LifeWiki - User contributions [en]

File:OT spaceship map.png

2026-03-10T01:08:06Z

Atavoidirc: fixed typo in code

== Summary ==
A map of the outer-totalistic rulespace (spanning all <tt>512<sup>2</sup></tt> rules), by support for spaceships.

Birth conditions are in a Gray code rightwards in the x axis (with b0 having the highest precedence, occupying the right half, b1 the central half, b2 the central halves of each half, etc.), survival ones are in one downwards in the y axis (with s0 having the highest precedence in the left half and s8 in the right half). In the bottom-right quadrant, the birth conditions' precedence is inverted again, to make it appear less fragmented.

Each one is coloured in accordance with the existence of spaceships in it. (For s8 rules, only the empty space of off cells is considered a valid background agar, except for the bottom-right quadrant, which has b0 so considers only the all-on agar, and as such duplicates all rules in the left half without S8, so may be excluded in a future version.)

Green rules have explicit examples known in the [https://github.com/jedlimlx/HROT-Glider-DB/blob/master/R1-C2-NM-gliders.db.txt extension] of David Eppstein's glider database, while the existence of spaceships in red ones is disproven. Black ones are unknown, grey rules are strobing thereof, and the white one (in a top-right corner of a green part in the top-left corner, and duplicated in the bottom-right) is Life.

The proofs regarding strobing rules come from [https://conwaylife.com/forums/viewtopic.php?f=11&t=1074&p=93966#p93966 this post] by LaundryPizza03.

Generated by means of the following program (the disproofs from LaundryPizza03 enclosed in double-brackets)<pre>
import os,sys
from functools import reduce
from itertools import product,chain,starmap
ORsum=lambda l: reduce(int.__or__,l,0)
tarmap=lambda f,*l:tuple(starmap(f,*l))
tilter=lambda f,i: tuple(filter(f,i))

def niceA030101(d,n):
b=d-1#d.bit_length()-1
l=b.bit_length()
o=c=(1<<(1<<l))-1
for i in range(l):
s=1<<l+~i #s=1<<i
o^=o<<s #o=c//((1<<(s<<1))-1)*((1<<s)-1)
n=(n&o)<<s|n>>s&o
return(n>>1+(~d^~0<<d.bit_length()) if d&d-1 else n)

from PIL import Image
mask=~(~0<<9)
rules=[False]*(1<<18)
with open(os.path.join(sys.path[0],'R1-C2-NM-gliders.db.txt'),newline='') as db: #https://github.com/jedlimlx/HROT-Glider-DB/blob/master/R1-C2-NM-gliders.db.txt
for s in db:
for _ in range(2): s=s[s.index(':')+1:]
minr=s[:(c:=s.index(':'))]
s=s[c+1:]
maxr=s[:s.index(':')]
minr,maxr=map(lambda r: (lambda b,s: b|s<<9)(*map(lambda t: ORsum(map(lambda i: (str(i) in t)<<i,range(9))),r.split('/'))),(minr,maxr))
diff=minr^maxr
indexes=tilter(lambda i: diff>>i&1,range(18))
for rule in map(ORsum,product(*map(lambda i: (0,1<<i),indexes))):
rules[rule|minr]=True
if minr&1 and ~minr&1<<17: #strobing
rules[niceA030101(18,~(~0<<18)^(rule|minr))]=True #black/white reversal
spaceship=lambda b,s: rules[b|s<<9]
img=Image.frombytes('RGB',2*(1<<9,),bytes(chain.from_iterable(tarmap(lambda b,s: (lambda b,s: 3*(0xff,) if b==0b1000 and s==0b1100 else (0,0xff,0) if spaceship(b,s) else ((0xff,spaceship(b,s) and 0xff,0) if not(~b&0b1110 or s&0b11100000) or not(~b&0b111110000 or s&0b11111) or not(~b&0b011110000 or s&0b11110) or not((b^0b0010)&0b1110 or (s^0b1100000)&0b11100000) or ~b&1<<1 and s&1<<7 or b&1<<1 and ~b&1<<2 and not ~s&0b11<<6 or (((~b&0b10 or ~b&0b1100 and not s&0b1111 or not b&0b1100 and not s&1 or not s&0b11111) and (s&1<<7 or not ~b&0b111110000 or not ~b&0b111100000 and s&0b1100000 or b&1<<8 and not ~s&0b1100000) or s&1<<6 and not b&0b110 or not ~s&0b11<<6 and not b&0b100 or not ~b&0b1110 and not s&0b111<<5)) else 3*(0x33,)) if b&1 else (0xff,spaceship(b,s) and 0xff,0) if not b&0b1110 or not ~s&0b1111 or b&0b10 or not(~b&0b1100) and s&1 or not (s^0b11110)&0b11111 or ((b&0b10 or not ~b&0b1100 and s&1 or not ~s&0b1111110 or not ~b&0b11000 and not ~s&0b111110 or not ~b&0b111000 and not ~s&0b11110 or ~b&0b100 and not ~s&0b11111100 or not ~s&0b11111 or b&0b11<<2 and not ~s&0b1111)) else 3*(0,))(*((niceA030101(9,mask^s),niceA030101(9,mask^b)) if b&1 and s&1<<8 else (b,s))),starmap(lambda x,y: map(lambda n: niceA030101(9,n^n>>1),(x,y)) if x<1<<8 else (niceA030101(9,x^x>>1),y^y>>1) if y<1<<8 else ((x&~(1<<8))^(x&~(1<<8))<<1|1,y^y>>1),product(range(1<<9),repeat=2)) if True else chain(product(map(lambda n: niceA030101(9,n^n>>1),range(1<<8)),map(lambda n: niceA030101(9,n^n>>1),range(1<<9))),product(map(lambda n: niceA030101(9,n^n>>1),range(1<<8,1<<9)),map(lambda n: n^n>>1,range(1<<9)))))))).transpose(5)
img.show()
</pre>

Catagolue naming conventions

2025-09-02T12:52:00Z

Atavoidirc: /* Objects */

[[Catagolue]] has been designed to be compatible with future expansion. In particular, it is very permissive to allow the following:

* Custom [[rule]]s;
* Custom symmetries;
* Custom objects.

To avoid breaking Catagolue, there are a number of conventions about how to name rules, symmetries, and objects.

==Census names==

The name of a census is of one of the following forms:

* <tt>[rule]/[symmetry]</tt> for a main census;
* <tt>[rule]/[symmetry]-[date]</tt> for a frozen backup of a main census.

The rule and symmetry should satisfy the conventions below, lest the census is potentially subject to automatic deletion. Likewise, for backup censuses, the date should be of the form yyyy-mm-dd.

==Rule names==

A Catagolue rule string must satisfy the regular expression <tt>[a-z][a-zA-Z0-9_-]+</tt>. The first letter describes the rule family, for example:

* '''b''': a 2-state Moore-neighbourhood outer-totalistic or isotropic rule;
* '''r''': an extended-range rule (such as [[Larger than Life]]);
* '''g''': a multi-state [[Generations]] rule;
* '''x''': a custom rule.

The custom rule syntax allows results from arbitrary rules (from [[Golly]], or other software) to be exchanged without infringing on existing rules. For instance, the rule <tt>xLangtons-Loops</tt> in Catagolue will map to the rule 'Langtons-Loops' in Golly. This should be used for rules that do not fit into any of the other rule families.

