Eppstein's Most Wanted is a list of 22 outer-totalistic rules , created by David Eppstein no later than October 8, 1999 ,[ 1]
Initially, it contained 23 rules, however eight were removed and seven added when the page was reformatted from plaintext into a table.[ 2]
Five of the fifteen rules in both versions, and four of the seven added in the new one, have had spaceships found, all following.
Of the removed rules, all are now known to contain spaceships. Eppstein himself found the first spaceships in five, and the other four had theirs found by Keith Amling in 2002, Josh Ball in 2008 and May13 in 2021. It is unknown whether Eppstein removed the four without spaceships known at the time because he considered them impossible.
Note that per the convention of glider.db at the time, David Eppstein used the term 'glider' to refer to any spaceship, not only the glider . His quotes are preserved as-is.
Rules
“
An interesting mixture of slow chaotic accretion and horizontal and vertical shoots. When a chaotic blob meets a shoot, it can occasionally form a "runner" that grows along the shoot; when the runner catches up to the head of the shoot it starts a new blob of chaos. Very similar to B3/S012345678 "Life without death" which of course has no spaceships.
”
Added later:
“
Also supports a few small oscillators including Life's clock.
”
still unknown
“
A very slowly growing black blob filled with intricate tree-like patterns of white dots. Has small oscillators of periods 3, 5, 6, 8, and 22.
”
Added later:
“
Searched unsuccessfully with gfind to level L128.
”
See its page, the first spaceship was found by Josh Ball in 2013, followed by a reduction by lordlouckster in December 5, 2023.
“
One of the rules studied by Wolfram . An expanding octagonal region filled with stable junk.
”
Has many small p2 and p4 oscillators.
still unknown
“
Extremely slowly growing black diamonds mostly filled with a stable bacterial matrix but with some long-term chaotic fluctuations. One of two narrow connections between the B35xx/S45xx and B34xx/S4xx blocks of rules.
”
still unknown
“
Stable black diamonds filled with white dots.
”
still unknown
“
Complicated long-lived oscillating patterns of alternating rows seem to be trapped inside a bounding diamond. Are they really unable to grow?
”
still unknown
Of the 256 equivalence classes of self-complementary outer-totalistic rules, 47 have spaceships known, 198 have them disproven, and B34567/S0678 is one of the 11 for which they are unknown.
Eppstein's remark that the mazes grow slowly is inaccurate, the only means of infinite growth is through naturally-occurring wickstretchers.
“
Dense expanding chaos. The only B3xx/S014578 rule for which no gliders are known.
”
still unknown
“
Stable filled octagons.
”
still unknown
“
Slowly expanding chaos.
”
A c/7 was found by Matthias Merzenich on July 15, 2020, using qfind ,[ 3] [ 4]
x = 42, y = 69, rule = B345678/S47
6b4o11b7o7b5o$20b2ob3ob2o8bo$3b10o8b2o3b2o5b2ob3ob2o$6bo2bo9b11o4b7o$b4o2b2o2b4o5bobobobobo4bo2b3o2bo$2b2ob6ob2o6bobobobobo5bo2bo2bo$ob2obob2obob2obo3b11o4b3ob3o$b3ob6ob3o5b3obob3o4bobobobobo$ob3obo2bob3obo3bo3b3o3bo5bobobo$b2o3b4o3b2o3bobob5obobo3b3ob3o$2o2b2o4b2o2b2o3bo3b3o3bo$b14o3b3obobobob3o3b2o3b2o$4ob2o2b2ob4o3b2o2bobo2b2o5b2ob2o$2bo3bo2bo3bo4b6ob6o3b2obob2o$2bo2b6o2bo5b11o5bo3bo$3bo2b4o2bo5b3obobobob3o3b2obob2o$6bo2bo9bob2obob2obo5bo3bo$b14o3bobo2b3o2bobo3bobobobo$2bobobo2bobobo4b6ob6o6bo$b2o2bob2obo2b2o5b9o5b3ob3o$3b10o5b6ob6o5b3o$b3o2b4o2b3o5b2ob3ob2o6bobobo$2ob2o6b2ob2o3bobobobobobo5bo3bo$2bo3b4o3bo4b2o3b3o3b2o5b3o$3o2b6o2b3o4bob2ob2obo5b7o$3b3ob2ob3o6b4o3b4o$2o3b2o2b2o3b2o4b3o3b3o$2b5o2b5o5b2ob5ob2o4b7o$obobo6bobobo4b3obob3o7b3o$bo2bo6bo2bo19b2o3b2o$3o10b3o3b2o2bobo2b2o5b5o$bo2bo6bo2bo5b4ob4o7bobo$2o12b2o6bobobo7b3ob3o$2b3o6b3o6b9o$4o8b4o18b7o$19bobo5bobo6bobo$5o6b5o7b3o10bobo$3bobo4bobo6b3o5b3o7bo$2obobo4bobob2o4b3o3b3o$b6o2b6o4bob3ob3obo$o3bo6bo3bo2bo2b2obob2o2bo$obob3o2b3obobo3b2o7b2o$2b2o2bo2bo2b2o4b2o3bobo3b2o$b4o6b4o7b2ob2o$3b2o6b2o7bo2b3o2bo$19bo3bobo3bo$20b3obob3o$19bob3ob3obo$23bobo$19b5ob5o$22b5o$19bo2bo3bo2bo$19bo2b2ob2o2bo$19b2o7b2o$19b3o2bo2b3o$20bo2b3o2bo$20bobobobobo$20b9o$21b7o$20b2o2bo2b2o$20bobobobobo2$19b11o$20b2obobob2o$19bo3b3o3bo$20b2ob3ob2o$20b3obob3o$24bo$22b5o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 4 HEIGHT 910 ZOOM 12 ]]
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“
Slowly expanding chaos.
