 17286
|title = Re: B35/S23
|author = praosylen
|date = February 27, 2015
}}</ref>
<ref name="post135647">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 135647
|title = Re: B35/S23
|author = FWKnightship
|date = September 10, 2021
}}</ref>
<ref name="post164523">{{LinkForumThread
|format = ref
|f = 11
|t = 757
|p = 164523
|title = Re: B35/S23
|author = AlbertArmStain
|date = August 3, 2023
}}</ref>
</references>

; Catagolue
<references group=c>
<ref name="C1_1e12">[https://web.archive.org/web/20221013093222/https://catagolue.hatsya.com/census/b35s23/C1 /census/b35s23/C1], [https://web.archive.org/web/20221013093138/https://catagolue.hatsya.com/haul/b35s23/C1 /haul/b35s23/C1] (archived copies as of 2022-10-13)</ref>
</references>

==External links==
* {{LinkCatagolueRule|b35s23}}

[[Category:Life-like cellular automata]]

OCA:Grounded Life

2023-08-04T17:06:06Z

MEisSCAMMER: created page

{{Rule|
b=35|s=23|
char=Chaotic|
ruleinteger=6184}}

'''B35/S23''' (sometimes '''Grounded Life''') is a [[Life-like cellular automaton]] in which a [[cell]] survives from one generation to the next if it has 2 or 3 [[Neighbourhood|neighbors]], and is born if it has 3 or 5 neighbors. Under this rule, patterns tend to stabilize more quickly than in standard [[Life]].<ref name="post5304" />
==Patterns==
The two most common objects in B35/S23 are the [[block]] and the [[blinker]].

Some patterns work as they do in life, but many instead die off completely, such as the [[beehive]], [[boat]], [[pi-heptomino]], and [[stairstep hexomino]].

Of particular note is the fact that neither the [[glider]] nor any of the [[xWSS]]es work in B35/S23 (all of them die off), giving the rule its alternate name. The most common spaceship according to Catagolue is glider 3736:

{{EmbedViewer
|rle = x = 7, y = 4, rule = B35/S23
3ob3o$o2bo2bo$bo3bo$2b3o!
|viewerconfig = #C [[ THUMBSIZE 3 HEIGHT 600 ]]
|position = center
|caption = Glider 3736}}

===Beehive/block fuse===
One of the most useful reactions is the following, in which a beehive spark interacts with a chain of blocks, moving it further down the chain:
{{EmbedViewer
|rle = x = 30, y = 4, rule = B35/S23
bo$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$obob2ob2ob2ob2ob2ob2ob2ob2ob2o$bo!
|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 140 ]]
|position = center
|caption = The beehive/block fuse.}}
Once the beehive reaches the end, it will reverse the direction while shortening the chain, and will eventually annihilate it given enough time. This can be stopped with a [[pond]]:
{{EmbedViewer
|rle = x = 32, y = 4, rule = B35/S23
bo27b2o$obob2ob2ob2ob2ob2ob2ob2ob2obo2bo$obob2ob2ob2ob2ob2ob2ob2ob2ob
o2bo$bo27b2o!|viewerconfig = #C [[ AUTOSTART ZOOM 20 WIDTH 1000 GPS 6 LOOP 45 ]]
|position = center}}

These chains can interact in different ways to form logic gates.
==Universality==
On August 3, 2023, AlbertArmStain published a [[OCA:Rule 110|Rule 110]] unit stripe based on the aforementioned beehive/block fuse, proving the rule's [[Universal computer|Turing-completeness]].<ref name="post164523" />
==References==
<references>
<ref name="post5304">{{LinkForumThread
|f=11
|t=757
|p=5304
|author=LumpsOfMuck
|date=October 14, 2011
|title=Re: B35/S23
|format=ref}}</ref>
<ref name="post164523">{{LinkForumThread
|f=11
|t=757
|p=164523
|author=AlbertArmStain
|date=August 3, 2023
|title=Re: B35/S23
|format=ref}}</ref>
</references>

Conway's Game of Life

2023-08-02T00:30:14Z

MEisSCAMMER: putting back soup; the animation of the octomino is nice but I don't see why we can't have the soup as well, it gives a better picture of the nature of Life

{{Rule
|name = Conway's Game of Life
|imgname = conwaylife
|char = Chaotic
|b = 3
|s = 23
|ruleinteger = 6152
|reversal = B0123478/S01234678
|animated = true
}}
'''Conway's Game of Life''', also known as the '''Game of Life''' or simply '''Life''', is a [[cellular automaton]] devised by the British mathematician [[John Horton Conway]] in 1970. It is the best-known example of a cellular automaton.

The "game" is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players. One interacts with the Game of Life by creating an initial configuration and observing how it evolves.

GOL and CGOL are commonly used acronyms.

== Rules ==
The universe of the Game of Life is an infinite two-dimensional orthogonal grid of square [[cell]]s, each of which (at any given time) is in one of two possible states, "live" (alternatively "on") or "dead" (alternatively "off").<ref>As expected, "birth" refers to a dead cell coming to life, and "death" refers to a live cell dying.</ref> Every cell interacts with its eight ''neighbours'', which are the cells that are directly horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:
# Any live cell with fewer than two live neighbours dies (referred to as '''underpopulation''' or '''exposure'''<ref>{{CiteLexicon|file=lex_e.htm#exposure|name=Exposure}}</ref>).
# Any live cell with more than three live neighbours dies (referred to as '''overpopulation''' or '''overcrowding''').
# Any live cell with two or three live neighbours lives, unchanged, to the next generation.
# Any dead cell with exactly three live neighbours will come to life.

{|style="float:right;width:300px;margin-left:16px;margin-bottom:8px;"
|{{EmbedViewer
|rle = x = 4, y = 4, rule = B3/S23
2b2o$2b2o$3o$bo!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 14 HEIGHT 600 X 8 Y 4 GPS 15 THEME Book AUTOSTART T 0 PAUSE 2 T 399 PAUSE 1 LOOP 400 ]]
|position = center
|caption = Animated evolution of a pattern known as the [[two-glider octomino]], with highlighted [[envelope]] (cells that were alive at some earlier point)
}}
|}

The initial pattern constitutes the 'seed' of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed — births and deaths happen simultaneously, and the discrete moment at which this happens is sometimes called a ''tick''. (In other words, each generation is a pure function of the one before.) The rules continue to be applied repeatedly to create further generations.

== Origins ==
Conway was interested in a problem presented in the 1940s by renowned mathematician John von Neumann, who tried to find a hypothetical machine that could build copies of itself and succeeded when he found a mathematical model for such a machine with very complicated rules on a rectangular grid. The Game of Life emerged as Conway's successful attempt to simplify von Neumann's ideas.

The game made its first public appearance in the October 1970 issue of ''Scientific American'', in [[Martin Gardner]]'s "Mathematical Games" column, under the title of ''The fantastic combinations of John Conway's new solitaire game "life"''. From a theoretical point of view, it is interesting because it has the power of a [[universal computer|universal Turing machine]]: that is, anything that can be computed algorithmically can be computed within Conway's Game of Life. Gardner wrote:
<blockquote>The game made Conway instantly famous, but it also opened up a whole new field of mathematical research, the field of [[cellular automaton|cellular automata]] ... Because of Life's analogies with the rise, fall and alterations of a society of living organisms, it belongs to a growing class of what are called 'simulation games' (games that resemble real life processes)</blockquote>

Ever since its publication, Conway's Game of Life has attracted much interest because of the surprising ways in which the patterns can evolve. Life is an example of emergence and self-organization. It is interesting for physicists, biologists, economists, mathematicians, philosophers, generative scientists and others to observe the way that complex patterns can emerge from the implementation of very simple rules. The game can also serve as a didactic analogy, used to convey the somewhat counterintuitive notion that "design" and "organization" can spontaneously emerge in the absence of a designer. For example, philosopher and cognitive scientist Daniel C. Dennett has used the analog of Conway's Life "universe" extensively to illustrate the possible evolution of complex philosophical constructs, such as consciousness and free will, from the relatively simple set of deterministic physical laws governing our own universe.<ref>Dennett, D.C. (1991). ''Consciousness Explained''. Boston: Back Bay Books. ISBN 0316180661</ref><ref>Dennett, D.C. (1995). ''Darwin's Dangerous Idea: Evolution and the Meanings of Life''. New York: Simon & Schuster. ISBN 068482471X</ref><ref>Dennett, D.C. (2003). ''Freedom Evolves''. New York: Penguin Books. ISBN 0142003840</ref>

The popularity of Conway's Life was helped by its coming into being just in time for a new generation of inexpensive minicomputers which were being released into the market, meaning that the game could be run for hours on these machines which were otherwise unused at night. In this respect it foreshadowed the later popularity of computer-generated fractals. For many, Life was simply a programming challenge; a fun way to waste CPU cycles. For some, however, Life had more philosophical connotations. It developed a cult following through the 1970s and beyond; current developments have gone so far as to create theoretic emulations of computer systems within the confines of a Life board.

Conway chose his rules carefully, after considerable experimentation, to meet three criteria:
# There should be no initial pattern for which there is a simple proof that the population can grow without limit.
# There should be initial patterns that apparently do grow without limit.
# There should be simple initial patterns that grow and change for a considerable period of time before coming to an end in the following possible ways:
#:* Fading away completely (from overcrowding or from becoming too sparse); or
#:* Settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase in which they repeat an endless cycle of two or more periods.

== Patterns ==
{{main|Pattern}}
Many different types of patterns occur in the Game of Life, including static patterns ("[[still life]]s"), repeating patterns ("[[oscillator]]s" – a superset of still lifes), and patterns that translate themselves across the board ("[[spaceship]]s"). Common examples of these three classes are shown below, with live cells shown in black, and dead cells shown in white.