For rules which fit into one of the rule families, the name of the rule should be canonical so as to avoid census fragmentation.

==Symmetries==

A Catagolue symmetry must satisfy the regular expression <tt>([A-Z][a-zA-Z0-9_]*~)?[a-zA-Z0-9+_]+</tt>. If a tilde is present in the symmetry, everything to its left denotes the ''topology'' of the universe (for unbounded Euclidean universes, omit this). The rest of the symmetry string specifies how to create the initial seed in the universe; for instance, 'C1' specifies a 16-by-16 seed derived in a standard way from a SHA-256 hash.

It is encouraged to use symmetries beginning with your initials and ending in 'Test' when experimenting with new symmetries.

The 20 official symmetries, for which Catagolue knows how to generate the RLE of the initial seed, are tabulated below:

* C1, 8x32, 4x64, 2x128, 1x256: asymmetric soups of various sizes
* C2_1, C2_2, C2_4: 180° (two-fold) rotational symmetry
* C4_1, C4_4: 90° (four-fold) rotational symmetry
* D2_+1, D2_+2: reflectional symmetry along an orthogonal line
* D2_x: reflectional symmetry along a diagonal line
* D4_+1, D4_+2, D4_+4: reflectional symmetry along two perpendicular orthogonal lines
* D4_x1, D4_x4: reflectional symmetry along two perpendicular diagonal lines
* D8_1, D8_4: reflectional symmetry along four orthogonal/diagonal through a common center

If a topology is specified, it will be appended to the rule with a delimiting colon, with any 'x' replaced by a comma, any 'f' replaced by an asterisk, and any 'p' replaced by a plus sign. This allows Catagolue to generate RLEs compatible with the bounded grid support in [[Golly]].

==Objects==

An object must satisfy one of the following regular expressions:

* <tt>zz_[A-Z]+</tt> for unclassifiable infinite-growth patterns;
* <tt>PATHOLOGICAL</tt> for unclassifiable objects which do not appear to grow infinitely;
* <tt>me(gasized|ssless|ethuselah)_[0-9]+(h|k)</tt> for long-lived soups;
* <tt>gun(true)?_[0-9]+</tt> for guns in the [https://catagolue.hatsya.com/census/b3s23/synthesis-costs/gun <tt>gun</tt>] and [https://catagolue.hatsya.com/census/b3s23/synthesis-costs/guntrue <tt>guntrue</tt>] tabulations of <tt>synthesis-costs</tt>;
* <tt>yl[0-9]+_[0-9]+_[0-9]+_[a-z]+</tt> for classifiable linear growth patterns;
* <tt>ov_[spq][0-9]+</tt> for oversized objects;
* <tt>x[spq][0-9]+(_[a-z0-9]+)+</tt> for everything else.

If an object begins with the letter 'x', it is assumed to be an [[apgcode]] giving an exact canonical form of the pattern. An object beginning with 'y' is a classifiable infinite-growth pattern, and an object beginning with 'ov' is oversized (too large to admit a Catagolue-friendly apgcode).

{{CatagolueNavbox}}

[[Category:Censuses]]

Catagolue naming conventions

2025-09-02T12:51:50Z

Atavoidirc: /* Objects */

[[Catagolue]] has been designed to be compatible with future expansion. In particular, it is very permissive to allow the following:

* Custom [[rule]]s;
* Custom symmetries;
* Custom objects.

To avoid breaking Catagolue, there are a number of conventions about how to name rules, symmetries, and objects.

==Census names==

The name of a census is of one of the following forms:

* <tt>[rule]/[symmetry]</tt> for a main census;
* <tt>[rule]/[symmetry]-[date]</tt> for a frozen backup of a main census.

The rule and symmetry should satisfy the conventions below, lest the census is potentially subject to automatic deletion. Likewise, for backup censuses, the date should be of the form yyyy-mm-dd.

==Rule names==

A Catagolue rule string must satisfy the regular expression <tt>[a-z][a-zA-Z0-9_-]+</tt>. The first letter describes the rule family, for example:

* '''b''': a 2-state Moore-neighbourhood outer-totalistic or isotropic rule;
* '''r''': an extended-range rule (such as [[Larger than Life]]);
* '''g''': a multi-state [[Generations]] rule;
* '''x''': a custom rule.

The custom rule syntax allows results from arbitrary rules (from [[Golly]], or other software) to be exchanged without infringing on existing rules. For instance, the rule <tt>xLangtons-Loops</tt> in Catagolue will map to the rule 'Langtons-Loops' in Golly. This should be used for rules that do not fit into any of the other rule families.

For rules which fit into one of the rule families, the name of the rule should be canonical so as to avoid census fragmentation.

==Symmetries==

A Catagolue symmetry must satisfy the regular expression <tt>([A-Z][a-zA-Z0-9_]*~)?[a-zA-Z0-9+_]+</tt>. If a tilde is present in the symmetry, everything to its left denotes the ''topology'' of the universe (for unbounded Euclidean universes, omit this). The rest of the symmetry string specifies how to create the initial seed in the universe; for instance, 'C1' specifies a 16-by-16 seed derived in a standard way from a SHA-256 hash.

It is encouraged to use symmetries beginning with your initials and ending in 'Test' when experimenting with new symmetries.

The 20 official symmetries, for which Catagolue knows how to generate the RLE of the initial seed, are tabulated below:

* C1, 8x32, 4x64, 2x128, 1x256: asymmetric soups of various sizes
* C2_1, C2_2, C2_4: 180° (two-fold) rotational symmetry
* C4_1, C4_4: 90° (four-fold) rotational symmetry
* D2_+1, D2_+2: reflectional symmetry along an orthogonal line
* D2_x: reflectional symmetry along a diagonal line
* D4_+1, D4_+2, D4_+4: reflectional symmetry along two perpendicular orthogonal lines
* D4_x1, D4_x4: reflectional symmetry along two perpendicular diagonal lines
* D8_1, D8_4: reflectional symmetry along four orthogonal/diagonal through a common center

If a topology is specified, it will be appended to the rule with a delimiting colon, with any 'x' replaced by a comma, any 'f' replaced by an asterisk, and any 'p' replaced by a plus sign. This allows Catagolue to generate RLEs compatible with the bounded grid support in [[Golly]].

==Objects==

An object must satisfy one of the following regular expressions:

* <tt>zz_[A-Z]+</tt> for unclassifiable infinite-growth patterns;
* <tt>PATHOLOGICAL</tt> for unclassifiable objects which do not appear to grow infinitely;
* <tt>me(gasized|ssless|ethuselah)_[0-9]+(h|k)</tt> for long-lived soups;
* <tt>gun(true)?_[0-9]+</tt> for guns in the [https://catagolue.hatsya.com/census/b3s23/synthesis-costs/gun <tt>gun</tt>] and [https://catagolue.hatsya.com/census/b3s23/synthesis-costs/guntrue <tt>guntrue</tt>] tabulations of <tt>synthesis-costs</tt>;
* <tt>yl[0-9]+_[0-9]+_[0-9]+_[a-z]+</tt> for classifiable linear growth patterns;
* <tt>ov_[spq][0-9]+ for oversized objects;
* <tt>x[spq][0-9]+(_[a-z0-9]+)+</tt> for everything else.

If an object begins with the letter 'x', it is assumed to be an [[apgcode]] giving an exact canonical form of the pattern. An object beginning with 'y' is a classifiable infinite-growth pattern, and an object beginning with 'ov' is oversized (too large to admit a Catagolue-friendly apgcode).