”
A c/7 was found in the same search as the previous rule.[ 3]
x = 15, y = 46, rule = B345678/S478
7bo2$5b5o$5bo3bo$3b2ob3ob2o$2bob2o3b2obo$b4ob3ob4o$b3ob5ob3o$4obo3bob4o$2b3o5b3o$3b2obobob2o$2b3o2bo2b3o$2bobobobobobo$2bobo5bobo$b3o2b3o2b3o$3b4ob4o$2bob2o3b2obo$2bo3b3o3bo$3b2obobob2o$b3ob5ob3o$2ob2obobob2ob2o$2bobob3obobo$5o5b5o$bo3b5o3bo$ob2o3bo3b2obo$obo2bobobo2bobo$2bobo2bo2bobo$4ob5ob4o$b4o5b4o$bob4ob4obo$3bobo3bobo$3bob5obo$3bobo3bobo$7bo$4b7o$6bobo$4b2o3b2o2$4b3ob3o$3b9o$4b2o3b2o$4b7o$4bobobobo$5bo3bo$4bob3obo$6bobo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 4 HEIGHT 1435 Y 1 ZOOM 28 AUTOSTART GPS 7 TRACK 0 -1/7 ]]
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A c/2 was known to David Eppstein and included in his database.
x = 29, y = 62, rule = B34678/S23578
12bo3bo$11b3ob3o$10b2ob3ob2o$9bo4bo4bo$11bo5bo$8b2ob7ob2o$8b13o$9bob7obo$8b3o3bo3b3o$7b6o3b6o$7b4o7b4o$9b2o7b2o$9bo4bo4bo$6b6ob3ob6o$6b3ob4ob4ob3o$7b3ob3ob3ob3o$5bo2bob2obobob2obo2bo$5b2ob13ob2o$5b2ob3ob2ob2ob3ob2o$3b4ob2o9b2ob4o$3bob2obo11bob2obo$5bobo2bo7bo2bobo$3bo2b5o7b5o2bo$8b3o7b3o$7bob4o3b4obo$9b3o5b3o$9bob2o3b2obo$7b3o9b3o$5bobobo9bobobo$4b6obob3obob6o$4b2o3bo2bobobo2bo3b2o$5b2obobob5obobob2o$4b2ob3obo5bob3ob2o$7b3o3bobo3b3o$5bobobobob3obobobobo$4bobobo11bobobo$5b2o2bob7obo2b2o$6b2ob3o5b3ob2o$5bo2b3ob5ob3o2bo$4bo3b13o3bo$6b17o$3b3ob15ob3o$5bob15obo$3bob3ob11ob3obo$4bob17obo$4bob17obo$2b2obob15obob2o$2b2o2b17o2b2o$b4ob17ob4o$2b25o$b2ob21ob2o$4b2ob6obob6ob2o$4b2ob2obobobobobob2ob2o$2bo2b3o2bobobobobo2b3o2bo$2b2obobo2b2obobob2o2bobob2o$2b2o4b5obob5o4b2o$6ob2ob3obob3ob2ob6o$b3ob2ob3o3bo3b3ob2ob3o$2obo3bobob7obobo3bob2o$b9obo5bob9o$3ob3ob2o3bobo3b2ob3ob3o$10bo7bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 4 HEIGHT 1190 Y 1/2 ZOOM 18 AUTOSTART GPS 2 TRACK 0 -1/2 ]]
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“
Has p2 and p4 oscillators, but most patterns quickly decay to nothing. One of two narrow connections between the B35xx/S45xx and B34xx/S4xx blocks of rules.
”
In 2024, May13 found a large c/3o using a combination of LLSSS and JLS[ 5]
x = 110, y = 98, rule = B35/S46
53b4o$54b2o$50b3ob2ob3o$52bo4bo$36bo10b3o10b3o10bo$36bo6b3o5b2o4b2o5b
3o6bo$33b7o4b6o10b6o4b7o$35bo3b4ob3o16b3ob4o3bo$30b3o3bo2b3obobo4bo8bo
4bobob3o2bo3b3o$25b2o6b2obo3b2obob2o6b4o6b2obob2o3bob2o6b2o$19b3o4b4o
2bo2bo4bobo7b2o6b2o7bobo4bo2bo2b4o4b3o$14bo6b4obo5b2o2bob3obo2b3o5bo2b
o5b3o2bob3obo2b2o5bob4o6bo$13bo2b3o3bo5b2ob2o2b3o3bobob4o2bo6bo2b4obob
o3b3o2b2ob2o5bo3b3o2bo$12b6obob5o6b3ob3ob4o2bobo12bobo2b4ob3ob3o6b5obo
b6o$10bob3o3b4o19bo4bo3b3o4b3o3bo4bo19b4o3b3obo$11b3ob4o3bo2bo3bob3o3b
o3bobo3bo2bo8bo2bo3bobo3bo3b3obo3bo2bo3b4ob3o$9b5o5b2o2bo7bo2bo7b3o3b
4o6b4o3b3o7bo2bo7bo2b2o5b5o$12bo2bobob2o4b5ob2o4b2o2bobob2o2bo10bo2b2o
bobo2b2o4b2ob5o4b2obobo2bo$12b2o6bob2o6bob3o6b2obo4bo10bo4bob2o6b3obo
6b2obo6b2o$8b2o2bo3b2o3b3obo2b4obob3o5b3o7b4o7b3o5b3obob4o2bob3o3b2o3b
o2b2o$7b3obo3b2obobo2bo5bob2o8bobo3bo6b2o6bo3bobo8b2obo5bo2bobob2o3bob
3o$7b2o3bo8b3o3b2o4bo2bo3b4o2b3ob3ob2ob3ob3o2b4o3bo2bo4b2o3b3o8bo3b2o$
7bobobobob4o2b5o5bo3bo3b2o2bobobo4bo4bo4bobobo2b2o3bo3bo5b5o2b4obobobo
bo$5b2o4bo6bo3b2o8b2o3bo4bo3bo2bo10bo2bo3bo4bo3b2o8b2o3bo6bo4b2o$8bob
3o3bob2obo4bo3b2o2bo5b2o9b2o4b2o9b2o5bo2b2o3bo4bob2obo3b3obo$4b4o2b3o
2bob2obo3bo7bo3b2o3b2o4bob2o8b2obo4b2o3b2o3bo7bo3bob2obo2b3o2b4o$8bobo
3b4obobo3bob3o4b3o11bob2o2b2o2b2obo11b3o4b3obo3bobob4o3bobo$4bo3bobo2b
2o3bob4o3bo14bo4bo2b2o6b2o2bo4bo14bo3b4obo3b2o2bobo3bo$8b5obo2bo2b2o2b
obo2bo6bo6b3o2bob2ob4ob2obo2b3o6bo6bo2bobo2b2o2bo2bob5o$4b2obo3b3o2bob
o2b3o4b2o5bobo9bo2bo8bo2bo9bobo5b2o4b3o2bobo2b3o3bob2o$10bo2bob3ob2obo
