Difference between revisions of "OCA:Eppstein's Most Wanted"

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m (1 spaceship is known for this rule.)
m (replace : indentation with leading spaces, which puts each unmodified quotation from David Eppstein into a shaded box in a different font. Hopefully this will make it less likely that people will confuse the original quotes with the follow-up notes.)
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==Rules==
==Rules==
===B3/S23456===
===B3/S23456===
: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. Also supports a few small oscillators including Life's clock.<!--this sentence also added--> Very similar to B3/S012345678 "Life without death" which of course has no spaceships.
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. Also supports a few small oscillators including Life's clock.<!--this sentence also added--> Very similar to B3/S012345678 "Life without death" which of course has no spaceships.
still unknown
still unknown
*{{cata|census/b3s23456|B3/S23456}} at Catagolue
*{{cata|census/b3s23456|B3/S23456}} at Catagolue
===B3/S45678 ({{rl|Coral}})===
===B3/S45678 ({{rl|Coral}})===
: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. Searched unsuccessfully with gfind to level L128.<!--this sentence new-->
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. Searched unsuccessfully with gfind to level L128.<!--this sentence new-->
See its page, the first spaceship was found by [[Josh Ball]] in 2013, followed by a reduction by [[lordlouckster]] in December 5, 2023.
See its page, the first spaceship was found by [[Josh Ball]] in 2013, followed by a reduction by [[lordlouckster]] in December 5, 2023.


*{{cata|census/b3s45678|Coral}} at Catagolue
*{{cata|census/b3s45678|Coral}} at Catagolue
===B34/S03456===
===B34/S03456===
:One of the rules studied by [[Stephen Wolfram|Wolfram]]. An expanding octagonal region filled with stable junk. Has many small p2 and p4 oscillators.<!--this sentence also added-->
One of the rules studied by [[Stephen Wolfram|Wolfram]]. An expanding octagonal region filled with stable junk. Has many small p2 and p4 oscillators.<!--this sentence also added-->
still unknown
still unknown
*{{cata|census/b34s03456|B34/S03456}} at Catagolue
*{{cata|census/b34s03456|B34/S03456}} at Catagolue
===B345/S456===
===B345/S456===
: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.
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
still unknown
*{{cata|census/b345s456|B345/S456}} at Catagolue
*{{cata|census/b345s456|B345/S456}} at Catagolue
===B345/S4567 ({{rl|Assimilation}})===
===B345/S4567 ({{rl|Assimilation}})===
:Stable black diamonds filled with white dots.
Stable black diamonds filled with white dots.
still unknown
still unknown
*{{cata|census/b345s4567|Assimilation}} at Catagolue
*{{cata|census/b345s4567|Assimilation}} at Catagolue
===B345/S5 ({{rl|LongLife}})===
===B345/S5 ({{rl|LongLife}})===
:Complicated long-lived oscillating patterns of alternating rows seem to be trapped inside a bounding diamond. Are they really unable to grow?
Complicated long-lived oscillating patterns of alternating rows seem to be trapped inside a bounding diamond. Are they really unable to grow?
still unknown
still unknown
*{{cata|census/b345s5|LongLife}} at Catagolue
*{{cata|census/b345s5|LongLife}} at Catagolue
===B34567/S0678===
===B34567/S0678===
:Slowly growing mazes. [[Self-complementary|Symmetric]] under [[black/white reversal]].
Slowly growing mazes. [[Self-complementary|Symmetric]] under [[black/white reversal]].
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.
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.


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*{{cata|census/b34567s0678|B34567/S0678}} at Catagolue
*{{cata|census/b34567s0678|B34567/S0678}} at Catagolue
===B345678/S014578===
===B345678/S014578===
:Dense expanding chaos. The only B3xx/S014578 rule for which no gliders are known.
Dense expanding chaos. The only B3xx/S014578 rule for which no gliders are known.
still unknown
still unknown
*{{cata|census/b345678s014578|B345678/S014578}} at Catagolue
*{{cata|census/b345678s014578|B345678/S014578}} at Catagolue