[[File:Gosperglidergun2.png|thumb|Gosper glider gun]]

Conway originally conjectured that no pattern can grow indefinitely – i.e., that for any initial configuration with a finite number of living cells, the population cannot grow beyond some finite upper limit. In the game's original appearance in "Mathematical Games", Conway offered a $50 prize to the first person who could prove or disprove the conjecture before the end of 1970. One way to disprove it would be to discover patterns that keep adding counters to the field: a "[[gun]]", which would be a configuration that repeatedly shoots out moving objects such as the "glider", or a "[[puffer train]]", which would be a configuration that moves but leaves behind a trail of persistent "smoke".

The prize was won in November of the same year by a team from the Massachusetts Institute of Technology, led by [[Bill Gosper]]; the "[[Gosper glider gun]]" shown to the right produces its first glider on the 15th generation, and another glider every 30th generation from then on. This first glider gun still has a smaller bounding box than any other known gun, and among single-barrelled guns shares the record for lowest population with the [[Simkin glider gun]].

Later discoveries included other guns, puffers, and "[[rake]]s", which move and emit spaceships. Gosper also constructed the first pattern with an asymptotically optimal [[quadratic growth]] rate, called a "[[breeder]]", or "lobster", which worked by leaving behind a trail of guns.

<gallery>
Block.png|[[Block]] (still life)
Blinker.gif|[[Blinker]] ({{period|2}} oscillator)
Glider.gif|[[Glider]] (spaceship)
Pulsar.png|[[Pulsar]] ({{period|3}} oscillator)
</gallery>

== Iteration ==
From a random initial pattern of living cells on the grid, observers will find the population constantly changing as the generations tick by. The patterns that emerge from the simple rules may be considered a form of beauty. Small isolated subpatterns with no initial symmetry tend to become symmetrical. Once this happens the symmetry may increase in richness, but it cannot be lost unless a nearby subpattern comes close enough to disturb it. In a very few cases the society eventually dies out, with all living cells vanishing, though this may not happen for a great many generations. Most initial patterns eventually "burn out", producing either stable figures or patterns that oscillate forever between two or more states (known as [[ash]]); many also produce one or more gliders or spaceships that travel indefinitely away from the initial location.

== Algorithms ==
{{related|Tutorials/Coding Life simulators}}
[[File:Rpentomino.png|right|thumb|R-pentomino]]
The earliest results in the Game of Life were obtained without the use of computers. The simplest still-lives and oscillators were discovered while tracking the fates of various small starting configurations using graph paper, blackboards, physical game boards (such as Go) and the like. During this early research, Conway discovered that the [[R-pentomino]] failed to stabilize in a small number of generations.

These discoveries inspired computer programmers over the world to write programs to track the evolution of Life patterns. Most of the early algorithms were similar. They represented Life patterns as two-dimensional arrays in computer memory. Typically two arrays are used, one to hold the current generation and one in which to calculate its successor. Often 0 and 1 represent dead and live cells, respectively. A double loop considers each element of the current array in turn, counting the live neighbours of each cell to decide whether the corresponding element of the successor array should be 0 or 1. The successor array is displayed. For the next iteration the arrays swap roles so that the successor array in the last iteration becomes the current array in the next iteration.

A variety of minor enhancements to this basic scheme are possible, and there are many ways to save unnecessary computation. A cell that did not change at the last time step, and none of whose neighbours changed, is guaranteed not to change at the current time step as well, so a program that keeps track of which areas are active can save time by not updating the inactive zones.

In principle, the Life field is infinite, but computers have finite memory, and usually array sizes must be declared in advance. This leads to problems when the active area encroaches on the border of the array. Programmers have used several strategies to address these problems. The simplest strategy is simply to assume that every cell outside the array is dead. This is easy to program, but leads to inaccurate results when the active area crosses the boundary. A more sophisticated trick is to consider the left and right edges of the field to be stitched together, and the top and bottom edges also, yielding a toroidal array. The result is that active areas that move across a field edge reappear at the opposite edge. Inaccuracy can still result if the pattern grows too large, but at least there are no pathological edge effects. Techniques of dynamic storage allocation may also be used, creating ever-larger arrays to hold growing patterns.

Alternatively, the programmer may abandon the notion of representing the Life field with a 2-dimensional array, and use a different data structure, like a vector of coordinate pairs representing live cells. This approach allows the pattern to move about the field unhindered, as long as the population does not exceed the size of the live-coordinate array. The drawback is that counting live neighbours becomes a search operation, slowing down simulation speed. With more sophisticated data structures this problem can also be largely solved.

For exploring large patterns at great time depths, sophisticated algorithms like [[Hashlife]] may be useful.

There is also a method for implementation of the Game of Life using arbitrary asynchronous updates but still exacting emulating the behaviour of the synchronous game, also applicable to other cellular automata.<ref>{{Citation|last=Nehaniv|first=Chrystopher L.|year=2002|contribution=Self-Reproduction in Asynchronous Cellular Automata|title=2002 NASA/DoD Conference on Evolvable Hardware (July 15-18, 2002, Alexandria, Virginia, USA)|publisher=IEEE Computer Society Press|pages=201-209}}</ref>

== Variations on Life ==
{{related|Cellular automaton|Life-like cellular automaton|Non-totalistic cellular automaton}}

Since Life's original inception, new rules have been developed based on similar ideas. The standard Game of Life, in which a cell is "born" if it has exactly 3 neighbours, stays alive if it has 2 or 3 living neighbours, and dies otherwise, is symbolised as "B3/S23". The first set of numbers, indicated by "B" for birth, is the list of numbers of neighbours a dead cell can have in order to be born in the next generation. The second set, indicated by "S" for survival, is what is required for a living cell to continue. Hence "B6/S16" means "a cell is born if there are 6 neighbours, and lives on if there are either 1 or 6 neighbours". {{rl|HighLife}} is B36/S23, because having 6 neighbours, in addition to the original game's B3/S23 rule, causes a birth. HighLife is best known for its replicators.

This can be further generalized to [[non-totalistic]] rules, which consider the positions of living cells in a given cell's neighbourhood rather than merely the number of them when determining birth and survival. Some well known non-totalistic variations on Life are {{rl|tlife}} and {{rl|Snowflakes}}, the former itself having many variants of interest. Additional variations on Life exist, although the vast majority of these universes are either too chaotic or desolate to warrant extensive exploration.

Other popular types of cellular automata include [[Generations]] rules such as {{rl|Brian's Brain}} in which cells "age" over time rather than dying immediately, and [[Larger than Life]] rules such as {{rl|Bugs}} which feature larger neighbourhoods to be considered. Some variations modify the geometry of the universe as well as the rule. In the above variations, the world is two-dimensional and laid out in a [[Square tiling|square grid]]. [[Three-dimensional cellular automaton|Three-dimensional]] and [[One-dimensional cellular automaton|one-dimensional]] variations have been developed, as have variations in which [[Hexagonal tiling|the grid is hexagonal]] or [[Triangular tiling|triangular]] instead of square.

Conway's rules may also be generalized so that instead of two states (''live'' and ''dead'') there are three or more. State transitions are then determined either by a weighting system or by a table specifying separate transition rules for each state; for example, [[Mirek's Cellebration]]'s multi-coloured "Rules Table" and "Weighted Life" rule families each include sample rules equivalent to Conway's Life.

Patterns relating to fractals and fractal systems may also be observed in certain Life-like variations. For example, the automaton 12/1 generates four very close approximations to the Sierpiński triangle when applied to a single live cell.

[[Immigration]] is a variation that is the same as the Game of Life, except that there are two ON states (often expressed as two different colours). Whenever a new cell is born, it takes on the ON state that is the majority in the three cells that gave it birth. This feature can be used to examine interactions between [[spaceship]]s and other objects within the game. Another similar variation, called [[QuadLife]], involves four different ON states. When a new cell is born from three different ON neighbours, it takes on the fourth value, and otherwise like Immigration it takes the majority value. Except for the variation among ON cells, both of these variations act identically to Life.

== See also ==
* [[Timeline of Life facts]]

== References ==
<references />

== External links ==
* {{LinkGoLNews|index.php|title=Recent news about Conway's Game of Life|archivedate=20140624090313}}
* [http://cafaq.com/lifefaq/index.php Cellular Automata FAQ – Conway's Game of Life]
* {{LinkLexicon|lex_l.htm#life|name=Life}}
* {{LinkWikipedia|Conway's_Game_of_Life}}
* {{LinkCatagolueRule|b3s23}}
* {{LinkEppsteinRule|b3s23|archivedate=20160309235206}}
* {{LinkMathworld|GameofLife.html|pagename=Game of Life}}

[[Category:Life-like cellular automata]]
[[Category:Cellular automata]]
[[Category:Everything else]]

OCA:DryLife

2022-11-26T20:01:19Z

MEisSCAMMER: grammar

{{Rule
|name = DryLife
|char = Explosive
|b = 37
|s = 23
|ruleinteger = 6280
|reversal = B0123478/S0234678
}}
'''DryLife''' is a [[Life-like cellular automaton]] in which [[cell]]s survive from one generation to the next if they have 2 or 3 [[neighbours]], and are born if they have 3 or 7 neighbours. The rule behaves in an [[explosive]] manner, as small patterns, such as the [[stairstep hexomino]], may exhibit [[chaotic growth]].

==Patterns==

DryLife is so named because the [[standard spaceship]]s from [[Conway's Life|normal life]]; [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]] — also known as "fishes" — do not work, though the [[glider]] does. Some other spaceships, such as the [[x66]], [[weekender]] and [[loafer]], work in this rule. The [[copperhead]] evolves into the closely related c/10 ''goldenhead'', differing from copperhead by two cells in one phase, and it supports the pseudo-tagalong in [[fireship]] as well.