2bo3b3o2b3o8bob3o10b3obo8b3o2b3o3bo2bob2ob3obo2bo$4bob2o4bobo2b4o3bob
2obo4bo2bo8bo3b2o6b2o3bo8bo2bo4bob2obo3b4o2bobo4b2obo$5bob3o5b2o4b2o2b
obo2b5obo36bob5o2bobo2b2o4b2o5b3obo$4bo8bo2b2o3b2o2b4o2b2ob2obobo4b3o
4bo6bo4b3o4bobob2ob2o2b4o2b2o3b2o2bo8bo$4b2o2bo5bo5b2o2b2obobo2bo2b2o
8b3o14b3o8b2o2bo2bobob2o2b2o5bo5bo2b2o$2b3obo6bo5b2obo5bobob3ob4o4b2o
3b2o8b2o3b2o4b4ob3obobo5bob2o5bo6bob3o$4bo2b2o4b3o3b4o2bobobo3bo42bo3b
obobo2b4o3b3o4b2o2bo$b2ob2ob3o3b3obo3b2obobo4b4obo2bo5bobob3o6b3obobo
5bo2bob4o4bobob2o3bob3o3b3ob2ob2o$b2ob2o2bo4bo2b3ob7o2bobo2bo18b4o18bo
2bobo2b7ob3o2bo4bo2b2ob2o$3b2obobo5bob3obo6bo2b2ob2o3b2o6b5o8b5o6b2o3b
2ob2o2bo6bob3obo5bobob2o$6o9bo4b3ob2o4bobo3bo15b6o15bo3bobo4b2ob3o4bo
9b6o$bobob3o6b2o2b2ob3o2b2ob2o2bo3bobo10bo8bo10bobo3bo2b2ob2o2b3ob2o2b
2o6b3obobo$3bobobo11bo2b3o10bo2bo32bo2bo10b3o2bo11bobobo$2b4o8bo3b2o2b
5obobo8bo30bo8bobob5o2b2o3bo8b4o$4b2ob2o6bo2bo3bob5o5b2o38b2o5b5obo3bo
2bo6b2ob2o$5b2o7bob3o2bo3bo2b3o7b2o30b2o7b3o2bo3bo2b3obo7b2o$2b2o4bo7b
3o3b3o3bo4bobo38bobo4bo3b3o3b3o7bo4b2o$4bobo10b5obobo3bob2o4b2o32b2o4b
2obo3bobob5o10bobo$b2obo2b3o5bo3b2o6b3o3bo42bo3b3o6b2o3bo5b3o2bob2o$4b
2obo8bo2b2o8b2obo3b3o32b3o3bob2o8b2o2bo8bob2o$bo6bo5b3ob4o5b4o4bo38bo
4b4o5b4ob3o5bo6bo$4bob3o9bob2o7b2ob2ob3o34b3ob2ob2o7b2obo9b3obo$b2o2bo
2bo4b3ob4o7b3obob5o32b5obob3o7b4ob3o4bo2bo2b2o$8b2o4b4ob4ob2o3bo5bo38b
o5bo3b2ob4ob4o4b2o$bobo4b2o4bo2b4o5b2o2b3o3b2o34b2o3b3o2b2o5b4o2bo4b2o
4bobo$4b5o8bo2bob4o3bo2b2o2bo36bo2b2o2bo3b4obo2bo8b5o$3bo2b2ob2o7bo2b
2obo5bo2b2o2bobo30bobo2b2o2bo5bob2o2bo7b2ob2o2bo$4bob2obo4b3ob3o2bo11b
4o32b4o11bo2b3ob3o4bob2obo$7b2ob2o9bobo14bo32bo14bobo9b2ob2o$4b2obobo
3b4o2b3o2bo10bo2bo32bo2bo10bo2b3o2b4o3bobob2o$8bo11bo3b2obo7b2o36b2o7b
ob2o3bo11bo$6bobo7bobo2bo3b3o7b3o34b3o7b3o3bo2bobo7bobo$14b2o2b2o3b3ob
2o5bo2b2o32b2o2bo5b2ob3o3b2o2b2o$8b2o7b2obo3bo3bo6b2o36b2o6bo3bo3bob2o
7b2o$14bo2bo8bo5bobobobo32bobobobo5bo8bo2bo$14bobobo5b2o3b3o46b3o3b2o
5bobobo$11bobobo6bob2o5b2ob3o36b3ob2o5b2obo6bobobo$10b5obo6b4o2bob3o2b
2o34b2o2b3obo2b4o6bob5o$10b3obobo5b3o4b2ob7o32b7ob2o4b3o5bobob3o$11b2o
8b3o2bo5b2o2b2o34b2o2b2o5bo2b3o8b2o$14bob2o7bo3bo3bobo38bobo3bo3bo7b2o
bo$15bobo3bo12bobob3o28b3obobo12bo3bobo$14bob2o6b3o5bob2o2bo32bo2b2obo
5b3o6b2obo$13b3o17b2o4b3o26b3o4b2o17b3o$12b6o6bobo4b2o2bo2bo32bo2bo2b
2o4bobo6b6o$10bob3o16bo8b2o26b2o8bo16b3obo$30bob3o4bo30bo4b3obo$9b2o
20bob2o6bo26bo6b2obo20b2o$31bob2o5bo28bo5b2obo$10b2o18bo3bob2o3bo26bo
3b2obo3bo18b2o$32b2obo3b2o28b2o3bob2o$31bo3b2o2bobo26bobo2b2o3bo$30b2o
bo3b3o30b3o3bob2o$31b2o3b3ob3o24b3ob3o3b2o$31bo4bo2bob2o24b2obo2bo4bo$
38b2o3bo22bo3b2o$30b2o4b3obo28bob3o4b2o$36b2o2bob2o22b2obo2b2o$31b2ob
5o3bo24bo3b5ob2o$35bob6o24b6obo$31b8o32b8o$34bo2bo34bo2bo$31bo5b2o32b
2o5bo$34b4o34b4o$31b2o4bo34bo4b2o$32b4obo34bob4o2$33bo3b2o32b2o3bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
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“
Chaotic growth evolves into stable patchwork of horizontally and vertically plowed regions. Ok, maybe there's no reason for it to have gliders but it's one of the more interesting rules I've seen. The stable regions can have small oscillators in them, maybe there are gliders and more complicated patterns if we're given an initial background of farmland rather than blank space.
”
Added later:
“
Has various small oscillators including Life's clock, and arbitrarily high period oscillators via a simulation of the one-dimensional B01/S02 automaton (e.g. between two out-of-phase rows of farmland).
”
still unknown
“
Quickly stabilizes to isolated domino still lifes and low-period oscillators. Has arbitrarily high-period oscillators formed out of 2x2 blocks of cells.