===B345678/S15678===
===B345678/S15678===
:Stable filled octagons.
Stable filled octagons.
still unknown
still unknown
*{{cata|census/b345678s15678|B345678/S15678}} at Catagolue
*{{cata|census/b345678s15678|B345678/S15678}} at Catagolue
===B345678/S47===
===B345678/S47===
:Slowly expanding chaos.
Slowly expanding chaos.
A c/7 was found by Matthias Merzenich on July 15, 2020, using [[qfind]],<ref name="post100479" /> followed by a c/9 and a c/11 on July 17.<ref>{{LinkForumThread|format=ref|f=11|t=1074|p=100546|title=Re: Spaceships in Life-like cellular automata|author=Sokwe|date=July 17, 2020}}</ref>
A c/7 was found by Matthias Merzenich on July 15, 2020, using [[qfind]],<ref name="post100479" /> followed by a c/9 and a c/11 on July 17.<ref>{{LinkForumThread|format=ref|f=11|t=1074|p=100546|title=Re: Spaceships in Life-like cellular automata|author=Sokwe|date=July 17, 2020}}</ref>
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*{{cata|census/b345678s47|B345678/S47}} at Catagolue
*{{cata|census/b345678s47|B345678/S47}} at Catagolue
===B345678/S478===
===B345678/S478===
:Slowly expanding chaos.
Slowly expanding chaos.
A c/7 was found in the same search as the previous rule.<ref name="post100479" />
A c/7 was found in the same search as the previous rule.<ref name="post100479" />
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===B34678/S23578===
===B34678/S23578===
:Expanding chaos.
Expanding chaos.
A c/2 was known to David Eppstein and included in his database.
A c/2 was known to David Eppstein and included in his database.
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===B35/S46===
===B35/S46===
: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.
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.
still unknown
still unknown
*{{cata|census/b35s46|B35/S46}} at Catagolue
*{{cata|census/b35s46|B35/S46}} at Catagolue
===B35/S234578 ({{rl|Land Rush}} variant)===
===B35/S234578 ({{rl|Land Rush}} variant)===
:Chaotic growth evolves into stable patchwork of horizontally and vertically plowed regions. 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).<!--this sentence was added in his edit--> 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.
Chaotic growth evolves into stable patchwork of horizontally and vertically plowed regions. 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).<!--this sentence was added in his edit--> 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.
still unknown
still unknown
*{{cata|census/b35s234578|B35/S234578}} at Catagolue
*{{cata|census/b35s234578|B35/S234578}} at Catagolue
===B36/S1567===
===B36/S1567===
:Quickly stabilizes to isolated domino still lifes and low-period oscillators. Has arbitrarily high-period oscillators formed out of 2x2 blocks of cells.
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.<ref>{{LinkForumThread|format=ref|f=11|t=1787|p=21765|title=Re: Eppstein's Most Wanted|author=velcrorex|date=August 8, 2015}}</ref>
On August 8, 2015, Josh Ball found a c/3 spaceship.<ref>{{LinkForumThread|format=ref|f=11|t=1787|p=21765|title=Re: Eppstein's Most Wanted|author=velcrorex|date=August 8, 2015}}</ref>
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==Added==
==Added==
===B01345/S01234===
===B01345/S01234===
: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.
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
still unknown
*{{cata|census/b01345s01234|B01345/S01234}} at Catagolue
*{{cata|census/b01345s01234|B01345/S01234}} at Catagolue
===B017/S1===
===B017/S1===
: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.
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.<ref>{{LinkForumThread|format=ref|p=1862|title=Re: Interesting Patterns in Normally Expanding Rulesets|author=Sokwe|date=February 5, 2010}}</ref>
On February 5, 2010, [[Matthias Merzenich]] corderised the 4c/8 replicator into two 8c/16 spaceships, and demonstrated a small puffer and dirty breeder.<ref>{{LinkForumThread|format=ref|p=1862|title=Re: Interesting Patterns in Normally Expanding Rulesets|author=Sokwe|date=February 5, 2010}}</ref>
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*{{cata|census/b017s1|B017/S1}} at Catagolue
*{{cata|census/b017s1|B017/S1}} at Catagolue
===B02/S===
===B02/S===
: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.
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
still unknown
*{{cata|census/b02s|B02/S}} at Catagolue
*{{cata|census/b02s|B02/S}} at Catagolue
===B34567/S348===
===B34567/S348===
:The only B3xx/S348 rule without known spaceships. Slightly rounded diamond-shaped growing chaos.
The only B3xx/S348 rule without known spaceships. Slightly rounded diamond-shaped growing chaos.
still unknown
still unknown
*{{cata|census/b34567s348|B34567/S348}} at Catagolue
*{{cata|census/b34567s348|B34567/S348}} at Catagolue
===B345678/S458===
===B345678/S458===
:Dense chaos fills an expanding diamond-shaped region.
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.<ref>{{LinkForumThread|format=ref|f=11|t=1787|p=132407|title=Re: Eppstein's Most Wanted|author=iNoMed|date=June 21, 2021}}</ref> On June 30 (nine days later), [[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/7's frontend with the same lateral width.<ref>{{LinkForumThread|format=ref|f=11|t=1074|p=132824|title=Re: Spaceships in Life-like cellular automata|author=Layz Boi|date=June 30, 2021}}</ref>
On June 21, 2021, [[iNoMed]] found the first c/7 diagonal spaceship, at 1237 cells, followed by a 430-cell c/9 diagonal.<ref>{{LinkForumThread|format=ref|f=11|t=1787|p=132407|title=Re: Eppstein's Most Wanted|author=iNoMed|date=June 21, 2021}}</ref> On June 30 (nine days later), [[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/7's frontend with the same lateral width.<ref>{{LinkForumThread|format=ref|f=11|t=1074|p=132824|title=Re: Spaceships in Life-like cellular automata|author=Layz Boi|date=June 30, 2021}}</ref>