{{CatagolueNavbox}}

[[Category:Censuses]]

List of natural spaceships

2025-09-01T22:43:18Z

Atavoidirc: /* Semi-natural spaceships */

This is a '''list of [[natural]] [[spaceship]]s''' in the [[Conway's Game of Life|Game of Life]], specifically [[Catagolue]]'s B3/S23/[[symmetry|C1]] census as of October 15, 2022, comprising slightly over 3 quadrillion object occurrences.

In addition, several objects that have appeared naturally or semi-naturally but are not in the Catagolue census are included in a separate table after the main natural objects table (pink).

This is not a list of [[common]] objects, as certainly only the first few rows occur frequently, and some would argue only [[glider]] truly fits the definition of common.

The [[relative frequency]] column gives an estimate of the fraction of all randomly-occurring spaceships. However, glider accounts for 99.8% of spaceship occurrences, and the patterns in this table beyond row 5 occur so infrequently that their order in the table should be viewed as approximate.

== Truly natural spaceships ==
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! Image
! Pattern
! [[Period]]
! [[Heat]]
! [[Speed]]
! Minimum # of [[cell]]s
! [[Glider synthesis|Glider cost]]
! [[Relative frequency]]
! [[Frequency class]]
! [[Apgcode]]
|-
! 1
| [[File:Glider.png|64px]]
| [[Glider]]
| {{periodS|4|brief}}
| 4
| [[c/4 diagonal]]
| 5
| {{gliders|2|brief}}
| 1 in 1.0019127<br>(99.809%)
| 1.8
| {{LinkCatagolue|xq4_153|style=tabulated}}
|-
! 2
| [[File:Lwss.png|64px]]
| [[Lightweight spaceship]]
| 4
| 11
| [[c/2 orthogonal|2c/4 orthogonal]]
| 9
| {{gliders|3|brief}}
| 1 in 685.81<br>(0.146%)
| 11.2
| {{LinkCatagolue|xq4_6frc|style=tabulated}}
|-
! 3
| [[File:Mwss.png|64px]]
| [[Middleweight spaceship]]
| 4
| 15
| 2c/4 orthogonal
| 11
| 3
| 1 in 2,603.1<br>(0.038%)
| 13.2
| {{LinkCatagolue|xq4_27dee6|style=tabulated}}
|-
! 4
| [[File:Hwss.png|64px]]
| [[Heavyweight spaceship]]
| 4
| 19
| 2c/4 orthogonal
| 13
| 3
| 1 in 14,979<br>(0.007%)
| 15.7
| {{LinkCatagolue|xq4_27deee6|style=tabulated}}
|-
! 5
| [[File:Mwssonmwss1.png|64px]]
| [[MWSS on MWSS 1]]
| 4
| 29
| 2c/4 orthogonal
| 20
| {{gliders|5|brief}}
| 1 in 5.32 billion
| 34.1
| {{LinkCatagolue|xq4_27dee6z4eb776|style=tabulated}}
|-
! 6
| [[File:Hwssonhwss1.png|64px]]
| [[HWSS on HWSS 1]]
| 4
| 36
| 2c/4 orthogonal
| 22
| {{gliders|6|brief}}
| 1 in 17.8 billion
| 35.9
| {{LinkCatagolue|xq4_27deee6z4eb7776|style=tabulated}}
|-
! 7
| [[File:Lwssonmwss1.png|64px]]
| [[LWSS on MWSS 1]]
| 4
| 26.5
| 2c/4 orthogonal
| 20
| {{gliders|7|brief}}
| 1 in 45.1 billion
| 37.2
| {{LinkCatagolue|xq4_27de6z4eb776|style=tabulated}}
|-
! 8
| [[File:Lwssonmwss2.png|64px]]
| [[LWSS on MWSS 2]]
| 4
| 26.5
| 2c/4 orthogonal
| 23
| 6
| 1 in 56.4 billion
| 37.5
| {{LinkCatagolue|xq4_0791h1az8smec|style=tabulated}}
|-
! 9
| [[File:Lwssonhwss1.png|64px]]
| [[LWSS on HWSS 1]]
| 4
| 29
| 2c/4 orthogonal
| 20
| 7
| 1 in 62.2 billion
| 37.7
| {{LinkCatagolue|xq4_27de6z4eb7776|style=tabulated}}
|-
! 10
| [[File:Lwssonmwss3.png|64px]]
| [[LWSS on MWSS 3]]
| 4
| 26
| 2c/4 orthogonal
| 23
| 7
| 1 in 117 billion
| 38.6
| {{LinkCatagolue|xq4_27du6ze98885|style=tabulated}}
|-
! 11
| [[File:Mwssonmwss4.png|64px]]
| [[MWSS on MWSS 4]]
| 4
| 30
| 2c/4 orthogonal
| 26
| 7
| 1 in 180 billion
| 39.2
| {{LinkCatagolue|xq4_06eed72zaghgis|style=tabulated}}
|-
! 12
| [[File:Lwssonhwss2.png|64px]]
| [[LWSS on HWSS 2]]
| 4
| 29
| 2c/4 orthogonal
| 20
| 7
| 1 in 346 billion
| 40.1
| {{LinkCatagolue|xq4_6ed72z6777be4|style=tabulated}}
|-
! 13
| [[File:Lwssonhwss7.png|64px]]
| [[LWSS on HWSS 7]]
| 4
| 29.5
| 2c/4 orthogonal
| 25
| 7
| 1 in 362 billion
| 40.2
| {{LinkCatagolue|xq4_27dumze988885|style=tabulated}}
|-
! 14
| [[File:Lwssonhwss3.png|64px]]
| [[LWSS on HWSS 3]]
| 4
| 30.5
| 2c/4 orthogonal
| 22
| 6
| 1 in 405 billion
| 40.4
| {{LinkCatagolue|xq4_27de6zw8smeeec|style=tabulated}}
|-
! 15
| [[File:Mwssonmwss5.png|64px]]
| [[MWSS on MWSS 5]]
| 4
| 29.5
| 2c/4 orthogonal
| 26
| 7
| 1 in 449 billion
| 40.5
| {{LinkCatagolue|xq4_27due6ze98885|style=tabulated}}
|-
! 16
| [[File:Lwssonhwss5.png|64px]]
| [[LWSS on HWSS 5]]
| 4
| 31
| 2c/4 orthogonal
| 22
| 7
| 1 in 450 billion
| 40.5
| {{LinkCatagolue|xq4_27de6z8smeeec|style=tabulated}}
|-
! 17
| [[File:Mwssonmwss2.png|64px]]
| [[MWSS on MWSS 2]]
| 4
| 29
| 2c/4 orthogonal
| 20
| 7
| 1 in 467 billion
| 40.6
| {{LinkCatagolue|xq4_27dee6zw4eb776|style=tabulated}}
|-
! 18
| [[File:Lwssonhwss4.png|64px]]
| [[LWSS on HWSS 4]]
| 4
| 31
| 2c/4 orthogonal
| 22
| 6
| 1 in 515 billion
| 40.7
| {{LinkCatagolue|xq4_027deee6z8smec|style=tabulated}}
|-
! 19
| [[File:Mwssonhwss2.png|64px]]
| [[MWSS on HWSS 2]]
| 4
| 33.5
| 2c/4 orthogonal
| 22
| 7
| 1 in 536 billion
| 40.8
| {{LinkCatagolue|xq4_27dee6z4eb7776|style=tabulated}}
|-
! 20
| [[File:Mwssonmwss3.png|64px]]
| [[MWSS on MWSS 3]]
| 4
| 30
| 2c/4 orthogonal
| 24
| 7
| 1 in 569 billion
| 40.9
| {{LinkCatagolue|xq4_677be4zx48889e|style=tabulated}}
|-
! 21
| [[File:Lwssonhwss6.png|64px]]
| [[LWSS on HWSS 6]]
| 4
| 31
| 2c/4 orthogonal
| 22
| 7
| 1 in 648 billion
| 41.0
| {{LinkCatagolue|xq4_06eeed72zcems8|style=tabulated}}
|-
! 22
| [[File:Mwssonhwss10.png|64px]]