A pair of correctly spaced [[B-heptomino]]es (as in the [[twin bees shuttle]]) evolves into a messy period-160 [[c/2 orthogonal]] [[puffer]].
{{EmbedViewer
|pname = drylife2engine9c28spaceship
|position = right
|viewerconfig = #C [[ ZOOM 16 HEIGHT 350 AUTOSTART GPS 7 TRACKLOOP 28 -9/28 0 ]]
|caption = A 2-engine 9c/28 spaceship found by [[Paul Tooke]] 
|apgcode = xq28_334p03x8e4zy03370czy0oo4j1ox2e4/b37s23
}}
A new speed allowed by DryLife is 9c/28 orthogonal. Technology travelling at this speed relies on the [[R-pentomino]]. Two R-pentominoes constitute a small symmetric 9c/28 orthogonal [[pond]] puffer, or a spaceship. A [[3-glider collision]] that [[synthesis]]es a R-pentomino via beehive works well, so [[gun]]s and [[breeder]]s have been constructed that fire spaceships and [[rake]]s of this speed respectively.

As for oscillators, there is a small period-32 [[reflectorless rotating oscillator]] called {{LinkCatagolue|xp32_1orq4|rule=b37s23|style=raw|patternname=spinner}}, which gives [[banana spark]]s and is therefore capable of reflecting gliders by 90 degrees. [[Jason Summers]] found that a collision between a glider and a half-open [[twirling T-tetsons 2]] produces two 90-degree gliders while sustaining the [[pre-pulsar]] engine, resulting in a period-60 glider gun; a [[blocker]] and a spinner can be added as [[filter]]s for a p480 gun.

{{EmbedViewer
|pname = drylifeflowergarden
|position = right
|caption = The flower garden
}}
The "flower garden", a common [[constellation]] composed of two [[bi-boat]]s and two [[cis-mirrored bun]]s which evolves from some [[honey farm]] [[predecessor]]s like [[bun]], is shown to the right.

== Universality ==
There is a proof sketch of DryLife's universality on ConwayLife.com forums. It is a proof-scheme covering all rules in the [[outer-totalistic]] [[rulespace]] between B3/S23 and B3678/S23678.<ref name="post38167" />

In {{year|2018}}, [[Peter Naszvadi]] constructed an explicit [[Rule 110]] [[unit cell]] in DryLife, proving its [[Turing-complete]]ness.<ref name="post58579" /> The pattern itself is basically a meta-[[polyglot]], covering some related cellular automata in which the pattern only differs in some parts (in this case, the guns).

== References ==
<references>
<ref name="post38167">{{LinkForumThread
|format = ref
|title = Re: List of the Turing-complete totalistic life-like CA
|p = 38167
|author = Peter Naszvadi
|date = December 12, 2016
}}</ref>
<ref name="post58579">{{LinkForumThread
|p = 58579
|format = ref
|title = Re: List of the Turing-complete totalistic life-like CA
|author = Peter Naszvadi
|date = March 29, 2018
}}</ref>
</references>

== External links ==
* {{LinkCatagolueRule|b37s23}}
* {{LinkForumThread|f=11|t=490|title=Puffer with unstable trail (B37/S23)}}
* {{LinkForumThread|f=11|t=2705|title=Taming B37/S23}}
* {{LinkEppsteinRule|b37s23}}

__NOTOC__

[[Category:Life-like cellular automata]]

Still life

2022-11-08T22:00:50Z

MEisSCAMMER: /* Pseudo still lifes */ uncapitalized "four-color theorem"

{{Glossary}}
[[File:Still life classification.png|thumb|right|Classification of still lifes (stable patterns). Click to enlarge.|link=https://conwaylife.com/w/images/7/73/Still_life_classification.png]]
A '''still life'''{{refn|group=notes|Still life derives from paintings not "being alive," thus the plural is still lifes.}} (or '''stable''' pattern) is a [[pattern]] that does not change from one generation to the next, and thus may be thought of as an [[oscillator]] with [[period]] 1. Still lifes are sometimes assumed to be finite and non-empty. The two main subgroups of still lifes are [[#Strict still lifes|strict still lifes]] and [[#Pseudo still lifes|pseudo still lifes]]. In some contexts, the term "still life" may refer to stable objects rather than stable patterns in general, or strict still lifes rather than stable objects in general.

== Strict still lifes ==
A '''strict still life''' is a still life that is either connected (i.e., has only one [[island]]), or is such that removing one or more its islands destroys the stability of the pattern. For example, [[beehive with tail]] is a strict still life because it is connected, and [[mirrored table]] is a strict still life because neither of the [[table]]s are stable by themselves.

<gallery widths="240px" style="text-align:center;">
Image:Beehive.png|[[Beehive]] is a strict still life because it is connected
Image:Beehivewithtail.png|Beehive with tail is a strict still life because it is connected, even though it contains a smaller still life
Image:Mirroredtable.png|Mirrored table is a strict still life because neither [[table]] is stable without the other
</gallery>

== Pseudo still lifes ==
A '''pseudo still life''' consists of two or more [[island]]s which can be partitioned (either individually or as sets) into non-interacting subpatterns which are by themselves each still lifes. Furthermore, there must be at least one dead cell that has more than three alive neighbours in the overall pattern but has less than three alive neighbours in the subpatterns. This final restriction removes patterns such as [[bakery]], [[blockade]] and [[fleet]] from consideration, as the islands are not "almost touching".

Note that a pattern may have multiple disconnected components and still be a strict (as opposed to pseudo) still life if the disconnected components are dependent on each other for stability (for example, [[mirrored table]] above). Some pseudo still lifes have also been found by [[Gabriel Nivasch]] that can be partitioned into a minimum of three and four stable subpatterns, respectively, as in the second and third images below.<ref name="gn_stilllife">{{cite web|url=http://www.gabrielnivasch.org/fun/life/still-lifes |title=Still lifes |author=Nivasch, Gabriel|date=July, 2001|accessdate=March 23, 2016}}</ref> The stable subpatterns themselves may be either strict or pseudo still lifes. It is not possible to construct a pseudo still life that can be partitioned into a minimum of greater than four stable subpatterns because of the four-color theorem.<ref name="gn_stilllife" />

<gallery widths="240px" style="text-align:center;">
Image:Biblock.png|[[Bi-block]] is a pseudo still life because each [[block]] is stable by itself
</gallery>

{|style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
|{{EmbedViewer
|pname = triplepseudostilllife
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = [[triple pseudo still life]]
}}
|{{EmbedViewer
|pname = quadpseudostilllife
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = [[quad pseudo still life]]
}}
|}

It has been shown that it is possible to determine whether a still life pattern is a strict still life or a pseudo still life in polynomial time by searching for cycles in an associated skew-symmetric graph.<ref name="cook">{{cite conference | author = Cook, Matthew | authorlink = Matthew Cook | title = Still life theory | date = 2003 | booktitle = New Constructions in Cellular Automata | publisher = Santa Fe Institute Studies in the Sciences of Complexity, Oxford University Press | pages = 93–118}}</ref><ref>{{cite web|url=http://msri.org/publications/ln/msri/2000/gametheory/cook/1/index.html |title=Still Life |author=Cook, Matthew |publisher=Mathematical Sciences Research Institute}}</ref>

== Constellations ==
A (stable) '''[[constellation]]''' is a still life that is composed of two or more non-interacting objects. This contrasts with pseudo and quasi still lifes, in which the objects in question must interact. Compare for instance the bi-block and blockade:

<gallery widths="240px" style="text-align:center;">
Image:Biblock.png|Bi-block is a pseudo still life because the two [[block]]s interact: the two dead cells between them (highlighted in red) are influenced by both
Image:Blockade.png|Blockade is a constellation because the four blocks do not interact in any way
</gallery>

Certain unstable (e.g. oscillating) patterns are sometimes also referred to as [[constellation]]s. The term "stable constellation" is used to refer specifically to still life constellations.

== Quasi still lifes ==
A stable constellation in which the constituent objects share dead cells, but where all cells that used to remain dead from under-population in the overall pattern still do so in the constituent objects, is called a '''quasi still life'''. In [[Conway's Game of Life|Conway's Life]], this occurs when objects are diagonally adjacent (e.g. two [[block]]s sharing a single diagonal neighbor), or when single protruding cells in two objects such as [[tub]]s share multiple neighbors.

<gallery widths="240px" style="text-align:center;">
Image:Quasistilllife.png|Two [[block]]s sharing a single diagonal neighbor, marked in yellow; this cell is dead from underpopulation and remains so after separation
</gallery>

The term "quasi still life" is due to Mark Niemiec.