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*{{cata|census/b345678s458|B345678/S458}} at Catagolue
*{{cata|census/b345678s458|B345678/S458}} at Catagolue
===B3478/S24568===
===B3478/S24568===
:Expanding chaos.
Expanding chaos.
A c/2 was known to David Eppstein, and a c/3 was found by LaundryPizza03 on April 21, 2020.<ref>{{LinkForumThread|format=ref|f=11|t=1787|p=95105|title=Re: Eppstein's Most Wanted|author=LaundryPizza03|date=April 21, 2020}}</ref>
A c/2 was known to David Eppstein, and a c/3 was found by LaundryPizza03 on April 21, 2020.<ref>{{LinkForumThread|format=ref|f=11|t=1787|p=95105|title=Re: Eppstein's Most Wanted|author=LaundryPizza03|date=April 21, 2020}}</ref>
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*{{cata|census/b3478s24568|B3478/S24568}} at Catagolue
*{{cata|census/b3478s24568|B3478/S24568}} at Catagolue
===B348/S4===
===B348/S4===
:Quickly decays to isolated 4-cell p2 oscillators.
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.<ref>{{LinkForumThread|format=ref|f=11|t=1787|p=p21700|title=Re: Eppstein's Most Wanted|author=velcrorex|date=August 6, 2015}}</ref>
At some time before making the thread about the page in 2015, Josh Ball found a c/5.<ref>{{LinkForumThread|format=ref|f=11|t=1787|p=p21700|title=Re: Eppstein's Most Wanted|author=velcrorex|date=August 6, 2015}}</ref>
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==Removed==
==Removed==
===B3/S4567 ({{rl|Lifeguard 2}})===
===B3/S4567 ({{rl|Lifeguard 2}})===
: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.
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.
David Eppstein found a 2c/6 and Layz Boi found a 2c/4 in 2021, see its rule page.
*{{cata|census/b3s4567|B3/S4567}} at Catagolue
*{{cata|census/b3s4567|B3/S4567}} at Catagolue
===B34/S0235===
===B34/S0235===
:Expanding chaos. One of the few rules [https://ics.uci.edu/~eppstein/ca/replicators/b34s0235.html known to support replicators].
Expanding chaos. One of the few rules [https://ics.uci.edu/~eppstein/ca/replicators/b34s0235.html known to support replicators].
In 2008, Josh Ball found a c/2.
In 2008, Josh Ball found a c/2.
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===B3456/S01567===
===B3456/S01567===
:The only B3xx/S01567 rule for which no gliders are known.
The only B3xx/S01567 rule for which no gliders are known.
In 2002, Keith Amling found a c/5.
In 2002, Keith Amling found a c/5.
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===B3456/S34===
===B3456/S34===
:An expanding chaotic region with large solid and empty patches. The only B3xx/S34 rule for which no gliders are known.
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.
In 2002, Keith Amling found a c/3.
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===B34567/S18===
===B34567/S18===
:Slowly growing patterns with chaotic fringes and periodic (multiple of two) centers.
Slowly growing patterns with chaotic fringes and periodic (multiple of two) centers.
A small 2c/44 diagonal was known to David Eppstein.
A small 2c/44 diagonal was known to David Eppstein.
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===B34567/S247===
===B34567/S247===
:Expanding chaos. The only B3xx/S247 rule for which no other gliders are known.
Expanding chaos. The only B3xx/S247 rule for which no gliders are known.
A small 2c/4 was known to David Eppstein.
A small 2c/4 was known to David Eppstein.  No other gliders are known.
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|rle          = x = 21, y = 14, rule = B34567/S247
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===B34568/S4===
===B34568/S4===
:Slowly expanding chaos with many small short-lived empty regions.
Slowly expanding chaos with many small short-lived empty regions.
A c/7 was known to David Eppstein.
A c/7 was known to David Eppstein.
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===B368/S123===
===B368/S123===
:The only B3xx/S123 rule for which no gliders are known.
The only B3xx/S123 rule for which no gliders are known.
On June 25, 2021, May13 found a glide-symmetric 2c/4.<ref>{{LinkForumThread|format=ref|f=11|t=1074|p=132587|title=Re: Spaceships in Life-like cellular automata|author=May13|date=June 25, 2021}}</ref>
On June 25, 2021, May13 found a glide-symmetric 2c/4.<ref>{{LinkForumThread|format=ref|f=11|t=1074|p=132587|title=Re: Spaceships in Life-like cellular automata|author=May13|date=June 25, 2021}}</ref>
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==Conjectures==
==Conjectures==
:''See also [[Spaceship#In other rules]]''
''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.
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,{{cn}}<!--cannot find it, I think it was by LaundryPizza03, since they seem to take it as a given--> 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).<ref>{{LinkForumThread|format=ref|f=11|t=1074|p=174682|title=Re: Spaceships in Life-like cellular automata|author=Layz Boi|date=January 1, 2024}}</ref> All known are photons.<!--not sure whether this was proven for all as part of the S0 nonexistence proof-->
It has been proven that B23 rules with S0 cannot support spaceships,{{cn}}<!--cannot find it, I think it was by LaundryPizza03, since they seem to take it as a given--> 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).<ref>{{LinkForumThread|format=ref|f=11|t=1074|p=174682|title=Re: Spaceships in Life-like cellular automata|author=Layz Boi|date=January 1, 2024}}</ref> All known are photons.<!--not sure whether this was proven for all as part of the S0 nonexistence proof-->