| [[MWSS on HWSS 10]]
| 4
| 33.5
| 2c/4 orthogonal
| 27
| 7
| 1 in 994 billion
| 41.7
| {{LinkCatagolue|xq4_6eeed72zaghgis|style=tabulated}}
|-
! 23
| [[File:Mwssonhwss6.png|64px]]
| [[MWSS on HWSS 6]]
| 4
| 35
| 2c/4 orthogonal
| 24
| 7
| 1 in 1.01 trillion
| 41.7
| {{LinkCatagolue|xq4_sighgazz791hh1a|style=tabulated}}
|-
! 24
| [[File:Mwssonhwss12.png|64px]]
| [[MWSS on HWSS 12]]
| 4
| 34
| 2c/4 orthogonal
| 28
| 7
| 1 in 1.14 trillion
| 41.9
| {{LinkCatagolue|xq4_0791hh1az8smeec|style=tabulated}}
|-
! 25
| [[File:Mwssonhwss14.png|64px]]
| [[MWSS on HWSS 14]]
| 4
| 34
| 2c/4 orthogonal
| 28
| 7
| 1 in 1.24 trillion
| 42.0
| {{LinkCatagolue|xq4_6eed72zaghhgis|style=tabulated}}
|-
! 26
| [[File:Mwssonhwss3.png|64px]]
| [[MWSS on HWSS 3]]
| 4
| 33.5
| 2c/4 orthogonal
| 22
| 7
| 1 in 1.41 trillion
| 42.2
| {{LinkCatagolue|xq4_06eeed72z677be4|style=tabulated}}
|-
! 27
| [[File:Mwssonhwss7.png|64px]]
| [[MWSS on HWSS 7]]
| 4
| 35
| 2c/4 orthogonal
| 24
| 7
| 1 in 1.57 trillion
| 42.3
| {{LinkCatagolue|xq4_aghgiszza1hh197|style=tabulated}}
|-
! 28
| [[File:Mwssonhwss15.png|64px]]
| [[MWSS on HWSS 15]]
| 4
| 33
| 2c/4 orthogonal
| 28
| 7
| 1 in 1.64 trillion
| 42.4
| {{LinkCatagolue|xq4_27dee6zw4eb7776|style=tabulated}}
|-
! 29
| [[File:Mwssonhwss5.png|64px]]
| [[MWSS on HWSS 5]]
| 4
| 34.5
| 2c/4 orthogonal
| 24
| 7
| 1 in 1.78 trillion
| 42.5
| {{LinkCatagolue|xq4_0sighhgazz791h1a|style=tabulated}}
|-
! 30
| [[File:Mwssonhwss8.png|64px]]
| [[MWSS on HWSS 8]]
| 4
| 34.5
| 2c/4 orthogonal
| 24
| 7
| 1 in 1.84 trillion
| 42.5
| {{LinkCatagolue|xq4_0aghhgiszza1h197|style=tabulated}}
|-
! 31
| [[File:Mwssonhwss11.png|64px]]
| [[MWSS on HWSS 11]]
| 4
| 33.5
| 2c/4 orthogonal
| 28
| 7
| 1 in 2.0 trillion
| 42.7
| {{LinkCatagolue|xq4_27duee6ze98885|style=tabulated}}
|-
! 32
| [[File:Mwssonhwss1.png|64px]]
| [[MWSS on HWSS 1]]
| 4
| 33
| 2c/4 orthogonal
| 22
| 7
| 1 in 2.1 trillion
| 42.7
| {{LinkCatagolue|xq4_27dee6zw4eb7776|style=tabulated}}
|-
! 33
| [[File:Mwssonhwss4.png|64px]]
| [[MWSS on HWSS 4]]
| 4
| 34.5
| 2c/4 orthogonal
| 24
| 7
| 1 in 2.1 trillion
| 42.7
| {{LinkCatagolue|xq4_27dee6zx8smeeec|style=tabulated}}
|-
! 34
| [[File:Mwssonhwss9.png|64px]]
| [[MWSS on HWSS 9]]
| 4
| 32.5
| 2c/4 orthogonal
| 25
| 7
| 1 in 2.1 trillion
| 42.8
| {{LinkCatagolue|xq4_02111197zcssqe4|style=tabulated}}
|-
! 35
| [[File:Mwssonhwss13.png|64px]]
| [[MWSS on HWSS 13]]
| 4
| 33.5
| 2c/4 orthogonal
| 28
| 7
| 1 in 2.4 trillion
| 43.0
| {{LinkCatagolue|xq4_27duu6ze988885|style=tabulated}}
|-
! 36
| [[File:Coeship.png|64px]]
| [[Coe ship]]
| {{periodS|16|brief}}
| 38
| 8c/16 orthogonal
| 28
| 7
| 1 in 3.6 trillion
| 43.5
| {{LinkCatagolue|xq16_gcbgzvgg826frc|style=tabulated}}
|-
! 37
| [[File:Hwssonhwss8.png|64px]]
| [[HWSS on HWSS 8]]
| 4
| 37
| 2c/4 orthogonal
| 29
| 7
| 1 in 4.4 trillion
| 43.8
| {{LinkCatagolue|xq4_06eeed72zaghhgis|style=tabulated}}
|-
! 38
| [[File:Hwssonhwss2.png|64px]]
| [[HWSS on HWSS 2]]
| 4
| 36
| 2c/4 orthogonal
| 22
| 7
| 1 in 5.8 trillion
| 44.2
| {{LinkCatagolue|xq4_27deee6zw4eb7776|style=tabulated}}
|-
! 39
| [[File:Hwssonhwss5.png|64px]]
| [[HWSS on HWSS 5]]
| 4
| 39
| 2c/4 orthogonal
| 26
| 7
| 1 in 6.1 trillion
| 44.3
| {{LinkCatagolue|xq4_aghhgiszzwa1hh197|style=tabulated}}
|-
! 40
| [[File:Hwssonhwss4.png|64px]]
| [[HWSS on HWSS 4]]
| 4
| 39
| 2c/4 orthogonal
| 26
| 6
| 1 in 6.6 trillion
| 44.4
| {{LinkCatagolue|xq4_0aghhgiszza1hh197|style=tabulated}}
|-
! 41
| [[File:Hwssonhwss6.png|64px]]
| [[HWSS on HWSS 6]]
| 4
| 37
| 2c/4 orthogonal
| 29
| 7
| 1 in 9.4 trillion
| 44.9
| {{LinkCatagolue|xq4_027deee6zsighhga|style=tabulated}}
|-
! 42
| [[File:Hwssonhwss10.png|64px]]
| [[HWSS on HWSS 10]]
| 4
| 37
| 2c/4 orthogonal
| 31
| 7
| 1 in 10 trillion
| 45.0
| {{LinkCatagolue|xq4_027deee6zsighhga|style=tabulated}}
|-
! 43
| [[File:Hwssonhwss7.png|64px]]
| [[HWSS on HWSS 7]]
| 4
| 37
| 2c/4 orthogonal
| 29
| 7
| 1 in 11 trillion
| 45.1
| {{LinkCatagolue|xq4_27duue6ze988885|style=tabulated}}
|-
! 44
| [[File:Hwssonhwss9.png|64px]]
| [[HWSS on HWSS 9]]
| 4
| 37
| 2c/4 orthogonal
| 30
| 7
| 1 in 13 trillion
| 45.4
| {{LinkCatagolue|xq4_a1hh197zx6777be4|style=tabulated}}
|-
! 45
| [[File:Sidecar.png|64px]]
| [[Sidecar]]
| 4
| 33.5
| 2c/4 orthogonal
| 24
| 8
| <1 in 50 trillion
| 47
| {{LinkCatagolue|xq4_027deee6z4eqscc6|style=tabulated}}
|-
! 46
| [[File:Lightweightschickengine.png|96px]]
| [[Lightweight Schick engine]]
| {{periodS|12|brief}}
| 43.2
| 6c/12 orthogonal
| 39
| {{gliders|9|brief}}
| <1 in 100 trillion
| 48
| {{LinkCatagolue|xq12_fh1i0i1hfzw8sms8zxfjf|style=tabulated}}
|-
! 47
| [[File:Loafer.png|64px]]
| [[Loafer]]
| {{periodS|7|brief}}
| 14.6
| c/7 othogonal
| 20
| {{gliders|8|brief}}
| <1 in 200 trillion
| 49
| {{LinkCatagolue|xq7_3nw17862z6952|style=tabulated}}
|-
! 48
| [[File:mwssandhwssdraggingblock.png|64px]]
| style="background:pink" | [[MWSS and HWSS dragging block]]
| style="background:pink" | 4
| style="background:pink" | 38.5
| style="background:pink" | 2c/4 orthogonal
| style="background:pink" | 28
| style="background:pink" | 9
| style="background:pink" |
| style="background:pink" |
| style="background:pink" | {{LinkCatagolue|xq4_gfvuwogwggz131y2crf7|style=tabulated}}
|}