== Enumerating still lifes ==
The number of strict and pseudo still lifes that exist for a given number of cells has been enumerated up to 34, and the number of quasi still lifes for a given number of cells up to 22.
* The values in the strict still life table below were originally computed by [[John Conway]] (4-7 cells), [[Robert Wainwright]] (8-10 cells), [[David Buckingham]] (11-13 cells), [[Peter Raynham]] (14 cells), [[Mark Niemiec]] (15-24 cells), [[Simon Ekström]] (25-28 cells),<ref name="post38931" /><ref name="post38965" /><ref name="post39082" /> Simon Ekström and "Apple Bottom" (29-30 cells),<ref name="post39322" /> and [[Nathaniel Johnston]] (31-34 cells).<ref name="post42106" /><ref name="post43762" /><ref name="post74524" /><ref name="post87225" />
* The values in the pseudo still life table were enumerated by Mark Niemiec (1-24 cells), Simon Ekström (25-28 cells),<ref name="post38931" /><ref name="post38965" /><ref name="post39082" /> Simon Ekström and "Apple Bottom" (29-30 cells),<ref name="post39322" /> and Nathaniel Johnston (31-34 cells).<ref name="post42106" /><ref name="post43762" /><ref name="post74524" /><ref name="post87225" />
* The values in the quasi still life table below were originally computed by [[Mark Niemiec]] (8-20 cells) and Simon Ekström (21-22 cells).<ref name="post39372" />

{| class="wikitable" style="text-align:center"
! rowspan="2" | Live cells
! colspan="3" | Strict still lifes
! colspan="3" | Pseudo still lifes
! colspan="3" | Quasi still lifes
|-
! Count ({{OEIS|A019473}})
! Examples
! List
! Count ({{OEIS|A056613}})
! Examples
! List
! Count ({{OEIS|A330283}})
! Examples
! List
|-
|1|| {{A019473|1}} || || || {{A056613|1}} || || || {{A330283|1}} || ||
|-
|2|| {{A019473|2}} || || || {{A056613|2}} || || || {{A330283|2}} || ||
|-
|3|| {{A019473|3}} || || || {{A056613|3}} || || || {{A330283|3}} || ||
|-
|4|| {{A019473|4}} || [[block]], [[tub]] || [[:Category:Strict still lifes with 4 cells|Full list]] || {{A056613|4}} || || || {{A330283|4}} || ||
|-
|5|| {{A019473|5}} || [[boat]] || [[:Category:Strict still lifes with 5 cells|Full list]] || {{A056613|5}} || || || {{A330283|5}} || ||
|-
|6|| {{A019473|6}} || [[beehive]], [[ship]] || [[:Category:Strict still lifes with 6 cells|Full list]] || {{A056613|6}} || || || {{A330283|6}} || ||
|-
|7|| {{A019473|7}} || [[eater 1]], [[loaf]] || [[:Category:Strict still lifes with 7 cells|Full list]] || {{A056613|7}} || || || {{A330283|7}} || ||
|-
|8|| {{A019473|8}} || [[canoe]], [[pond]] || [[:Category:Strict still lifes with 8 cells|Full list]] || {{A056613|8}} || [[bi-block]] || [[Small pseudo still lifes#8 cells|Full list]] || {{A330283|8}} || ||
|-
|9|| {{A019473|9}} || [[hat]], [[integral sign]] || [[:Category:Strict still lifes with 9 cells|Full list]] || {{A056613|9}} || [[block on boat]] || [[Small pseudo still lifes#9 cells|Full list]] || {{A330283|9}} || ||
|-
|10|| {{A019473|10}} || [[boat-tie]], [[loop]] || [[:Category:Strict still lifes with 10 cells|Full list]] || {{A056613|10}} || [[cis-bi-boat]] || [[Small pseudo still lifes#10 cells|Full list]] || {{A330283|10}} || ||
|-
|11|| {{A019473|11}} || [[elevener]] || [[:Category:Strict still lifes with 11 cells|Full list]] || {{A056613|11}} || || || {{A330283|11}} || ||
|-
|12|| {{A019473|12}} || [[honeycomb]], [[mirrored table]] || [[:Category:Strict still lifes with 12 cells|Full list]] || {{A056613|12}} || ''tri-block'' || [[Small pseudo still lifes#Larger examples|Partial list]] || {{A330283|12}} || ||
|-
|13|| {{A019473|13}} || [[sesquihat]] || [[:Category:Strict still lifes with 13 cells|Partial list]] || {{A056613|13}} || || || {{A330283|13}} || ||
|-
|14|| {{A019473|14}} || [[fourteener]], [[paperclip]] || [[:Category:Strict still lifes with 14 cells|Partial list]] || {{A056613|14}} || || || {{A330283|14}} || ||
|-
|15|| {{A019473|15}} || [[moose antlers]] || [[:Category:Strict still lifes with 15 cells|Partial list]] || {{A056613|15}} || || || {{A330283|15}} || ||
|-
|16|| {{A019473|16}} || [[mirrored cap]], [[scorpion]] || [[:Category:Strict still lifes with 16 cells|Partial list]] || {{A056613|16}} || ''pond on pond'' || [[Small pseudo still lifes#Larger examples|Partial list]] || {{A330283|16}} || ||
|-
|17|| {{A019473|17}} || [[twin hat]] || [[:Category:Strict still lifes with 17 cells|Partial list]] || {{A056613|17}} || || || {{A330283|17}} || ||
|-
|18|| {{A019473|18}} || [[dead spark coil]] || [[:Category:Strict still lifes with 18 cells|Partial list]] || {{A056613|18}} || || || {{A330283|18}} || ||
|-
|19|| {{A019473|19}} || [[eater 2]] || [[:Category:Strict still lifes with 19 cells|Partial list]] || {{A056613|19}} || || || {{A330283|19}} || ||
|-
|20|| {{A019473|20}} || [[spiral]] || [[:Category:Strict still lifes with 20 cells|Partial list]] || {{A056613|20}} || || || {{A330283|20}} || ||
|-
|21|| {{A019473|21}} || [[tri-loaf 2]] || [[:Category:Strict still lifes with 21 cells|Partial list]] || {{A056613|21}} || || || {{A330283|21}} || ||
|-
|22|| {{A019473|22}} || [[cis-mirrored worm]] || [[:Category:Strict still lifes with 22 cells|Partial list]] || {{A056613|22}} || || || {{A330283|22}} || ||
|-
|23|| {{A019473|23}} || [[Large natural still lifes|xs23_259e0ehu0ui]] || || {{A056613|23}} || || || {{A330283|23}} || ||
|-
|24|| {{A019473|24}} || [[lake 2]] || [[:Category:Strict still lifes with 24 cells|Partial list]] || {{A056613|24}} || || || {{A330283|24}} || ||
|-
|25|| {{A019473|25}} || [[squid]] || [[:Category:Strict still lifes with 25 cells|Partial list]] || {{A056613|25}} || || || {{A330283|25}} || ||
|-
|26|| {{A019473|26}} || [[Mickey Mouse]] || [[:Category:Strict still lifes with 26 cells|Partial list]] || {{A056613|26}} || || || {{A330283|26}} || ||
|-
|27|| {{A019473|27}} || [[hat siamese vase]] || [[:Category:Strict still lifes with 27 cells|Partial list]] || {{A056613|27}} || || || {{A330283|27}} || ||
|-
|28|| {{A019473|28}} || [[O quad-loaf]] || [[:Category:Strict still lifes with 28 cells|Partial list]] || {{A056613|28}} || || || {{A330283|28}} || ||
|-
|29|| {{A019473|29}} || [[xs29_cc0s2ticz330fgkc]] || [[:Category:Strict still lifes with 29 cells|Partial list]] || {{A056613|29}} || || || {{A330283|29}} || ||
|-
|30|| {{A019473|30}} || [[Clips]] || [[:Category:Strict still lifes with 30 cells|Partial list]] || {{A056613|30}} || || || {{A330283|30}} || ||
|-
|31|| {{A019473|31}} || [[Aries betwixt two blocks]] || [[:Category:Strict still lifes with 31 cells|Partial list]] || {{A056613|31}} || || || {{A330283|31}} || ||
|-
|32|| {{A019473|32}} || [[Inflected 30-great sym]] || [[:Category:Strict still lifes with 32 cells|Partial list]] || {{A056613|32}} || [[triple pseudo still life]] || [[:Category:Pseudo still lifes with 32 cells|Partial list]] || {{A330283|32}} || ||
|-
|33|| {{A019473|33}} || || || {{A056613|33}} || || || {{A330283|33}} || ||
|-
|34|| {{A019473|34}} || [[Cis-mirrored elf-shoe]] || [[:Category:Strict still lifes with 34 cells|Partial list]] || {{A056613|34}} || [[quad pseudo still life]] || [[:Category:Pseudo still lifes with 34 cells|Partial list]] || {{A330283|34}} || ||
|}

As the number of bits increases, these counts increase exponentially; the rate for strict still lifes is about O(2.46n), while for pseudo still lifes it is around O(2.56n), and approximately O(3.04n) for quasi still lifes.

== See also ==
* [[List of common still lifes]]
* [[:Category:Pseudo still lifes|List of pseudo still lifes]]
* [[:Category:Still lifes|List of still lifes]]
* [[:Category:Strict still lifes|List of strict still lifes]]
* [[Object]]

==Notes==
<references group=notes />

== References ==
<references>
<ref name="post38931">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 38931
|author = Simon Ekström
|date = January 2, 2017
}}</ref>
<ref name="post38965">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 38965
|author = Simon Ekström
|date = January 3, 2017
}}</ref>
<ref name="post39082">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 39082
|author = Simon Ekström
|date = January 7, 2017
}}</ref>
<ref name="post39322">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 39322
|author = Simon Ekström
|date = January 14, 2017
}}</ref>
<ref name="post42106">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 42106
|author = Nathaniel Johnston
|date = March 27, 2017
}}</ref>
<ref name="post43762">{{LinkForumThread
|p = 43762
|title = Re: Enumerating Still Lifes (in C)
|author = Nathaniel Johnston
|format = ref
|date = May 25, 2017
}}</ref>
<ref name="post74524">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 74524
|author = Nathaniel Johnston
|date = April 5, 2019
}}</ref>
<ref name="post87225">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 87225
|author = Nathaniel Johnston
|date = January 9, 2020
}}</ref>
<ref name="post39372">{{LinkForumThread
|author = Mark Niemiec
|title = Re: Enumerating Still Lifes (in C)
|format = ref
|p = 39372
|date = January 15, 2017
}}</ref>
</references>

== External links ==
* {{LinkWikipedia|Still_life_(cellular_automaton)}}
* {{LinkLexicon|lex_s.htm#stilllife|name=Still life}}
* {{LinkLexicon|lex_p.htm#pseudostilllife|name=Pseudo still life}}
* {{LinkLexicon|lex_q.htm#quasistilllife|name=Quasi still life}}
* {{LinkNiemiec|objcount.htm|patternname=Life Object Counts}}

Lifeline Volume 11

2022-11-07T22:48:43Z

MEisSCAMMER: /* Page 1 */ I believe we are not supposed to correct spelling while transcribing? Because 'trafic lites' is kinda sad. Anyway, finished transcribing page 1

__NOTOC__{{LifeLine|vol=11|date=September 1973}}

<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 11 SEPTEMBER 1973</pre>

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

====Page 1====
The unique letter published in [[Lifeline Volume 10|LIFELINE Number Ten]] has triggered quite a few similar responses by other readers. In fact so many replies were received that I decided to extend this issue of [[Lifeline|LIFELINE]] to 24 pages to give proper credit. This overwhelming response is especially appreciated since as the masthead indicates, I have just recently moved and now find editorial time even more scarce. Repeating what was said in Number Ten, I certainly welcome any and all letters of this nature no matter how long or short!