”
On August 8, 2015, Josh Ball found a c/3 spaceship.[ 6]
x = 44, y = 65, rule = B36/S1567
11b3obob3ob2ob3obob3o$9b2o5bo10bo5b2o$12bo4b2o6b2o4bo$7b2o5bo14bo5b2o$6b3o2b2o3bo10bo3b2o2b3o$8bo26bo$7b2o2bo3bob2o6b2obo3bo2b2o$7bob2o5bob2o4b2obo5b2obo$7b5o4bo2b2o2b2o2bo4b5o$6bo2b4o4b3ob2ob3o4b4o2bo$5bo3bo2bo7b4o7bo2bo3bo$12bo2b3o2b4o2b3o2bo$4bobo5b2o5bo4bo5b2o5bobo$5b2o8b2o3bo2bo3b2o8b2o$5b2o5bobo6b2o6bobo5b2o$4b2o6bo8b2o8bo6b2o$13b2o6b2o6b2o$6bo4bo2b2o12b2o2bo4bo$7bo3bo8bo2bo8bo3bo$9b2obo7bo2bo7bob2o$5bobo6b2ob3ob2ob3ob2o6bobo$19bo4bo$6bobo9bo6bo9bobo$6bo9bo10bo9bo$4bo4bo7bo8bo7bo4bo$2bo4bo2bo22bo2bo4bo$3bobo32bobo$2o3bob2o26b2obo3b2o$7bobo24bobo$4bo34bo$3b2o4bo24bo4b2o$4b3o30b3o$2b3o4b2o22b2o4b3o$o3b3ob2o24b2ob3o3bo$b2obo3bobobo2bo3bo4bo3bo2bobobo3bob2o$bo7b2o3bobobo2b2o2bobobo3b2o7bo$12bo5bo6bo5bo$13bob4o2b2o2b4obo$14bo6b2o6bo$15b4o2b2o2b4o$17b2o2b2o2b2o$15bo2bo6bo2bo$14bo4b2o2b2o4bo$13bo3b2o6b2o3bo$15bo2b2ob2ob2o2bo$18b2o4b2o2$16bobo6bobo$18bo6bo$15bo12bo$16bo10bo$14b2o12b2o2$15bobo8bobo2$15bob2o6b2obo$20bo2bo$14b2o2b2o4b2o2b2o$15bob3o4b3obo$15bobo8bobo$17bo8bo2$17b2o6b2o$20b4o$20bo2bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 HEIGHT 840 ZOOM 12 AUTOSTART GPS 3 TRACK 0 -1/3 ]]
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In spite of looking as though it was constructed manually or by a novel search program, the majority of this spaceship is found as the frontend of an ikpx2 search at the appropriate width.
Added
“
Most random initial configurations quickly decay into small oscillating blobs, mostly with period two. If the initial density is around 59%, the phase ambiguity leads to much larger intertwined black and white blobs with stable boundaries edged by higher period oscillators.
”
still unknown
“
Random fields at 50% turn into grids of 4c/8 and 7c/14 replicators blocked between small black blobs. Random fields at 25% turn into blobby unmoving mixtures of black and white areas. Very sparse random fields form grids of replicators again, gradually accumulating blobs where the replicators interact until all replicators are blocked between pairs of blobs. Except for the replicators, random patterns become static very quickly.
”
On February 5, 2010, Matthias Merzenich corderised the 4c/8 replicator into two 8c/16 spaceships, and demonstrated a small puffer and dirty breeder.[ 7]
x = 41, y = 16, rule = B017/S1
2o12b2o4b2o16b2o2$2o3b2o2b2o3b2o9b2o2b2o2b2o2$5b2o2b2o$26bo6bo2$26bo6bo$20b2o15bo2bo$2bo10bo$25b2o2b2obo2bo$4bo6bo$22bo9bo$33bo5bo$24bo7bo$33bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 ZOOM 12 Y 1 AUTOSTART GPS 8 TRACK 0 -4/8 ]]
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“
Random fields at 25% turn into long-lasting blobs which decay into small low-period oscillators. Higher density random fields form a single large blob.
”
still unknown
“
The only B3xx/S348 rule without known spaceships. Slightly rounded diamond-shaped growing chaos.
”
still unknown
“
Dense chaos fills an expanding diamond-shaped region.
”
On June 21, 2021, iNoMed found the first c/7 diagonal spaceship, at 1237 cells, followed by a 430-cell c/9 diagonal.[ 8] Layz Boi , apparently unaware of the rule's status in Eppstein's list or iNoMed's discovery, found a 609-cell stabilisation of the c/7d's frontend with the same lateral width.[ 9] [ 10]
x = 181, y = 150, rule = B345678/S458
143b2o$141b6o$141b3ob2o$139b10o$139b4o2b4o$137b2ob4o2bob2o$137bo3bob2ob4o$135bobo2bo3b5o$135b3ob3ob6o$133b2obo2b4ob3o$133b9o3b2o$131b4o2bobo4bo$132bo2b5ob4o10b2o$129b4o2bobob3o11b6o$129b4o3b2obob2o10b3ob2o$127bobobo6b3o10b10o$127b3o2b2o4b3o10b4o2b4o$125b2ob2o2b2ob4o10b2ob4o2bob2o$125bobo3bo2b3obo10bo3bob2ob4o$124b5o6b2o10bobo2bo3b5o$125b5o2b5o10b3ob3ob6o$123b2ob2ob2ob2o11b2obo2b4ob3o$119b2obo4b5ob2o10b9o3b2o$119b5obo2b3obo10b4o2bobo4bo8bobo$117b2ob5obo2b4o11bo2b5ob4o8b5o$117b2o2b5o2bobo10b4o2bobob3o9b8o$115b2o4b2ob3obo12b4o3b2obob2o8b2ob5o$115b13o11bobobo6b3o8bobobob5o$113bobob10o12b3o2b2o4b3o8b4o3b3o$113b4o2b4o2b3o9b2ob2o2b2ob4o8b2ob3o2bob3o$111bobo2bobob3o3b2o9bobo3bo2b3obo9b2o2b3ob2o$111b6ob2ob2ob2o10b5o6b2o8b2o2bobob5o$109b3obob2o4b2ob2o11b5o2b5o8b3o5b2o7bobo$109b2ob9ob2o11b2ob2ob2ob2o9b2o6b2ob2o6b5o$107bo5bob4ob4o6b2o2bo4b5ob2o8b2ob3o3b2o6b8o$107bo8bobobo11b4obo2b3obo8b6obobo2bo6b2ob5o$105b5obobob7o6b9obo2b4o8b3ob4ob2o6bobobob5o$106bob3obo3bobo9b2o3b5o2bobo