== Semi-natural spaceships ==
There are also a handful of spaceships which have occurred in symmetric soups, but not asymmetric soups.
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! Image
! Pattern
! [[Period]]
! [[Heat]]
! [[Speed]]
! Minimum # of [[cell]]s
! [[Glider synthesis|Glider cost]]
! [[Relative frequency]]
! [[Frequency class]]
! [[Apgcode]]
|-
! 1
| [[File:x66.png|64px]]
| style="background:pink" | [[x66]]
| style="background:pink" | 4
| style="background:pink" | 31
| style="background:pink" | 2c/4 orthogonal
| style="background:pink" | 34
| style="background:pink" | {{gliders|11|brief}}
| style="background:pink" |
| style="background:pink" |
| style="background:pink" | {{LinkCatagolue|xq4_0oorxroozdjio404oijd|style=tabulated}}
|-
! 2
| [[File:Copperhead.png|64px]]
| style="background:pink" | [[Copperhead]]
| style="background:pink" | 10
| style="background:pink" | 26.8
| style="background:pink" | c/10 orthogonal
| style="background:pink" | 28
| style="background:pink" | {{gliders|13|brief}}
| style="background:pink" |
| style="background:pink" |
| style="background:pink" | {{LinkCatagolue|xq10_o5995ozes88sezw33|style=tabulated}}
|-
! 3
| [[File:bigabehindtwolwss.png|64px]]
| style="background:pink" | [[Big A]]
| style="background:pink" | 4
| style="background:pink" | 51
| style="background:pink" | 2c/4 orthogonal
| style="background:pink" | 32
| style="background:pink" | {{gliders|18|brief}}
| style="background:pink" |
| style="background:pink" |
| style="background:pink" | {{LinkCatagolue|xq4_7911azy0ehhvhzsigga|style=tabulated}}
|-
! 4
| [[File:dart.png|64px]]
| style="background:pink" | [[Dart]]
| style="background:pink" | 3
| style="background:pink" | 32
| style="background:pink" | c/3 orthogonal
| style="background:pink" | 34
| style="background:pink" | {{gliders|24|brief}}
| style="background:pink" |
| style="background:pink" |
| style="background:pink" | {{LinkCatagolue|xq3_mhqkzarahh0heezdhb5|style=tabulated}}
|-
! 5
| [[File:58p8h4v0.png|96px]]
| style="background:pink" | [[58P8H4V0]]
| style="background:pink" | 8
| style="background:pink" | 50
| style="background:pink" | 2c/4 orthogonal
| style="background:pink" | 58
| style="background:pink" | {{gliders|25|brief}}
| style="background:pink" |
| style="background:pink" |
| style="background:pink;max-width:40px;overflow-wrap:break-word;" | {{LinkCatagolue|xq8_ciire2272hm0mh2722eriiczw1x2c8960698c2x1|style=tabulated}}
|-
! 6
| [[File:44p5h2v0.png|64px]]
| style="background:pink" | [[44P5H2V0]]
| style="background:pink" | 5
| style="background:pink" | 47.2
| style="background:pink" | 2c/5 orthogonal
| style="background:pink" | 44
| style="background:pink" | {{gliders|23|brief}}
| style="background:pink" |
| style="background:pink" |
| style="background:pink" | {{LinkCatagolue|xq5_0sg3pnxnp3gsz4s01tve0evt10s4|style=tabulated}}
|-
! 7
| [[File:54p12h6v0.png|96px]]
| style="background:pink" | [[54P12H6V0]]
| style="background:pink" | 16
| style="background:pink" | 46.0
| style="background:pink" | 6c/12 orthogonal
| style="background:pink" | 54
| style="background:pink" | {{gliders|22|brief}}
| style="background:pink" |
| style="background:pink" |
| style="background:pink;max-width:40px;overflow-wrap:break-word;" | {{LinkCatagolue|xq12_cur6wgs2i6o0o6i2sgw6ruczy2nh011x110hn|style=tabulated}}
|}
{{CatagolueNavbox}}

[[Category:Lists of patterns]]
[[Category:Lists of patterns with synthesis costs]]

Canada goose

2025-07-25T19:51:22Z

Atavoidirc: /* Glider synthesis */

{{About|the [[glider]] [[tagalong]]|the [[extensible]] [[greyship]]|Canada Grey}}
{{Spaceship
|name = Canada goose
|pname = canadagoose
|type = Tagalong
|c = 36
|bx = 13
|by = 12
|dir = Diagonal
|p = 4
|m = 2
|s = c/4
|z = c/4
|h = 28.0
|symmetry = n/e
|discoverer = Jason Summers
|discoveryear = 1999
|rulemin = B3/S23
|rulemax = B378/S023678
|isorulemin = B3-ky/S2-n3-cey
|isorulemax = B2in34ceqw5aceky6-k78/S0234-aikrz5ekny678
|plaintext = true
|rle = true
|animated = true
|viewerconfig = #C [[ HEIGHT 600 THUMBSIZE 3 ZOOM 36 GPS 4 TRACKLOOP 4 -1/4 -1/4 ]]
|apgcode = xq4_3518ow8c4624zwgc2e0kt288zw33
|pentadecathlonid = 36P4H1V1.1
}}
The '''Canada goose''' was found by [[Jason Summers]] in January {{year|1999}}. It consists of a [[glider]] pulling a [[tagalong]].