As the contents of this issue testify, [[Conway's Game of Life|Life]] continues to yield more new and interesting discoveries.

<pre>
Thompson's piece de resistance
OOO
O OO
O O
O
</pre>

Three years ago, before we even knew about Life, Conway was busy tracking the smaller ominoes and tabulating the outcomes of each. Had he continued his research, he would have made an amazing discovery for one of the nominoes spawns a lightweight spaceship which successfully escapes! This discovery, shown here on the cover page of LIFELINE Number Eleven, was just recently made by Hugh W. Thompson of Lefrak City, New York who has now successfully tracked all th ominoes up to and including the 1285 nonominoes. The final census of Thompson's 'piece de resistance' includes 13 blocks, 1 boat, 1 beehive, 1 ship, 4 blinkers, 2 trafic lites, 3 gliders (NW,SW,SE) and 1 lightweight spaceship (E)! Formed in generation 198, the 'natural light weight' is about 300 cells east of the debris which finally subsides by generation 800.

Now for some interesting and varied replies and articles sent in by the more energetic Lifenthusiasts and Lifanatics:

==Page Scans==
<gallery>
Image:Lifeline_vol_11.png|Page 1
Image:Lifeline_vol_11_p2.jpg|Page 2
Image:Lifeline_vol_11_p3.jpg|Page 3
Image:Lifeline_vol_11_p4.jpg|Page 4
Image:Lifeline_vol_11_p5.jpg|Page 5
Image:Lifeline_vol_11_p6.jpg|Page 6
Image:Lifeline_vol_11_p7.jpg|Page 7
Image:Lifeline_vol_11_p8.jpg|Page 8
Image:Lifeline_vol_11_p9.jpg|Page 9
Image:Lifeline_vol_11_p10.jpg|Page 10
Image:Lifeline_vol_11_p11.jpg|Page 11
Image:Lifeline_vol_11_p12.jpg|Page 12
Image:Lifeline_vol_11_p13.jpg|Page 13
Image:Lifeline_vol_11_p14.jpg|Page 14
Image:Lifeline_vol_11_p15.jpg|Page 15
Image:Lifeline_vol_11_p16.jpg|Page 16
Image:Lifeline_vol_11_p17.jpg|Page 17
Image:Lifeline_vol_11_p18.jpg|Page 18
Image:Lifeline_vol_11_p19.jpg|Page 19
Image:Lifeline_vol_11_p20.jpg|Page 20
Image:Lifeline_vol_11_p21.jpg|Page 21
Image:Lifeline_vol_11_p22.jpg|Page 22
Image:Lifeline_vol_11_p23.jpg|Page 23
Image:Lifeline_vol_11_p24.jpg|Page 24
</gallery>

OCA:HighLife

2022-10-24T21:43:11Z

MEisSCAMMER: /* Spaceships */ I meant to say in the last edit, "it doesn't work in HighLife", but my keyboard is not nice to me

{{Rule
|name = HighLife
|imgname = highlife
|char = Chaotic
|b = 36
|s = 23
|ruleinteger = 6216
|reversal = B0123478/S0134678
|animated = true
}}
'''HighLife''' is a [[cellular automaton#Well-known Life-like cellular automata|Life-like cellular automaton]] in which [[cell]]s survive from one generation to the next if they have 2 or 3 [[neighbours]], and are born if they have 3 or 6 neighbours. It was named by [[John Conway]] and was first considered in 1994 by Nathan Thompson. It is mainly of interest due to a simple [[replicator]] that it allows.

Because its [[rulestring]] is so similar to that of [[Conway's Game of Life]], many simple patterns exhibit the same behavior in both rules; only when patterns get complex do their behavior differ. Nonetheless, it exhibits such rich structure that [[John Conway]] himself stated

<blockquote>''"It seems to me that 'B36/S23' is really the game I should have found, since it's so rich in nice things."''<ref>[http://www.tip.net.au/~dbell/articles/HighLife.zip HighLife - An Interesting Variant of Life] by David Bell (.zip file)</ref></blockquote>

==Notable patterns==
[[File:Highlifefourboats.png|frame|right|The "four boats" constellation.]]
All of the most common [[still life]]s, [[oscillator]]s and [[spaceship]]s from the standard Life rules behave the exact same way under the HighLife rules, including the [[block]], [[beehive]], [[blinker]], [[toad]], [[beacon]], [[glider]], [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]]. On the other hand, even though [[traffic light]]s and [[honey farm]]s themselves behave the same in both rules, they do not occur naturally in HighLife with any sort of regularity due to their common [[predecessor]]s instead evolving differently. The T-tetromino and other common traffic light predecessors instead result in nothing but sparks, and while not all patterns that evolve into a honey farm in ConwayLife evolve the same way in HighLife, some of them (as well as some other patterns, such as a [[hat]]) evolve into a new familiar four that consists of four boats.

Certain patterns act differently from their Life counterparts. For example, the [[dead spark coil]] will act extremely similarly to its living counterpart, with a single cell oscillating on and off inside (a rotor impossible in regular Life). Also, blinkers can be placed against one or two houses and will oscillate normally.

An infinitely-long line will replicate according to [[Rule 54]] due to the presence of B6, which is absent in regular Life which causes such lines to follow [[Rule 22]] instead.

===The replicator===
By far the most notable pattern in HighLife is the simple [[replicator]], shown to the right. It is by far the most well-known replicator in any [[Life-like cellular automaton]]. It repeatedly copies itself along a diagonal line according to [[Rule 90]]. It copies itself the first time after 12 [[generation]]s, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2n copies of the replicator at generation 12(2n - 1) and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a [[speed]] of c/6.

Because of the way the replicator duplicates itself, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. Because the replicator is so small, it often occurs naturally from [[soup]] (the Life equivalent is [[butterfly]]). This contrasts with the standard Game of Life, where all known sawtooths are complex, precisely-engineered patterns.

{| style="margin-left:auto;margin-right:auto;"
|-
|{{EmbedViewer
|pname = replicator
|position = center
|caption = The replicator
}}
|{{EmbedViewer
|pname = replicatorpredecessor
|position = center
|caption = A 6-cell, 3-generation predecessor of the replicator 
}}
|[[Image:replicator_gen12.png|framed|right|The replicator after 12 generations]]
|[[Image:replicator_gen36.png|framed|right|The replicator after another 24 generations]]
|}

A natural [[period]] 96 [[oscillator]] based on the replicator and a pair of [[block]]s functioning as [[eater]]s exists:

{{EmbedViewer
|pname = highlifereplicatorxp96
|position = center
|caption = The period 96 replicator oscillator. 
|apgcode = xp96_33y3gokezyasa62zzytcc/b36s23
}}

===Still lifes===
Because the only difference between the HighLife rules and the standard Life rules is that there is another way for cells to be born (when they have exactly six alive [[Moore neighbourhood|neighbours]]), all [[still life]]s in the HighLife rule are necessarily still lifes under Conway's rules as well. Also, very few small still lifes under the standard Life rules have dead cells with six alive neighbours, so the list of still lifes for the two rules are almost identical for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in HighLife are [[ship]] (with {{slcells|6}} cells) and [[hat]] (with {{slcells|9}} cells). Also, any pattern using a [[bun]] or a [[cap]] as an [[induction coil]] that is a still life under the standard rules is not a still life in HighLife.

<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view a list of still lives in HighLife.
<div class="mw-collapsible-content">

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
! Image
! Links
|-
| ≤3
| 0
|
|
|-
| 4
| 2
| [[Image:highlife4cellstilllifes.png]]
| {{JavaRLE|highlife4cellstilllifes}}
|-
| 5
| 1
| [[Image:highlife5cellstilllifes.png]]
| {{JavaRLE|highlife5cellstilllifes}}
|-
| 6
| 4
| [[Image:highlife6cellstilllifes.png]]
| {{JavaRLE|highlife6cellstilllifes}}
|-
| 7
| 4
| [[Image:highlife7cellstilllifes.png]]
| {{JavaRLE|highlife7cellstilllifes}}
|-
| 8
| 9
| [[Image:highlife8cellstilllifes.png]]
| {{JavaRLE|highlife8cellstilllifes}}
|-
| 9
| 9
| [[Image:highlife9cellstilllifes.png]]
| {{JavaRLE|highlife9cellstilllifes}}
|-
| 10
| 25
| [[Image:highlife10cellstilllifes.png]]
| {{JavaRLE|highlife10cellstilllifes}}
|-
| 11
| 44
| [[Image:highlife11cellstilllifes.png]]
| {{JavaRLE|highlife11cellstilllifes}}
|-
| 12
| 111
| [[Image:highlife12cellstilllifes.png]]
| {{JavaRLE|highlife12cellstilllifes}}
|-
| 13
| 218
| [[Image:highlife13cellstilllifes.png]]
| {{JavaRLE|highlife13cellstilllifes}}
|}
</div>
</div>

===Change in frequency===
{{main|OCA:HighLife/List of common still lifes}}
From the same random starting conditions, HighLife usually settles into fewer objects than in [[Conway's Game of Life|Life]]. This chart shows the change in frequency of common or notable objects in Life and in HighLife. In the chart, objects are ranked by their formation density (the number of objects per cell of empty space) rather than total frequency out of all objects. This is because the frequency of total objects also changes between Life and HighLife.