8b2o2bo2b2o2b2o6b4o3b3o$103b7o3bo3b3o6b2o4b3ob3obo11bob2o3b3o6b2ob3o2bob3o$103b2o4bo2bo3b2o8b2o2bob2ob5o9b2ob2ob7o7b2o2b3ob2o$101b2o2b3o2b4o2b2o6b3o4b8o11bobo3bob2o6b2o2bobob5o$101bob6o2b3o13b3obob3ob2o8b2o2bo3bo2b2o4bob3o5b2o$101b2o5b2obob3o6b4ob7o3bobo7b2o5b4o6b2o6b2ob2o$99b3ob4ob2ob3o8b4obo2b2o2bo2bobo5b2o2bo3bo3bo4b8o3b2o$99b6obob2obobo6b4o3b3ob2o3b2o8bo2b2o3b2o6bo2b3obobo2bo$98bob2o3b2obob2o8bo3bob4ob2o3b2o5bob2o2b3o3bo4b4ob2ob2ob2o$96b2o4b2ob2obob2o6b3o6b6ob2o7b2ob2o4b2o6b2o2b2ob3ob2o$96bo5b2obobobo10b2ob3o2bo4b3o5b8o3b2o4bo2b4ob5o$94bobo2bobo2b6o8bob3o3bo3b2obo9b9o6bo3b5o2b3o$94b5obo3b3o11bob5obobob2obo5b6ob2obobo5b2o5b2obobo$92bobo4bobo3b2o9bob2o2b3obo2b3o7b3ob6o10b4ob2ob3o$92b3o3bobo3bo11bobobob4o3b3o5b2o2b9o12bo2b3o$90b7o3bo2bo9b5o2bo3b3o2bo8b4obobobo14bo3b2o$88b6ob3o2b4o9b3o4b3ob6o10b6obo14bo$88b2obo4b2o2bo10bobobo2bo4bo3bo6b3o4b2ob2o17b3o$86b2ob4obo2b5o9b3ob5o2b4obo14bob2o17bo$86b2ob5o2b3o10bo2bo3b3o2bo10b7o3b2o$84bobo2b2ob3ob4o9bo3bo3b2o2b3o8b4ob2o4bo$84b2o3b2o2b5o9b4o2b2o3b4o8b5o3bobo$83bo2bo2b6ob2o9bob3o2b2o4b2o9b5ob2obo$81b2ob2ob10o8bobob3obob2ob4o6b4ob6obo$81bo2b6o5b2o7bob3ob3o4b2o10b3o2b5o$80bo3b6o3b2o9b4ob6o3b2o6b3o2bo3b4o$78b2o3b6obob3o7b3ob10o12bo2b6o$78bo4b7obo14b6ob5o6b4o2bo2b2obo$76bo2bo2bob6ob2o7b2o4b5obo2bo8b3o2bo3b2o$80b4ob2o3bo9b3o2bo2b8o7b2o3bo2b2obo$74b2obobob4o4bo8b2ob2o5b5o12b3o2bobo$74b3ob2ob3o4b2o8b2o4b2obo3bobo6bobo4bob2obo$72bo2b5o3bo3bo8bo3bo2b3o4b3o7b2obo3bob2o$73b2o2bob4obobo10bob3ob2o5bo7bo2b3o4b3o$75b4ob2o3b2o7b2obobo2bo3b2o2bo7b5ob2o2bo$70bo2b2ob5obo11b8obo2b3o8b2ob5obo$68b2ob3obob2ob2o2bo8bo2b3ob2ob2o2b2o6bobob2ob4o$69bo4b3obob3o10bobo2bo2b3ob2o8bobo2b4ob2o$66b4obo3bobobob2o12b7o3b2o6b5o3bobo$66b2ob2o2bo2b2obo18bob4o12bobo3b3o$64b2o2b3o5bo3bo17bob2o2bo6b7ob4o$65bo3b3o2bobo21b2ob2o11b2ob3o$62b12o3bo23b2o6b4o2b3ob3o$62b2ob3ob8o22b2o8bo4bob2obo$62bo2bo4bobobobo32bo2b2o3bobo$61b2o3b2ob2o2b2o33b2o3bobobo$64bo2bob2o2b2o34b2o4bobo$60bo7b5o35b2obo3bo$60b3obobo3bobo37b6o$58b6o5b2o39bobo$58bo3b3o2b4o$56b3o2bob2o2bo$56bob2o3b3o$54bobobobo2bo$54bobob6o$52bo2b2o4bo$53b9o$50bobob4o$50bobo2b2ob2o$47b4ob2o2bo$47b5ob3obo$45bob6o$45b11o$43b4ob6o$43b5ob5o$41b2o2b2obob4o$41bobob6o$39b2o2bob7o$40bo7b2o$37b3obobob2ob2o$37b2o3bo4bo$35b2o6bo2b2o$35b6o3b2o$33b2ob5o2bobo$34bo2b4ob2o$30bobob3ob3ob2o$30b2ob5ob3o$28b3o2b2ob2o2b2o$28bo2b3ob5o$26b11o2bo$26b9o2bo$24bob2obo2b3obo$26b2ob2ob2ob3o$22b2o2b2ob5obo$22b3o2b2o3b4o$20bo2b2o2b7o$22bo6b5o$18b2ob3obo$19bob3o3b2o2bo$16b5o3b2ob3o$17b6ob3ob2o$16b3o2b2ob2o$17b3o2b2o3bo$16bob3ob4o$14b2ob7obo$14b2o2bob4o$12b2o2bo2bobobo$13b3ob2o$10b6ob2o$11b6o$8b7obo$9bo2b3o$7bo2bobobo$5b3o3b2o$3b6o3bo$3b8o$bob7o$2bobob4o$obo2b4o$6b3o$4b2o$6bo$4bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 WIDTH 945 HEIGHT 770 ZOOM 5 ]]
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iNoMed's and Layz Boi's c/7ds, and iNoMed's c/9d(click above to open LifeViewer )
A c/2 was known to David Eppstein, and a c/3 was found by LaundryPizza03 on April 21, 2020.[ 11]
x = 57, y = 64, rule = B3478/S24568
2b4o22b4o12b3o$3b5o5bo6bo5b5o10b4ob4o$2b2ob5ob3ob4ob3ob5ob2o7bob2ob3ob2obo$5b4ob4obo2bob4ob4o11bob2obob2obo$2bo2bobo2b4ob4ob4o2bobo2bo7b4ob3ob4o$bo4b4obobob4obobob4o4bo6bob2ob3ob2obo$2bobobo3bobo2b4o2bobo3bobobo5b3ob2ob3ob2ob3o$2bo4bob3o2b2o2b2o2b3obo4bo5b6ob3ob6o$3obo4bo14bo4bob3o3bob4ob3ob4obo$obobo4bo6b2o6bo4bobobo4b5ob3ob5o$2b3o11b2o11b3o8bobob3obobo$3bo26bo9bo2b5o2bo$3bo26bo8b4o2bo2b4o$5bo22bo10b2o4bo4b2o$3bo26bo10bob5obo$3bob2o20b2obo9bo2b5o2bo$2b3obo20bob3o7bobo3bo3bobo$5bo22bo11b2ob5ob2o$4bo24bo12bob3obo$37bobobobobobobobobo$36b2obobobobobobobob2o$36b2o3bobobobobo3b2o$40b11o$37b17o$34b4ob2obo2bo2bob2ob4o$34b2ob2ob2ob5ob2ob2ob2o$36b3ob4obob4ob3o$38b2o2b7o2b2o$37b2obobo2bo2bobob2o$40bob7obo$39b2ob7ob2o$39bobobo3bobobo$40b2o3bo3b2o$38b2o2bo5bo2b2o$40b11o$37bobo3b5o3bobo$40b11o$42bob3obo$41b4ob4o$42b7o$39bob2obobob2obo$40b2o2b3o2b2o$39b3obobobob3o$39b3obobobob3o$41b2o5b2o$40bo9bo$37b4o9b4o$37b3o11b3o$34bo2b4o9b4o2bo$34b4obo11bob4o$34b3obo13bob3o$39bo11bo$38bobo9bobo$36bo2b2o9b2o2bo$40bo9bo$38b3o9b3o$41bo7bo$37b3o11b3o$37bo15bo$36bo2bo11bo2bo2$37b2obo9bob2o$35bobob2o9b2obobo$35b2ob2o11b2ob2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 WIDTH 770 HEIGHT 875 ZOOM 12 ]]
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(click above to open LifeViewer )
“
Quickly decays to isolated 4-cell p2 oscillators.