At the time of its discovery, the Canada goose was the smallest known diagonal [[spaceship]] other than the glider, but this record has since been beaten, first by [[Orion 2]], and more recently by the [[crab]].

== Modifications ==
It was discovered in January 1999 by [[Stephen Silver]] that Canada geese can be welded together by their wings, creating an [[extensible]] spaceship. [[Gabriel Nivasch]], later that same month, reported that because the [[swan]] uses the same wing, swans and Canada geese can be welded together. He also found that a [[glider emulator]] can replace the glider at the front end of the Canada goose.

The [[crane]] has the same wing as well, so may also be welded.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = weldedgeese
|viewerconfig = #C [[ HEIGHT 400 THUMBSIZE 2 ZOOM 8 ]]
|position = center
|caption = Two Canada geese welded together, as discovered by Stephen Silver
|apgcode = xq4_y63518ow8c4624zy88k2e0kt288z3518ow8c0222bzwgc2e0kt288zw33
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = swanweldgoose
|viewerconfig = #C [[ HEIGHT 400 THUMBSIZE 2 ZOOM 8 ]]
|position = center
|caption = A swan and a Canada goose welded together, as discovered by Gabriel Nivasch
|apgcode = xq4_xgc1hbzsm0201zfnhea82ez01ppozy0lskoogwgg0a64zy21p0qf3ppozy31021x26
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 29, y = 30, rule = B3/S23
16b3o$16bo9b2o$17bo6b3obo$2o17b2o2b2o$obo17bo$o23bo$3bo4bo11b2o3bo$3b2o2bobo9bobob2o$7bobo8bo2bo2bob2o$7b2o10bo3b2o$7bo11bo$6bo2bo6b4o$14bo$7bobo3b2o4bo$9b2o$10bo3bo2$12bo$10b2o$10bo$11bo$12bo2$12b2ob2o$14b2obo$14b2obo2$15bobo$17bo$17bo!
|viewerconfig = #C [[ HEIGHT 400 THUMBSIZE 2 ZOOM 8 ]]
|position = center
|caption = A crane and a Canada goose welded together
|apgcode = xq4_x235g88zy3ss02csozy9gcv721160848zc68y0ggg0sbv6y433451a8zxjfs8rj8gz04b92w222
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = longcanadagoose
|viewerconfig = #C [[ HEIGHT 400 THUMBSIZE 2 ZOOM 8 ]]
|position = center
|caption = A Canada goose with the front glider replaced by a [[glider emulator]].
|apgcode = xq4_wgmg8g0gt6zgg1klc08py7ob8ooz111y3e730440ui2902069hsgzy62ge6gg011619asgx147m2gzy2dc4ic813w3so8y02e70ko8031zy51224scgx10d6ugzyb2ceaoc011
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 19, y = 19, rule = B3/S23
3o$o9b2o$bo6b3obo$3b2o2b2o$4bo$8bo$4b2o3bo$3bobob2o5b2o$3bobo2bob2ob2o3bo$2bo4b2o6bob2o$2b2o9bo$2b2o7b3o$10bo3bo$8bo$7b2o4bo$8b2o$8b3o$8bo$9b2o!
|viewerconfig = #C [[ HEIGHT 400 THUMBSIZE 2 ZOOM 8 ]]
|position = center
|caption = A Canada goose pulling an unnamed tagalong (which may itself support a larger tagalong still: {{LinkCatagolue|xq4_y6cc488g0go217zxg8ooc8xc9dh80cozx101o0ghe80rgy053zgouigsf42xd81ze0e|style=brief}} with the same backend as a different such spaceship: {{LinkCatagolue|xq4_y1oo4h93z0o6n211hvc8ea153zk6n455lbfz303x1|style=brief}})
|apgcode = xq4_3518ow8c4624zwgc2e0kt28808ck0gozw33xgo0422j4zy47ba
|style = width:300px;
}}}}
{{gallery bottom}}

== Glider synthesis ==
As of July 2025, the Canada goose is tied for the smallest spaceship to have no glider synthesis discovered.

== External links ==
* {{LinkLexicon|lex_c.htm#canadagoose}}
* {{LinkCatagolue|xq4_3518ow8c4624zwgc2e0kt288zw33}}
* {{LinkPentadecathlonObject|36P4H1V1.1}}

Density

2024-05-02T13:17:44Z

Atavoidirc: /* Densities of other objects */

{{Glossary}}
The '''density''' of a pattern is the proportion of live [[cell]]s within its [[bounding box]].

==Still lifes==
The maximum densities of square still lifes up to {{times|20|20}} were known in 2002.<ref>{{cite web|url=https://web.archive.org/web/20130731001049/http://www.ai.sri.com/~nysmith/life |title=Maximum Density Still Life |publisher=Neil Yorke-Smith|date=August 4, 2003}}</ref>

The general problem of finding the maximum population of an {{times|n|n}} square [[pseudo]] [[still life]] (<tt>{{OEIS|A055397|tt=tt}}(n)</tt>) was solved for all n in 2012.<ref name=ref1>{{cite web|url=https://people.eng.unimelb.edu.au/pstuckey/papers/still-life.pdf | title=A Complete Solution to the Maximum Density Still Life Problem | publisher=Geoffrey Chu, Peter J. Stuckey, NICTA Victoria Laboratory, Department of Computing and Information Systems, University of Melbourne, Australia | date=November 8, 2013}}</ref> It is given by the following function:

<tt>first=(0,0,4,6,8,16,18,28,36,43,54,64,76,90,104,119,136,152,171,190,210,232,253,276,302,326,353,379,407,437,467,497,531,563,598,<br />
<span style="opacity: 0">. . . .</span>633,668,706,744,782,824,864,907,949,993,1039,1085,1132,1181,1229,1280,1331,1382,1436,1490,1545,1602,1658,1717,1776,1835)<br />def cells(n):<br /><span style="opacity: 0">. . </span>if n<61:<br /><span style="opacity: 0">. . . . </span>return first[n]<br /><span style="opacity: 0">. . </span>elif n%54 in {0,1,3,8,9,11,16,17,19,25,27,31,33,39,41,47,49}:<br /><span style="opacity: 0">. . . . </span>return ⌊(27*n<sup>2</sup>+34*n)/54⌋-2<br /><span style="opacity: 0">. . </span>else:<br /><span style="opacity: 0">. . . . </span>return ⌊(27*n<sup>2</sup>+34*n)/54⌋-1</tt>.

The following table contains maximum density still life information for side lengths through 25.