<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view statistics of object densities.
<div class="mw-collapsible-content">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Object
! Density in HighLife
! Density in Life
! Change in Density
! Notes
|-
| All Objects
| 4.30×10-3
| 6.64×10-3
| -35%
| The overall decrease of objects and increase of sparks causes HighLife to stabilize over twice as fast on average. Many common methuselahs in ConwayLife, such as the [[R-pentomino]], [[block and glider]], and the [[stairstep hexomino]], die without leaving any trace. Also, patterns that make traffic lights in ConwayLife are simply sparks in HighLife; [[block and glider]], the [[two-glider octomino]], and many patterns that converge to the same evolutionary sequence as the [[I-heptomino]] (although not the I-heptomino itself) die this way in HighLife.
|-
| [[Block]]
| 1.83×10-3
| 2.11×10-3
| -13%
| Although the block is less common in HighLife, it is still the most common object.
|-
| [[Beehive]]
| 7.46×10-4
| 1.25×10-3
| -40%
| Beehives are also less common, but more common than the blinker.
|-
| [[Blinker]]
| 6.88×10-4
| 2.15×10-3
| -68%
| Blinkers are much less common, since the [[t-tetromino]] and related patterns evolves in HighLife into a large [[spark]] (see the '''bomber''' below), rather than [[traffic light]].
|-
| [[Loaf]]
| 4.19×10-4
| 3.89×10-4
| +8%
| Loaves are slightly more common in HighLife, but still far behind the beehive.
|-
| [[Boat]]
| 4.14×10-4
| 3.58×10-4
| +16%
| In HighLife, a [[hat]], as well as other predecessors, will evolve into a very common formation of four boats.
|-
| [[Tub]]
| 9.73×10-5
| 8.00×10-5
| +21%
| Tubs experience a 21% increase - the largest of the top ten most common objects.
|-
| [[Pond]]
| 3.49×10-5
| 7.53×10-5
| -54%
| Ponds, which are almost as common as tubs in Life, are almost three times rarer than tubs in HighLife. Life's four-cell [[Pond#prepond|Prepond]] dies out in HighLife.
|-
| [[Aircraft carrier]]
| 1.30×10-5
| 5.00×10-7
| +2516%
| Aircraft carriers are 26 times more common. A common heptaplet [[Image:Pi1.png]] evolves into two aircraft carriers and a blinker (in Life it is a parent of the [[pi heptomino]] sequence).
|-
| [[Elevener]]
| 2.50×10-7
| 4.55×10-9
| +5395%
| Eleveners appear 55 times as often in HighLife, because of a predecessor involving a [[pi-heptomino]] and a [[blinker]].
|-
| [[Ship]]
| 0
| 4.92×10-5
| -100%
| The center cell of a ship has six living neighbors and is born in HighLife. This birth causes it all to die.
|}
</div>
</div>

===Spaceships===
All of the [[standard spaceship]]s from the standard Life rules work in HighLife, but only a few non-standard Life spaceships are known to work in HighLife, notably [[turtle]] and [[crab]]. There are also several known spaceships that are specific to HighLife<ref>{{LinkEppsteinRule|b36s23|rulename=HighLife (B36/S23)|archivedate=20160310000038}}</ref>, the most well-known of which is the bomber.

Currently the speeds known for elementary Life spaceships but not elementary HighLife spaceships are (1,0)c/7, (3,0)c/7, (1,1)c/7 and (2,1)c/6, and speeds known for HighLife and not Life are (1,0)c/8 and (1,0)c/98.



====Elementary====

{| class="wikitable"
|-
! Speed
! Direction
! Smallest known
! Minimum # of [[cell]]s
|-
! [[c/2 orthogonal|c/2]]
| orthogonal
| [[lightweight spaceship]]
| {{cells|9}}
|-
! [[c/3 orthogonal|c/3]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?p=104902#p104902 27P3H1V0]
| {{cells|27}}
|-
! [[c/4 orthogonal|c/4]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?p=104902#p104902 43P4H1V0]
| {{cells|43}}
|-
! [[c/5 orthogonal|c/5]]
| orthogonal
| [http://fano.ics.uci.edu/ca/rules/b36s23/g5.html 52P5H1V0]
| {{cells|52}}
|-
! [[c/6 orthogonal|c/6]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?p=25212#p25212 179P6H1V0]
| {{cells|179}}
|-
! [[c/8 orthogonal|c/8]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&p=59378#p59363 138P8H1V0]
| {{cells|138}}
|-
! c/98
| orthogonal
| [https://catagolue.hatsya.com/object/xq98_mgw4b6z31zsoz6x2d6/b36s23 24P98H1V0]
| {{cells|24}}
|-
! [[2c/5 orthogonal|2c/5]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=25#p59382 106P5H2V0]
| {{cells|106}}
|-
! [[2c/7 orthogonal|2c/7]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&p=64436#p64436 28P7H2V0]
| {{cells|28}}
|-
! colspan="5" |
|-
! [[c/4 diagonal|c/4]]
| diagonal
| [[glider]]
| {{cells|5}}
|-
! [[c/5 diagonal|c/5]]
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&p=59424#p59424 28P5H1V1]
| {{cells|28}}
|-
! [[c/6 diagonal|c/6]]
| diagonal
| [[#Bomber|bomber]]
| {{cells|19}}
|-
|}

==== Engineered ====

{| class="wikitable"
|-
! Speed
! Direction
! Smallest known
! Minimum # of [[cell]]s
|-
! c/9
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=75#p105221 boxship]
| 9334
|-
! [[c/12 diagonal|c/12]]
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=25#p52577 unnamed]
| 760
|-
! c/18
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=25#p53404 unnamed]
| 280
|-
! c/24
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=75#p106192 unnamed]
| 1244
|-
! c/30
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=25#p52577 unnamed]
| 353
|-
! c/32
| diagonal
| [http://pentadecathlon.com/lifeNews/2013/01/new_highlife_velocities.html basilisk]
| 117483
|-
! c/63
| diagonal
| [http://pentadecathlon.com/lifeNews/2013/01/new_highlife_velocities.html basilisk]
| ?
|-
|-
! c/69
| diagonal
| [http://pentadecathlon.com/lifeNews/2013/01/new_highlife_velocities.html basilisk]
| 859 billion
|-
|}

====Bomber====
{{disambiglink|name=bomber|link=Bomber|text=For other uses of the term}}
The '''bomber''' is a replicator-based spaceship that occurs naturally and was discovered by Nathan Thompson. It can be formed by placing a [[blinker]] in the path of the replicator as shown below. The spaceship itself has a [[period]] 48 and travels diagonally at [[speed]] c/6. The blinker reacts with one of the spawned replicators such that it destroys itself and the spawned replicator while leaving another blinker on the other side of the spaceship. It is thus a [[glide symmetric]] spaceship with [[mod]] equal to 24. It is the 3rd most common spaceship in HighLife, being slightly more common than the [[middleweight spaceship]].<ref>{{CiteCatagolue|page=census/b36s23/C1|title=Census|accessdate=July 3, 2019}}</ref>

{| style="margin-left:auto;margin-right:auto;"
|{{EmbedViewer
|pname = bomber
|position = center
|caption = The bomber 
|apgcode = xq48_07z8ca7zy1e531/b36s23
|viewerconfig = #C [[ AUTOSTART GPS 8 TRACKLOOP 48 1/6 1/6 ]]
}}
|{{EmbedViewer
|pname = bomberpredecessor
|position = center
|caption = A 9-cell predecessor of the bomber
}}
|}

==Universality==
There is a proof sketch of this rule's universality as well as an explicit [[Rule 110]] [[unit cell]].<ref name="post62446" /> In the same topic on ConwayLife forums, there is a proof-scheme covering all rules in the [[outer-totalistic]] [[rulespace]] between [[B3/S23]] and B3678/S23678.<ref name="post38167" />

An explicit Rule 110 unit cell construction proves its Turing-completeness;<ref name="post62217" /> the pattern itself is a polyglot working in three other life-like cellular automata rules between B36/S23 and B368/S238; the last rule is also known as [[LowDeath]], in which the native replicator - of which several components of the unit cell based on - has a slightly different evolution sequence.