”
At some time before making the thread about the page in 2015, Josh Ball found a c/5.[ 12]
x = 23, y = 174, rule = B348/S4
10b3o2$7b4ob4o2$5bo2bo5bo2bo$6b3o5b3o$3b2o3bo5bo3b2o$5b2ob2o3b2ob2o$3bobobo7bobobo$3bob2ob3ob3ob2obo$b2o4b2o5b2o4b2o$8bob3obo$obo4b2o5b2o4bobo$2b2o2b2o7b2o2b2o$2ob3o2b7o2b3ob2o$5bob2o5b2obo$3bo3b3obob3o3bo$b2obobobobobobobobob2o$4b3o4bo4b3o$4bo13bo$5bo11bo$4b6o3b6o$4bo13bo$4bo2b3obob3o2bo$4bo4b2ob2o4bo2$2b3o4b5o4b3o$5b4o5b4o$2bo6b2ob2o6bo$3bo3bo3bo3bo3bo$2b2o4bobobobo4b2o$3b2o3b2o3b2o3b2o$3bo5b5o5bo$5bo11bo$2bobo4b5o4bobo$5b4o5b4o$3b3o11b3o$4b2ob3o3b3ob2o$2bo6bobobo6bo$4bo2b2obobob2o2bo$3b2o2b3obob3o2b2o$5b2obob3obob2o$3bobo2bobobobo2bobo$5b4o5b4o2$7b3o3b3o2$4b4ob2ob2ob4o$8bo5bo$4bo3b2o3b2o3bo2$4bob4o3b4obo$7bo7bo$5bo4b3o4bo$6b2obo3bob2o$11bo$5bo3b2ob2o3bo$7b3obob3o$4b2o2bo5bo2b2o$6bo3bobo3bo$4bo2b9o2bo$5bo3bo3bo3bo$4bo3bob3obo3bo$5bo2bo2bo2bo2bo$4bo2b4ob4o2bo$6bob2obob2obo$5bob3o3b3obo$4bo2bo2bobo2bo2bo$5b2ob2o3b2ob2o$4bob2ob5ob2obo$5bobo7bobo$3b2obo3b3o3bob2o2$2bo7bobo7bo2$2b8obob8o$7bob2ob2obo$4b2obo7bob2o$2bobo2bo7bo2bobo$5b4o5b4o$2b3o4b5o4b3o$7b2o5b2o$2bobo3b2obob2o3bobo$2bobo5bobo5bobo$3bobobo7bobobo$2bobo2bo7bo2bobo$3b2o2bo7bo2b2o$2b3obo9bob3o$4b2ob2o5b2ob2o$3b5o7b5o$6bo2b2ob2o2bo$4bo3b2o3b2o3bo$4b4ob2ob2ob4o$3bobo3bobobo3bobo$3bo3b2obobob2o3bo$7bo3bo3bo$4b2ob4ob4ob2o$5b2obob3obob2o$6bo3bobo3bo$6bobo5bobo$5bobobo3bobobo$7b9o$4bo2bo3bo3bo2bo$4bob2o2bobo2b2obo$5b4o5b4o$5bo11bo$5b2o2b2ob2o2b2o$7bo3bo3bo$5bob3o3b3obo$8bob3obo$5bo2bobobobo2bo$7b2o5b2o$4b2o4b3o4b2o$6b4obob4o$4b3o3bobo3b3o2$4bo13bo$7b9o$5b2o9b2o$8b7o2$5bobo7bobo2$4b2ob2o5b2ob2o$6bo9bo$4bob11obo2$4b2o2b7o2b2o2$4bo3b2o3b2o3bo$5b3o7b3o$4bo5b3o5bo$5b3o7b3o$5bobo2b3o2bobo$6bo9bo$5b2ob2o3b2ob2o$7bobo3bobo$5b2o4bo4b2o$7bobobobobo$5b3ob5ob3o$8b2obob2o$7bo2bobo2bo$8b2o3b2o$9b2ob2o$11bo$9b2ob2o$9bo3bo$7b2o5b2o$10bobo$7bo2b3o2bo$7b4ob4o$6bo2b2ob2o2bo$7bo2bobo2bo$6bo2bo3bo2bo$8b3ob3o$5b5obob5o$8bob3obo$5bo4bobo4bo$6b2o2bobo2b2o$5bo3bo3bo3bo$6bobo2bo2bobo$6bob2o3b2obo2$6b2obo3bob2o$11bo$6b5ob5o$8bo5bo$6bobo5bobo$7b4ob4o$10bobo2$9b2ob2o$9bobobo$9b5o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 4 HEIGHT 3990 Y 1 ZOOM 22 AUTOSTART GPS 5 TRACK 0 -1/5 ]]
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(click above to open LifeViewer ) Catagolue here
Removed
“
Stable or slowly shrinking dark black-and-white blobs with stable interiors and chaotic boundaries. Has xor-based oscillators of all periods but no still lifes. Dominique Giard's favorite rule.