{|class="wikitable sortable" style="text-align:center"
|-
! Side length !! Max. density !! Max. population<sup>&dagger;</sup><br/>(example) !! Example pattern(s) !! Total patterns
|-
| 1 || 0 || 0 || || 0
|-
| 2 || 1 || 4<br/>[[block]] || {{EmbedViewer|pname=block|viewerconfig= #C [[ THUMBSIZE 3 ]]}} || 1
|-
| 3 || 0.6667 || 6<br/>[[ship]] || {{EmbedViewer|pname=ship|viewerconfig= #C [[ THUMBSIZE 3 ]]}} || 1
|-
| 4 || 0.5 || 8<br/>[[pond]]<br/>[[long ship]] || {{EmbedViewer|pname=pond|viewerconfig= #C [[ THUMBSIZE 3 ]]}}<br>{{EmbedViewer|pname=longship|viewerconfig= #C [[ THUMBSIZE 3 ]]}} || 2
|-
| 5 || 0.64 || 16<br/>{{LinkCatagolue|xs16_rr0rr|name=four blocks|style=raw}} || {{EmbedViewer|pname=4blocks|viewerconfig= #C [[ THUMBSIZE 3 ]]}} || 1
|-
| 6 || 0.5 || 18<br/>two [[long shillelagh]]s<br/>{{LinkCatagolue|xs18_j5mgdbz1101|name=trans-snake-tie with ship|style=raw}}<br/>[https://catagolue.hatsya.com/object/xs18_gbr0rrz11/b3s23 three blocks with ship] || {{EmbedViewer|pname=twolongshillelaghs|viewerconfig= #C [[ THUMBSIZE 3 ]]}} <br />{{EmbedViewer|pname=transsnaketiewithship|viewerconfig= #C [[ THUMBSIZE 3 ]]}} <br />{{EmbedViewer|pname=3blockswithship|viewerconfig= #C [[ THUMBSIZE 3 ]]}} <br />{{EmbedViewer|pname=6x6maxdensitystilllifes|viewerconfig= #C [[ THUMBSIZE 3 ]]}} || 9
|-
| 7 || 0.5714 || 28<br/>{{LinkCatagolue|xs28_db8n9arz3123032|name=tub of snakes|style=raw}} || {{EmbedViewer|pname=7x7maxdensity |viewerconfig= #C [[ THUMBSIZE 3 ]]}} || 1
|-
| 8 || 0.5625 || 36<br/>nine blocks || {{EmbedViewer|pname=9blocks|viewerconfig= #C [[ THUMBSIZE 3 ]]}} || 1
|-
| 9 || 0.5309 || 43 || {{EmbedViewer|pname=43cell9x9pseudostilllifes|viewerconfig= #C [[ THUMBSIZE 3 ]]}} || 10
|-
| 10 || 0.5400 || 54 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=10x10maxdensity }} || >100
|-
| 11 || 0.5289 || 64<br/>sixteen blocks|| {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=11x11maxdensity }} || 1
|-
| 12 || 0.5278 || 76 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=12x12maxdensity }}
|-
| 13 || 0.5325 || 90 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=13x13maxdensity }}
|-
| 14 || 0.5306 || 104 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=14x14maxdensity }}
|-
| 15 || 0.5289 || 119 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=15x15maxdensity }}
|-
| 16 || 0.531 || 136 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=16x16maxdensity }}
|-
| 17 || 0.526 || 152 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=17x17maxdensity }}
|-
| 18 || 0.528 || 171 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=18x18maxdensity }}
|-
| 19 || 0.526 || 190 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=19x19maxdensity }}
|-
| 20 || 0.525 || 210 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=20x20maxdensity }}
|-
| 21 || 0.526 || 232 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=21x21maxdensity }}
|-
| 22 || 0.523 || 253 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=22x22maxdensity }}
|-
| 23 || 0.522 || 276 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=23x23maxdensity }}
|-
| 24 || 0.523 || 301 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=24x24maxdensity }}
|-
| 25 || 0.522 || 326 || {{EmbedViewer|viewerconfig= #C [[ THUMBSIZE 3 ]] | pname=25x25maxdensity }}
|}

*For any side length of the form 3n-1, a segment of [[block agar]] can be used to reach a population of 4n<sup>2</sup>; to n=4 this is the optimal solution, as can be seen in the above table.
*The maximum density of an {{times|n|n}} still life is greater than or equal to 1/2 for all finite n>1.<ref name="cgolmc_1">{{citeCGoLMC|section=2.5}}</ref>

== Densities of other objects ==
* The maximum density of a still life agar was proven to be 1/2 by [[Noam Elkies]]<ref>{{cite web|url=https://arxiv.org/abs/math/9905194 |title=The still-Life density problem and its generalizations|author=Noam D. Elkies| accessdate=May 26, 2022| date=May 31, 1999}}</ref> (this is known as the '''still life conjecture''').
* The maximum average density of an oscillating agar is conjectured but not proven to be 1/2. The current upper bound is 1176/2087≈0.563, proven by [[Keith Amling]] in {{year|2024}}.<ref name="post175245" />
* The density of [[ash]] is [[Achim Flammenkamp's census|approximately 0.0287]] (1 in 35).
* By observation, the density of a [[space dust]]y oscillator or spaceship is usually between 0.25 and 0.3.<ref name="post146282" />

==References==
<references>
<ref name="post175245">{{LinkForumThread
|format = ref
|title = Re: Unproven conjectures
|p = 175245
|author = Keith Amling
|date = January 9, 2024
}}</ref>
<ref name="post146282">{{LinkForumThread
|format = ref
|title = Re: Can we substantiate this claim?
|p = 146282
|author = David Raucci
|date = May 29, 2022
}}</ref>
</references>

==External links==
{{LinkLexicon|lex_d.htm#density}}
*[https://golhobby.com/patman Maximum Density Still Lifes-PatMan pattern collection] all n=2...200

User:Atavoidirc

2024-03-22T17:31:34Z

Atavoidirc: /* Other Pages */

__NOTOC__
This is a hub page
[[User:Atavoidirc/Spaceship table]]
==[[User:GUYTU6J]]/Neighbourhood==
{{User:GUYTU6J/Neighbourhood}}
==Life wiki Pages==
* [[LifeWiki:Game of Life Status page]]
* [[LifeWiki:Spaceship Search Status Page]]
* [[LifeWiki:Smallest Spaceships Supporting Specific Speeds]]
* [[LifeWiki:Project OmniOsci/Overview]]
* [[LifeWiki:LifeViewer cheatsheet for LifeWiki articles]]
* [[LifeWiki:List of ongoing projects]]

==Other Pages==
* [[Table of oscillators by period]]
* [https://conwaylife.com/wiki/Special:PrefixIndex?prefix=Galoomba&namespace=2 Galoombauserpages]

==Rules in Userspace==
* [[User:Carbon6/Gnarl]]
* [[User:Drc/GlideLife]]
* [[User:Prime Raptor21/Nothing (Rule)]]
* [[User:Evin/BiLife]]
* [[User:Moosey/eatsplosion]]
* [[User:Evin/Silverseeds]]
* [[User:Evin/OCA:E1]]
* [[User:Evin/Wlife]]
* [[User:GUYTU6J/OCA:Glimmering Garden]]
* [[User:Yujh/B34kz5e7c8/S23-a4ityz5k]]
* [[User:Cvojan/TubularTest]]
* [[User:Ultimium/OCA:LeapLife]]
* [[User:Cgoler2/rrlife]]
* [[User:Cgoler2/Clife]]
* [[User:Pzq Alex/BitLife]]

User:Atavoidirc

2024-03-22T17:30:25Z

Atavoidirc: /* Other Pages */

__NOTOC__
This is a hub page
[[User:Atavoidirc/Spaceship table]]
==[[User:GUYTU6J]]/Neighbourhood==
{{User:GUYTU6J/Neighbourhood}}
==Life wiki Pages==
* [[LifeWiki:Game of Life Status page]]
* [[LifeWiki:Spaceship Search Status Page]]
* [[LifeWiki:Smallest Spaceships Supporting Specific Speeds]]
* [[LifeWiki:Project OmniOsci/Overview]]
* [[LifeWiki:LifeViewer cheatsheet for LifeWiki articles]]
* [[LifeWiki:List of ongoing projects]]