==See also==
*[[OCA:HighLife/List of common oscillators]]
*[[OCA:HighLife/List of common spaceships]]

==References==
<references>
<ref name="post62446">{{LinkForumThread
|format = ref
|p = 62446
|title = Re: List of the Turing-complete totalistic life-like CA
|author = Peter Naszvadi
|date = August 7, 2018
}}</ref>
<ref name="post38167">{{LinkForumThread
|format = ref
|p = 38167
|title = Re: List of the Turing-complete totalistic life-like CA
|author = Peter Naszvadi
|date = December 12, 2016
}}</ref>
<ref name="post62217">{{LinkForumThread
|format = ref
|p = 62217
|title = Re: List of the Turing-complete totalistic life-like CA
|author = Peter Naszvadi
|date = July 29, 2018
}}</ref>
</references>

== External links ==
* {{LinkWikipedia|Highlife_(cellular_automaton)}}
* {{LinkCatagolueRule|b36s23}}
* {{LinkEppsteinRule|b36s23|archivedate=20150422142748}}
* {{LinkMirek|rullex_life.html#HighLife|title=MCell built-in Life rules: HighLife}}
* {{LinkForumThread|f=11|t=2332|title=HighLife}}
* {{LinkGoLNews|2013/01/new_highlife_velocities.html|title=New HighLife velocities|author=Adam P. Goucher|date=January 19, 2013}}

[[Category:Life-like cellular automata]]

OCA:HighLife

2022-10-24T21:41:03Z

MEisSCAMMER: /* Spaceships */ it doesn

{{Rule
|name = HighLife
|imgname = highlife
|char = Chaotic
|b = 36
|s = 23
|ruleinteger = 6216
|reversal = B0123478/S0134678
|animated = true
}}
'''HighLife''' is a [[cellular automaton#Well-known Life-like cellular automata|Life-like cellular automaton]] in which [[cell]]s survive from one generation to the next if they have 2 or 3 [[neighbours]], and are born if they have 3 or 6 neighbours. It was named by [[John Conway]] and was first considered in 1994 by Nathan Thompson. It is mainly of interest due to a simple [[replicator]] that it allows.

Because its [[rulestring]] is so similar to that of [[Conway's Game of Life]], many simple patterns exhibit the same behavior in both rules; only when patterns get complex do their behavior differ. Nonetheless, it exhibits such rich structure that [[John Conway]] himself stated

<blockquote>''"It seems to me that 'B36/S23' is really the game I should have found, since it's so rich in nice things."''<ref>[http://www.tip.net.au/~dbell/articles/HighLife.zip HighLife - An Interesting Variant of Life] by David Bell (.zip file)</ref></blockquote>

==Notable patterns==
[[File:Highlifefourboats.png|frame|right|The "four boats" constellation.]]
All of the most common [[still life]]s, [[oscillator]]s and [[spaceship]]s from the standard Life rules behave the exact same way under the HighLife rules, including the [[block]], [[beehive]], [[blinker]], [[toad]], [[beacon]], [[glider]], [[lightweight spaceship]], [[middleweight spaceship]], and [[heavyweight spaceship]]. On the other hand, even though [[traffic light]]s and [[honey farm]]s themselves behave the same in both rules, they do not occur naturally in HighLife with any sort of regularity due to their common [[predecessor]]s instead evolving differently. The T-tetromino and other common traffic light predecessors instead result in nothing but sparks, and while not all patterns that evolve into a honey farm in ConwayLife evolve the same way in HighLife, some of them (as well as some other patterns, such as a [[hat]]) evolve into a new familiar four that consists of four boats.

Certain patterns act differently from their Life counterparts. For example, the [[dead spark coil]] will act extremely similarly to its living counterpart, with a single cell oscillating on and off inside (a rotor impossible in regular Life). Also, blinkers can be placed against one or two houses and will oscillate normally.

An infinitely-long line will replicate according to [[Rule 54]] due to the presence of B6, which is absent in regular Life which causes such lines to follow [[Rule 22]] instead.

===The replicator===
By far the most notable pattern in HighLife is the simple [[replicator]], shown to the right. It is by far the most well-known replicator in any [[Life-like cellular automaton]]. It repeatedly copies itself along a diagonal line according to [[Rule 90]]. It copies itself the first time after 12 [[generation]]s, then produces another two copies after another 24 generations, followed by another four copies after another 48 generations, and so on. In general there are 2n copies of the replicator at generation 12(2n - 1) and their centers are evenly spaced 4 cells apart. The two ends of the replicator line expand at a [[speed]] of c/6.

Because of the way the replicator duplicates itself, it can be considered a [[sawtooth]] with expansion factor 2 and a minimum repeating population of 22. Because the replicator is so small, it often occurs naturally from [[soup]] (the Life equivalent is [[butterfly]]). This contrasts with the standard Game of Life, where all known sawtooths are complex, precisely-engineered patterns.

{| style="margin-left:auto;margin-right:auto;"
|-
|{{EmbedViewer
|pname = replicator
|position = center
|caption = The replicator
}}
|{{EmbedViewer
|pname = replicatorpredecessor
|position = center
|caption = A 6-cell, 3-generation predecessor of the replicator 
}}
|[[Image:replicator_gen12.png|framed|right|The replicator after 12 generations]]
|[[Image:replicator_gen36.png|framed|right|The replicator after another 24 generations]]
|}

A natural [[period]] 96 [[oscillator]] based on the replicator and a pair of [[block]]s functioning as [[eater]]s exists:

{{EmbedViewer
|pname = highlifereplicatorxp96
|position = center
|caption = The period 96 replicator oscillator. 
|apgcode = xp96_33y3gokezyasa62zzytcc/b36s23
}}

===Still lifes===
Because the only difference between the HighLife rules and the standard Life rules is that there is another way for cells to be born (when they have exactly six alive [[Moore neighbourhood|neighbours]]), all [[still life]]s in the HighLife rule are necessarily still lifes under Conway's rules as well. Also, very few small still lifes under the standard Life rules have dead cells with six alive neighbours, so the list of still lifes for the two rules are almost identical for small cell counts. The smallest patterns that are still lifes in the standard Life rules but not in HighLife are [[ship]] (with {{slcells|6}} cells) and [[hat]] (with {{slcells|9}} cells). Also, any pattern using a [[bun]] or a [[cap]] as an [[induction coil]] that is a still life under the standard rules is not a still life in HighLife.

<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view a list of still lives in HighLife.
<div class="mw-collapsible-content">

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Size
! Count
! Image
! Links
|-
| ≤3
| 0
|
|
|-
| 4
| 2
| [[Image:highlife4cellstilllifes.png]]
| {{JavaRLE|highlife4cellstilllifes}}
|-
| 5
| 1
| [[Image:highlife5cellstilllifes.png]]
| {{JavaRLE|highlife5cellstilllifes}}
|-
| 6
| 4
| [[Image:highlife6cellstilllifes.png]]
| {{JavaRLE|highlife6cellstilllifes}}
|-
| 7
| 4
| [[Image:highlife7cellstilllifes.png]]
| {{JavaRLE|highlife7cellstilllifes}}
|-
| 8
| 9
| [[Image:highlife8cellstilllifes.png]]
| {{JavaRLE|highlife8cellstilllifes}}
|-
| 9
| 9
| [[Image:highlife9cellstilllifes.png]]
| {{JavaRLE|highlife9cellstilllifes}}
|-
| 10
| 25
| [[Image:highlife10cellstilllifes.png]]
| {{JavaRLE|highlife10cellstilllifes}}
|-
| 11
| 44
| [[Image:highlife11cellstilllifes.png]]
| {{JavaRLE|highlife11cellstilllifes}}
|-
| 12
| 111
| [[Image:highlife12cellstilllifes.png]]
| {{JavaRLE|highlife12cellstilllifes}}
|-
| 13
| 218
| [[Image:highlife13cellstilllifes.png]]
| {{JavaRLE|highlife13cellstilllifes}}
|}
</div>
</div>

===Change in frequency===
{{main|OCA:HighLife/List of common still lifes}}
From the same random starting conditions, HighLife usually settles into fewer objects than in [[Conway's Game of Life|Life]]. This chart shows the change in frequency of common or notable objects in Life and in HighLife. In the chart, objects are ranked by their formation density (the number of objects per cell of empty space) rather than total frequency out of all objects. This is because the frequency of total objects also changes between Life and HighLife.

<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view statistics of object densities.
<div class="mw-collapsible-content">
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! Object
! Density in HighLife
! Density in Life
! Change in Density
! Notes
|-
| All Objects
| 4.30×10-3
| 6.64×10-3
| -35%
| The overall decrease of objects and increase of sparks causes HighLife to stabilize over twice as fast on average. Many common methuselahs in ConwayLife, such as the [[R-pentomino]], [[block and glider]], and the [[stairstep hexomino]], die without leaving any trace. Also, patterns that make traffic lights in ConwayLife are simply sparks in HighLife; [[block and glider]], the [[two-glider octomino]], and many patterns that converge to the same evolutionary sequence as the [[I-heptomino]] (although not the I-heptomino itself) die this way in HighLife.
|-
| [[Block]]
| 1.83×10-3
| 2.11×10-3
| -13%
| Although the block is less common in HighLife, it is still the most common object.
|-
| [[Beehive]]
| 7.46×10-4
| 1.25×10-3
| -40%
| Beehives are also less common, but more common than the blinker.
|-
| [[Blinker]]
| 6.88×10-4
| 2.15×10-3
| -68%
| Blinkers are much less common, since the [[t-tetromino]] and related patterns evolves in HighLife into a large [[spark]] (see the '''bomber''' below), rather than [[traffic light]].
|-
| [[Loaf]]
| 4.19×10-4
| 3.89×10-4
| +8%
| Loaves are slightly more common in HighLife, but still far behind the beehive.
|-
| [[Boat]]
| 4.14×10-4
| 3.58×10-4
| +16%
| In HighLife, a [[hat]], as well as other predecessors, will evolve into a very common formation of four boats.
|-
| [[Tub]]
| 9.73×10-5
| 8.00×10-5
| +21%
| Tubs experience a 21% increase - the largest of the top ten most common objects.
|-
| [[Pond]]
| 3.49×10-5
| 7.53×10-5
| -54%
| Ponds, which are almost as common as tubs in Life, are almost three times rarer than tubs in HighLife. Life's four-cell [[Pond#prepond|Prepond]] dies out in HighLife.
|-
| [[Aircraft carrier]]
| 1.30×10-5
| 5.00×10-7
| +2516%
| Aircraft carriers are 26 times more common. A common heptaplet [[Image:Pi1.png]] evolves into two aircraft carriers and a blinker (in Life it is a parent of the [[pi heptomino]] sequence).
|-
| [[Elevener]]
| 2.50×10-7
| 4.55×10-9
| +5395%
| Eleveners appear 55 times as often in HighLife, because of a predecessor involving a [[pi-heptomino]] and a [[blinker]].
|-
| [[Ship]]
| 0
| 4.92×10-5
| -100%
| The center cell of a ship has six living neighbors and is born in HighLife. This birth causes it all to die.
|}
</div>
</div>

===Spaceships===
All of the [[standard spaceship]]s from the standard Life rules work in HighLife, but only a few non-standard Life spaceships are known to work in HighLife, notably [[turtle]] and [[crab]]. There are also several known spaceships that are specific to HighLife<ref>{{LinkEppsteinRule|b36s23|rulename=HighLife (B36/S23)|archivedate=20160310000038}}</ref>, the most well-known of which is the bomber.