Revision as of 15:34, 26 February 2024

Eppstein's Most Wanted is a list of 22 outer-totalistic rules, created by David Eppstein no later than October 8, 1999,[1] in which spaceships at the time were not known, but would be of significant interest if found.

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 four, and the others 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

B3/S23456

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. Also supports a few small oscillators including Life's clock. Very similar to B3/S012345678 "Life without death" which of course has no spaceships.

still unknown

B3/S45678 (Coral)

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. 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.

B34/S03456

One of the rules studied by Wolfram. An expanding octagonal region filled with stable junk. Has many small p2 and p4 oscillators.

still unknown

B345/S456

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

B345/S4567 (Assimilation)

Stable black diamonds filled with white dots.

still unknown

B345/S5 (LongLife)

Complicated long-lived oscillating patterns of alternating rows seem to be trapped inside a bounding diamond. Are they really unable to grow?

still unknown

B34567/S0678

Slowly growing mazes. Symmetric under black/white reversal.

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.

B345678/S014578

Dense expanding chaos. The only B3xx/S014578 rule for which no gliders are known.

still unknown

B345678/S15678

Stable filled octagons.

still unknown

B345678/S47

Slowly expanding chaos.

A c/7 was found by Matthias Merzenich on July 15, 2020, using qfind,[3] followed by a c/9 and a c/11 on July 17.[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 ]]
(click above to open LifeViewer)

B345678/S478

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 ]]
(click above to open LifeViewer)
Catagolue: here

B34678/S23578

Expanding chaos.

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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Catagolue: here

B35/S46

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.

still unknown

B35/S234578 (Land Rush variant)

Chaotic growth evolves into stable patchwork of horizontally and vertically plowed regions. 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). 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.

still unknown

B36/S1567

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.[5]

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 ]]
(click above to open LifeViewer)
Catagolue: here

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

B01345/S01234

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

B017/S1

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.[6]

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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B02/S

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

B34567/S348

The only B3xx/S348 rule without known spaceships. Slightly rounded diamond-shaped growing chaos.