”
David Eppstein found a 2c/6 and Layz Boi found a 2c/4 in 2021, see its rule page.
In 2008, Josh Ball found a c/2.
x = 127, y = 18, rule = B34/S0235
7b3o3b3o95b3o3b3o$7b3o3b3ob2o10b3o63b3o10b2ob3o3b3o$6b3o2b3o3bob2o7bo2bo63bo2bo7b2obo3b3o2b3o$5bo4b2o2bo2bo2bob2o3b2o2b2o3bo53bo3b2o2b2o3b2obo2bo2bo2b2o4bo$3b7o2b3o3b2o3bob3o2bob2ob3o3bo5bo31bo5bo3b3ob2obo2b3obo3b2o3b3o2b7o$2b2o4bobo2b2ob2ob2o4b10o2b3ob2o3b3o29b3o3b2ob3o2b10o4b2ob2ob2o2bobo4b2o$2b2o2bo3bo4bob5o2bob3o2bo3bo2bo4bo2b2ob2o8bo7bo8b2ob2o2bo4bo2bo3bo2b3obo2b5obo4bo3bo2b2o$2o2bo2b2obo2bo3b2o5bo4b2o3b5o2b10o3bo3b3o5b3o3bo3b10o2b5o3b2o4bo5b2o3bo2bob2o2bo2b2o$bo3b2obobo2bobob2ob2ob2o2bobo2b2ob2obo2bo2b2o3b3ob4o3b2o3b2o3b4ob3o3b2o2bo2bob2ob2o2bobo2b2ob2ob2obobo2bobob2o3bo$o3bobo3bob4ob3o21b12o2bob2ob2o3b2ob2obo2b12o21b3ob4obo3bobo3bo$3b2obobobo10b2o2b2ob2ob2o2bo3b4o2b4o2b2ob2obobo2bobo2bobob2ob2o2b4o2b4o3bo2b2ob2ob2o2b2o10bobobob2o$3b4o7bo3bo17bo4bob2o5b2obobobobo2bobo2bobobobob2o5b2obo4bo17bo3bo7b4o$3bob2o2b2o2bobobobo2b3o3bo3b3o5bob3o2bobo3bo3bobo2bobo2bobo3bo3bobo2b3obo5b3o3bo3b3o2bobobobo2b2o2b2obo$28bo10b7o5bobobobobo7bobobobobo5b7o10bo$39b2obo2b5ob3o3b3ob5ob3o3b3ob5o2bob2o$43b4ob3ob2o3b2ob3ob3ob2o3b2ob3ob4o$44bo5bo9bo5bo9bo5bo$44bo5bo9bo5bo9bo5bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 WIDTH 1540 ZOOM 12 AUTOSTART GPS 2 TRACK 0 -1/2 ]]
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(click above to open LifeViewer ) Catagolue here
“
A growing black polygon with up to 16 sides.
”
A c/5 was found by David Eppstein
x = 22, y = 41, rule = B34/S45678
7b8o2$6b4o2b4o$2b3o12b3o$2b3obo3b2o3bob3o$ob2o2bo8bo2b2obo$4b14o$ob2o2b2o6b2o2b2obo$6b2o6b2o$b4ob3o4b3ob4o$4bo12bo$2b2ob5o2b5ob2o$8bob2obo$4b2ob2o4b2ob2o$8b6o$5bo10bo$8bo4bo$6bobo4bobo$8bob2obo$6bobo4bobo$7bobo2bobo$5b2o8b2o$3b3obo6bob3o$5bo10bo$3b3o10b3o2$3b16o2$4bo12bo2$4bob10obo2$5bob8obo$6b2o6b2o$8b6o$6b3o4b3o$8bo4bo2$6b3o4b3o2$7bo6bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 3 HEIGHT 1260 ZOOM 26 Y -1 AUTOSTART GPS 5 TRACK 0 -1/5 ]]
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(click above to open LifeViewer ) Catagolue here
“
The only B3xx/S01567 rule for which no gliders are known.
”
In 2002, Keith Amling found a c/5.
x = 20, y = 49, rule = B3456/S01567
6b3o2b3o$5b3ob2ob3o$3bo12bo$4b12o$3bo12bo$5bobob2obobo$3b2o10b2o$2bo2bobob2obobo2bo$2b16o$b3o2b3o2b3o2b3o$5b2ob4ob2o$o6b2o2b2o6bo$2b6o4b6o$b4o2b6o2b4o$2b5o6b5o$b3obob6obob3o$2b5o6b5o$7b6o$2b5o6b5o$2bo2b3ob2ob3o2bo$2b7o2b7o$bo3b4o2b4o3bo$b3ob3o4b3ob3o$bob5ob2ob5obo$2ob14ob2o$6o2b4o2b6o$bob4ob4ob4obo$4bobob4obobo$b2o2b2ob4ob2o2b2o$2b2obobo4bobob2o$2bob3ob4ob3obo$bo5bo4bo5bo$bob4ob4ob4obo$2b4obo4bob4o$3b14o$2bobo10bobo$2bo2bob6obo2bo$3bob2obo2bob2obo$5b3ob2ob3o$4b12o$5bob6obo$5b3ob2ob3o$5bob6obo$6b2o4b2o$8b4o2$8b4o2$7b2o2b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 3 HEIGHT 1400 ZOOM 26 AUTOSTART GPS 5 TRACK 0 -1/5 ]]
Please enable Javascript to view this LifeViewer.
(click above to open LifeViewer ) Catagolue here
“
An expanding chaotic region with large solid and empty patches. The only B3xx/S34 rule for which no gliders are known.