Currently the speeds known for elementary Life spaceships but not elementary HighLife spaceships are (1,0)c/7, (3,0)c/7, (1,1)c/7 and (2,1)c/6, and speeds known for HighLife and not Life are (1,0)c/8 and (1,0)c/98.



====Elementary====

{| class="wikitable"
|-
! Speed
! Direction
! Smallest known
! Minimum # of [[cell]]s
|-
! [[c/2 orthogonal|c/2]]
| orthogonal
| [[lightweight spaceship]]
| {{cells|9}}
|-
! [[c/3 orthogonal|c/3]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?p=104902#p104902 27P3H1V0]
| {{cells|27}}
|-
! [[c/4 orthogonal|c/4]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?p=104902#p104902 43P4H1V0]
| {{cells|43}}
|-
! [[c/5 orthogonal|c/5]]
| orthogonal
| [http://fano.ics.uci.edu/ca/rules/b36s23/g5.html 52P5H1V0]
| {{cells|52}}
|-
! [[c/6 orthogonal|c/6]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?p=25212#p25212 179P6H1V0]
| {{cells|179}}
|-
! [[c/8 orthogonal|c/8]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&p=59378#p59363 138P8H1V0]
| {{cells|138}}
|-
! c/98
| orthogonal
| [https://catagolue.hatsya.com/object/xq98_mgw4b6z31zsoz6x2d6/b36s23 24P98H1V0]
| {{cells|24}}
|-
! [[2c/5 orthogonal|2c/5]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=25#p59382 106P5H2V0]
| {{cells|106}}
|-
! [[2c/7 orthogonal|2c/7]]
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&p=64436#p64436 28P7H2V0]
| {{cells|28}}
|-
! colspan="5" |
|-
! [[c/4 diagonal|c/4]]
| diagonal
| [[glider]]
| {{cells|5}}
|-
! [[c/5 diagonal|c/5]]
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&p=59424#p59424 28P5H1V1]
| {{cells|28}}
|-
! [[c/6 diagonal|c/6]]
| diagonal
| [[#Bomber|bomber]]
| {{cells|19}}
|-
|}

==== Engineered ====

{| class="wikitable"
|-
! Speed
! Direction
! Smallest known
! Minimum # of [[cell]]s
|-
! c/9
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=75#p105221 boxship]
| 9334
|-
! [[c/12 diagonal|c/12]]
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=25#p52577 unnamed]
| 760
|-
! c/18
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=25#p53404 unnamed]
| 280
|-
! c/24
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=75#p106192 unnamed]
| 1244
|-
! c/30
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=2332&start=25#p52577 unnamed]
| 353
|-
! c/32
| diagonal
| [http://pentadecathlon.com/lifeNews/2013/01/new_highlife_velocities.html basilisk]
| 117483
|-
! c/63
| diagonal
| [http://pentadecathlon.com/lifeNews/2013/01/new_highlife_velocities.html basilisk]
| ?
|-
|-
! c/69
| diagonal
| [http://pentadecathlon.com/lifeNews/2013/01/new_highlife_velocities.html basilisk]
| 859 billion
|-
|}

====Bomber====
{{disambiglink|name=bomber|link=Bomber|text=For other uses of the term}}
The '''bomber''' is a replicator-based spaceship that occurs naturally and was discovered by Nathan Thompson. It can be formed by placing a [[blinker]] in the path of the replicator as shown below. The spaceship itself has a [[period]] 48 and travels diagonally at [[speed]] c/6. The blinker reacts with one of the spawned replicators such that it destroys itself and the spawned replicator while leaving another blinker on the other side of the spaceship. It is thus a [[glide symmetric]] spaceship with [[mod]] equal to 24. It is the 3rd most common spaceship in HighLife, being slightly more common than the [[middleweight spaceship]].<ref>{{CiteCatagolue|page=census/b36s23/C1|title=Census|accessdate=July 3, 2019}}</ref>

{| style="margin-left:auto;margin-right:auto;"
|{{EmbedViewer
|pname = bomber
|position = center
|caption = The bomber 
|apgcode = xq48_07z8ca7zy1e531/b36s23
|viewerconfig = #C [[ AUTOSTART GPS 8 TRACKLOOP 48 1/6 1/6 ]]
}}
|{{EmbedViewer
|pname = bomberpredecessor
|position = center
|caption = A 9-cell predecessor of the bomber
}}
|}

==Universality==
There is a proof sketch of this rule's universality as well as an explicit [[Rule 110]] [[unit cell]].<ref name="post62446" /> In the same topic on ConwayLife forums, there is a proof-scheme covering all rules in the [[outer-totalistic]] [[rulespace]] between [[B3/S23]] and B3678/S23678.<ref name="post38167" />

An explicit Rule 110 unit cell construction proves its Turing-completeness;<ref name="post62217" /> the pattern itself is a polyglot working in three other life-like cellular automata rules between B36/S23 and B368/S238; the last rule is also known as [[LowDeath]], in which the native replicator - of which several components of the unit cell based on - has a slightly different evolution sequence.

==See also==
*[[OCA:HighLife/List of common oscillators]]
*[[OCA:HighLife/List of common spaceships]]

==References==
<references>
<ref name="post62446">{{LinkForumThread
|format = ref
|p = 62446
|title = Re: List of the Turing-complete totalistic life-like CA
|author = Peter Naszvadi
|date = August 7, 2018
}}</ref>
<ref name="post38167">{{LinkForumThread
|format = ref
|p = 38167
|title = Re: List of the Turing-complete totalistic life-like CA
|author = Peter Naszvadi
|date = December 12, 2016
}}</ref>
<ref name="post62217">{{LinkForumThread
|format = ref
|p = 62217
|title = Re: List of the Turing-complete totalistic life-like CA
|author = Peter Naszvadi
|date = July 29, 2018
}}</ref>
</references>

== External links ==
* {{LinkWikipedia|Highlife_(cellular_automaton)}}
* {{LinkCatagolueRule|b36s23}}
* {{LinkEppsteinRule|b36s23|archivedate=20150422142748}}
* {{LinkMirek|rullex_life.html#HighLife|title=MCell built-in Life rules: HighLife}}
* {{LinkForumThread|f=11|t=2332|title=HighLife}}
* {{LinkGoLNews|2013/01/new_highlife_velocities.html|title=New HighLife velocities|author=Adam P. Goucher|date=January 19, 2013}}

[[Category:Life-like cellular automata]]

Dead spark coil

2022-10-12T21:47:38Z

MEisSCAMMER: /* In other rules */ removing parenthetical comment; it is probably understood already that HighLife is different than Life

{{Stilllife
|name = Dead spark coil
|pname = deadsparkcoil
|c = 18
|bx = 7
|by = 5
|fc = 16.3
|rulemin = B/S23
|rulemax = B378/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B/S2-cn3n
|isorulemax = B1e2kn34-i5-eq6-i78/S012345678
|synthesis = 4
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs18_rhe0ehr
|niemiecid = 18.287
|pentadecathlonid = 18.636
}}
'''Dead spark coil''' is an {{slcells|18}}-[[cell]] strict [[still life]] consisting of two mutually stabilising [[house]]s. It is one of three ways in which two houses can be arranged to create a still life, and one of the two which have two separate [[island]]s.

Skewing the two constituent houses gives [[rotated house]], whereas connecting them diagonally to stabilise each other gives [[house bridge house]].

One half of the dead spark coils can eat gliders, but both the top and bottom of that side must have a glider to eat, or else the other side of the house will interfere.

== [[List of common still lifes|Commonness]] ==
Dead spark coil is the forty-fifth most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[trans-mirrored bun]] but more common than [[cis-mirrored bookend]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is also the thirty-ninth most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref>

Dead spark coils are typically formed when two pi heptominoes face each other three cells apart. If they are four cells apart, they instead form a live [[spark coil]].

In [[D2 +1]] symmetry, it is the 12th most common still life, being about 100 times more common than in an asymmetric soup, and it is the most common still life that takes advantage of symmetry to be much more common.

== [[Glider synthesis]] ==
{{Small constructible periodic object}}

== In other rules ==
In [[OCA:HighLife|HighLife]], dead spark coil is an oscillator in much the same way as spark coil is, with a single-cell on-off [[rotor]].

== See also ==
* [[Mirrored dock]]
* [[Herschel transmitter]]
* [[House#House-house still lifes|House-house still lifes]]

== References ==
<references />

== External links ==
{{LinkLexicon|filename=lex_d.htm#deadsparkcoil}}
{{LinkCatagolue|xs18_rhe0ehr}}
{{LinkNiemiec|p1-18.htm|patternname=The 19044 eighteen-bit still-lifes}}

{{Symmetry|orthogonal4}}

__NOTOC__

NOT gate

2022-10-08T21:41:42Z

MEisSCAMMER: creating page; redirect to Inverter

#REDIRECT [[Inverter]]