still unknown

B345678/S458

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.[7] On June 30 (nine days later), 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/7's frontend with the same lateral width.[8]

x = 172, 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$109b3obob2o4b2ob2o11b5o2b5o8b3o5b2o$109b2ob9ob2o11b2ob2ob2ob2o9b2o6b2ob2o$107bo5bob4ob4o6b2o2bo4b5ob2o8b2ob3o3b2o$107bo8bobobo11b4obo2b3obo8b6obobo2bo$105b5obobob7o6b9obo2b4o8b3ob4ob2o$106bob3obo3bobo9b2o3b5o2bobo8b2o2bo2b2o2b2o$103b7o3bo3b3o6b2o4b3ob3obo11bob2o3b3o$103b2o4bo2bo3b2o8b2o2bob2ob5o9b2ob2ob7o$101b2o2b3o2b4o2b2o6b3o4b8o11bobo3bob2o$101bob6o2b3o13b3obob3ob2o8b2o2bo3bo2b2o$101b2o5b2obob3o6b4ob7o3bobo7b2o5b4o$99b3ob4ob2ob3o8b4obo2b2o2bo2bobo5b2o2bo3bo3bo$99b6obob2obobo6b4o3b3ob2o3b2o8bo2b2o3b2o$98bob2o3b2obob2o8bo3bob4ob2o3b2o5bob2o2b3o3bo$96b2o4b2ob2obob2o6b3o6b6ob2o7b2ob2o4b2o$96bo5b2obobobo10b2ob3o2bo4b3o5b8o3b2o$94bobo2bobo2b6o8bob3o3bo3b2obo9b9o$94b5obo3b3o11bob5obobob2obo5b6ob2obobo$92bobo4bobo3b2o9bob2o2b3obo2b3o7b3ob6o$92b3o3bobo3bo11bobobob4o3b3o5b2o2b9o$90b7o3bo2bo9b5o2bo3b3o2bo8b4obobobo$88b6ob3o2b4o9b3o4b3ob6o10b6obo$88b2obo4b2o2bo10bobobo2bo4bo3bo6b3o4b2ob2o$86b2ob4obo2b5o9b3ob5o2b4obo14bob2o$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 875 HEIGHT 770 ZOOM 5 ]]
iNoMed's and Layz Boi's c/7ds, and iNoMed's c/9d
(click above to open LifeViewer)

B3478/S24568

Expanding chaos.

A c/2 was known to David Eppstein, and a c/3 was found by LaundryPizza03 on April 21, 2020.[9]

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 ]]
(click above to open LifeViewer)

B348/S4

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.[10]

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 ]]
(click above to open LifeViewer)
Catagolue: here

Removed

B3/S4567 (Lifeguard 2)

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.

B34/S0235

Expanding chaos. One of the few rules known to support replicators.

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 ]]
(click above to open LifeViewer)
Catagolue: here

B3456/S01567

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 ]]
(click above to open LifeViewer)
Catagolue: here

B3456/S34

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 ]]
(click above to open LifeViewer)
Catagolue: here

B34567/S18

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 ]]
(click above to open LifeViewer)
Catagolue: here

B34567/S247

Expanding chaos. The only B3xx/S247 rule for which no gliders are known.

A small 2c/4 was known to David Eppstein. No other gliders 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 ]]
(click above to open LifeViewer)
Catagolue: here

B34568/S4

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 ]]
(click above to open LifeViewer)
Catagolue: here

B368/S123

The only B3xx/S123 rule for which no gliders are known.

On June 25, 2021, May13 found a glide-symmetric 2c/4.[11]

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 ]]
(click above to open LifeViewer)
Catagolue: here

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).[12] All known are photons.

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

  1. ↑ the archive of the first version
  2. ↑ removal occurred between the archives taken on February 26 and April 16, 2000
  3. ↑ 3.0 3.1 Sokwe (July 15, 2020). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
  4. ↑ Sokwe (July 17, 2020). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
  5. ↑ velcrorex (August 8, 2015). Re: Eppstein's Most Wanted (discussion thread) at the ConwayLife.com forums
  6. ↑ Sokwe (February 5, 2010). Re: Interesting Patterns in Normally Expanding Rulesets (discussion thread) at the ConwayLife.com forums
  7. ↑ iNoMed (June 21, 2021). Re: Eppstein's Most Wanted (discussion thread) at the ConwayLife.com forums
  8. ↑ Layz Boi (June 30, 2021). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
  9. ↑ LaundryPizza03 (April 21, 2020). Re: Eppstein's Most Wanted (discussion thread) at the ConwayLife.com forums
  10. ↑ velcrorex (August 6, 2015). Re: Eppstein's Most Wanted (discussion thread) at the ConwayLife.com forums
  11. ↑ May13 (June 25, 2021). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums
  12. ↑ Layz Boi (January 1, 2024). Re: Spaceships in Life-like cellular automata (discussion thread) at the ConwayLife.com forums

External links

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