”
In 2002, Keith Amling found a c/3.
x = 28, y = 35, rule = B3456/S34
13b2o$13b2o$11b2o2b2o$11b6o$10b8o$9bo2bo2bo2bo$8bo4b2o4bo$9bo8bo$7b4o6b4o$11b6o$6b2o2b3o2b3o2b2o$7b4obo2bob4o$6bob3obo2bob3obo$6bo2b4o2b4o2bo$5bo3b2obo2bob2o3bo$5bo3b2obo2bob2o3bo$4bo2bob4o2b4obo2bo$4bob6ob2ob6obo$3bo4b3o6b3o4bo$3bo5bobo4bobo5bo$3bo4b2ob2o2b2ob2o4bo$3b6o2b2o2b2o2b6o$6b2o3b6o3b2o$bobobo2bob8obo2bobobo$b4o3bo2bo4bo2bo3b4o$3b2o3bo2bo4bo2bo3b2o$b5o2b5o2b5o2b5o$b3o3b5o4b5o3b3o$3bo5b2o6b2o5bo$o3bo4b10o4bo3bo$o9b3o2b3o9bo$o2b2o3b4ob2ob4o3b2o2bo$3o6b2o6b2o6b3o$3b2o3b2o8b2o3b2o$2b2o20b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 HEIGHT 700 Y 1 ZOOM 18 AUTOSTART GPS 3 TRACK 0 -1/3 ]]
Please enable Javascript to view this LifeViewer.
(click above to open LifeViewer ) Catagolue here
“
Slowly growing patterns with chaotic fringes and periodic (multiple of two) centers.
”
A small 2c/44 diagonal was known to David Eppstein.
x = 9, y = 9, rule = B34567/S18
2b3o$3o2bo$2b5o$o5b2o$ob3obobo$4bobobo$b2obob3o$2bo4bo$4b2obo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 HEIGHT 560 X -1/4 Y 5/4 ZOOM 36 AUTOSTART GPS 44 TRACK 2/44 -2/44 ]]
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“
Expanding chaos. The only B3xx/S247 rule for which no gliders are known.
”
A small 2c/4 was known to David Eppstein. No other spaceships are known.
x = 21, y = 14, rule = B34567/S247
7b7o$6b2ob3ob2o$5b2o3bo3b2o$3b2o2bob3obo2b2o$2b2o2bo3bo3bo2b2o$3b2o11b2o$ob4o4bo4b4obo$ob4o2bo3bo2b4obo$5o2bo5bo2b5o$b2o15b2o$7o7b7o2$bo2b3o7b3o2bo$2b2o13b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 HEIGHT 480 Y 1/2 ZOOM 24 AUTOSTART GPS 4 TRACK 0 -2/4 ]]
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“
Slowly expanding chaos with many small short-lived empty regions.
”
A c/7 was known to David Eppstein.
x = 15, y = 56, rule = B34568/S4
5b5o2$4bo2bo2bo$3b2o5b2o$b2ob7ob2o$2bo3b3o3bo$2b2o7b2o$2bo2bobobo2bo$4b7o$b4o2bo2b4o$3b2o5b2o$o2bo2bobo2bo2bo$b2ob2obob2ob2o$o4b2ob2o4bo$2bo2b2ob2o2bo$3o3bobo3b3o$2b2o2bobo2b2o$2b2obobobob2o$2o4b3o4b2o$4bo5bo$3ob7ob3o$bobo2bobo2bobo$ob2ob2ob2ob2obo$b3obo3bob3o$2obo7bob2o$bobo7bobo$3o9b3o$ob3o5b3obo$3b3o3b3o$5o5b5o$bo3bo3bo3bo$o13bo$bo2bo5bo2bo$bo2b2o3b2o2bo$bo11bo$3b3o3b3o$b3o7b3o$4bo5bo$b4o5b4o2$b5o3b5o$4bo2bo2bo$bo4b3o4bo$6b3o$2b2o2b3o2b2o$5bobobo$5b5o$7bo$5b5o2$4bob3obo$5bo3bo$4bo5bo$5b2ob2o$3bob2ob2obo$5bobobo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 4 HEIGHT 1960 Y -1/2 ZOOM 32 AUTOSTART GPS 7 TRACK 0 -1/7 ]]
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“
The only B3xx/S123 rule for which no gliders are known.
”
On June 25, 2021, May13 found a glide-symmetric 2c/4.[ 13]
x = 22, y = 30, rule = B368/S123
3bo14bo$2b3o12b3o$2b3o12b3o$bo3bo10bobobo$o5bo3b2o3b7o$3bo3bob2ob2ob2o3b2o$4bo7b3o2b2o$3b2ob6o3b2o$5b6o6b2o$2b2o2b2o3b2o4bobo$2b2obo2b4obo4b3o$2b2obo2bo2bo4b2ob2o$3bo2bo2b2o6bo$2b2obo$4b2o4bo2bo4b2o$2bo2bob2obo2b2ob2o$b3ob4obob2ob2o2b2o$b3o2b3ob2obob3o$2b5o2b4o$8b2o5bo$10bob2obo2bo$5b2o4b2o2bo$7bo6b3o$8bo2bo2b3o$7b5o2b2o$6b2o2bo$6b3ob4o$7b3ob3o$12bo$13bo!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 HEIGHT 784 Y 1/2 ZOOM 24 AUTOSTART GPS 4 TRACK 0 -2/4 ]]
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Conjectures
See also Spaceship#In other rules
“
Even more than gliders for these rules, I would like a mathematical proof that certain rules (e.g. rules with B23, with B3 and none of S0-S5, or with all of B3/S34567) are unable to support gliders.
”
It has been proven that B23 rules with S0 cannot support spaceships,[citation needed ] however examples are known in the ten rules B2367(8)/S2467(8), B235(78)/S14678, and B2357(8)/S3678 (where transitions in brackets are optional).[ 14]
The second conjecture has not been proven, and no counterexamples have been found.
The third conjecture has not been proven, but the weaker statement that all (non-strobing) rules containing B3/S234567 are spaceshipless has been.[citation needed ]
References
↑ the archive of the first version ↑ removal occurred between the archives taken on February 26 and April 16 , 2000
↑ 3.0 3.1 Sokwe (July 15, 2020). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
↑ Sokwe (July 17, 2020). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
↑ May13 (July 9, 2024). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
↑ velcrorex (August 8, 2015). Re: Eppstein's Most Wanted (discussion thread) at the ConwayLife.com forums
↑ Sokwe (February 5, 2010). Re: Interesting Patterns in Normally Expanding Rulesets (discussion thread) at the ConwayLife.com forums
↑ iNoMed (June 21, 2021). Re: Eppstein's Most Wanted (discussion thread) at the ConwayLife.com forums
↑ Layz Boi (June 30, 2021). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
↑ iNoMed (December 30, 2023). Message in #naturalistic on the Conwaylife Lounge Discord server
↑ LaundryPizza03 (April 21, 2020). Re: Eppstein's Most Wanted (discussion thread) at the ConwayLife.com forums
↑ velcrorex (August 6, 2015). Re: Eppstein's Most Wanted (discussion thread) at the ConwayLife.com forums
↑ May13 (June 25, 2021). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
↑ Layz Boi (January 1, 2024). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
External links