==Other Pages==
* [[Table of oscillators by period]]
* [[Special:PrefixIndex?prefix=Galoomba&namespace=2]]

==Rules in Userspace==
* [[User:Carbon6/Gnarl]]
* [[User:Drc/GlideLife]]
* [[User:Prime Raptor21/Nothing (Rule)]]
* [[User:Evin/BiLife]]
* [[User:Moosey/eatsplosion]]
* [[User:Evin/Silverseeds]]
* [[User:Evin/OCA:E1]]
* [[User:Evin/Wlife]]
* [[User:GUYTU6J/OCA:Glimmering Garden]]
* [[User:Yujh/B34kz5e7c8/S23-a4ityz5k]]
* [[User:Cvojan/TubularTest]]
* [[User:Ultimium/OCA:LeapLife]]
* [[User:Cgoler2/rrlife]]
* [[User:Cgoler2/Clife]]
* [[User:Pzq Alex/BitLife]]

User:Atavoidirc

2024-03-22T16:29:29Z

Atavoidirc: /* Other Pages */

__NOTOC__
This is a hub page
[[User:Atavoidirc/Spaceship table]]
==[[User:GUYTU6J]]/Neighbourhood==
{{User:GUYTU6J/Neighbourhood}}
==Life wiki Pages==
* [[LifeWiki:Game of Life Status page]]
* [[LifeWiki:Spaceship Search Status Page]]
* [[LifeWiki:Smallest Spaceships Supporting Specific Speeds]]
* [[LifeWiki:Project OmniOsci/Overview]]
* [[LifeWiki:LifeViewer cheatsheet for LifeWiki articles]]
* [[LifeWiki:List of ongoing projects]]

==Other Pages==
* [[Table of oscillators by period]]
* [[Special:PrefixIndex?prefix=Galoomba&namespace=2

==Rules in Userspace==
* [[User:Carbon6/Gnarl]]
* [[User:Drc/GlideLife]]
* [[User:Prime Raptor21/Nothing (Rule)]]
* [[User:Evin/BiLife]]
* [[User:Moosey/eatsplosion]]
* [[User:Evin/Silverseeds]]
* [[User:Evin/OCA:E1]]
* [[User:Evin/Wlife]]
* [[User:GUYTU6J/OCA:Glimmering Garden]]
* [[User:Yujh/B34kz5e7c8/S23-a4ityz5k]]
* [[User:Cvojan/TubularTest]]
* [[User:Ultimium/OCA:LeapLife]]
* [[User:Cgoler2/rrlife]]
* [[User:Cgoler2/Clife]]
* [[User:Pzq Alex/BitLife]]

LifeWiki:Moderators

2024-03-20T15:38:26Z

Atavoidirc: added INoMed

'''Moderators''', also known as '''sysops''' (and formerly known as '''Administrators'''), are users who have special tools that aid them in the maintenance of the site. These users may be recommended by the community and are promoted at the discretion of [[User:Nathaniel|Nathaniel]]. They have the ability to protect and delete pages, block malicious users, and undo these actions as well. By default, moderators are appointed for life, but may step down at any time.

This is a list of the current Moderators of LifeWiki (an automatically-generated list is also available from [[Special:Listusers/sysop]]). If you need to tell them something or request their services, feel free to [[LifeWiki:Contact|contact]] one of them.

* [[User:Nathaniel|Nathaniel]] ([[User talk:Nathaniel|Talk]]) – ''Site administrator''
* [[User:Codeholic|Codeholic]] ([[User talk:Codeholic|Talk]])
* [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|Talk]])
* [[User:Sokwe|Sokwe]] ([[User talk:Sokwe|Talk]])
* [[User:Apple_Bottom|Apple Bottom]] ([[User talk:Apple_Bottom|Talk]])
* [[User:Ian07|Ian07]] ([[User talk:Ian07|Talk]])
* [[User:INoMed|INoMed]] ([[User talk:INoMed|Talk]])

Moderators have a few more permissions than [[LifeWiki:Editors|Editors]] on the wiki. Most notably, Moderators can [[LifeWiki:Dispute_resolution|moderate disputes]] and issue bans/warnings while Editors cannot.

== Moderator responsibilities ==
The community looks to moderators to perform essential chores and tasks that require the extra tools that moderators are entrusted with. These duties include:
* '''Deleting pages''': Moderator are responsible for monitoring the [[:Category:Pending deletion|Marked for deletion]] category and carrying out any requested deletions.
** All deletions should be in accordance with the LifeWiki's [[LifeWiki:Deletion policy|deletion policy]].
* '''Blocking users''': Moderator are able to block users in cases where it is necessary to prevent damage to the site. Vandalism is an example of a reason to block.
* '''Protecting pages''': Some pages on the wiki are [[:LifeWiki:Protection policy|protected]].
* '''Editing protected pages''': Any edits to fully protected pages need to be made by moderators. These pages include:
** [[Main Page]] - The main page of LifeWiki
** [[MediaWiki:Common.css]] - The style sheet that determines the overall appearance of all LifeWiki pages
** [[MediaWiki:Sidebar]] - The list of links shown on the left-hand side of all LifeWiki pages
Finally, since moderators are expected to be experienced with the procedures of LifeWiki, editors will often turn to one when they need information or advice.

== Moderator conflicts ==
Moderators should not override or undo another's administrative actions; any such action can lead to a [http://en.wikipedia.org/wiki/Wikipedia:Wheel_war wheel war]. This includes deleting official warnings or notifications placed on a user's talk page; however, another moderator may choose to add their own comments to a user talk page (e.g., for emphasis, clarification, or to point out an overlooked circumstance). This does not apply in cases where there have been new developments since the first action was taken: for example, if one moderator warned a user about inappropriate behaviour (first action), and the user then resumed the behaviour (new developments), any moderator may then proceed to take further action (i.e., blocking) against the user. Also, this does not apply to regular contributions (such as routine editing) done by a moderator; the standard etiquette that applies to all editors should be used for any non-administrative types of contributions.

If a moderator has a disagreement with another moderator's actions, it is recommended that a discussion be started on that moderator's talk page: ask why the first moderator chose that course of action, and point out what other alternatives there may have been (in particular whether any policies apply). If the first moderator agrees, it should be left up to the first moderator to undo their own actions. If there is no existing policy covering the situation, or the policy is ambiguous, a more general discussion involving the rest of the community may be needed to try to establish an appropriate policy.

If you believe that another moderator has in some way undone one of your administrative actions, it is best to assume that the moderator was not aware of your previous action. Do not override the new action; instead, explain the situation to the other moderator and follow the same guidelines as in the previous paragraph.

If two moderators can not reach an agreement on what is appropriate, other moderators may be asked to provide their opinion on the situation. As a last resort, Nathaniel can be asked to provide arbitration.

== See also ==
* [[LifeWiki:Dispute resolution]]

==External links==
* [http://en.wikipedia.org/wiki/Wikipedia:Administrators Wikipedia:Administrators] – Wikipedia's article about moderators and their roles
* [http://en.wikipedia.org/wiki/Wikipedia:Administrators'_how-to_guide How-to guide for administrators] at Wikipedia
* [http://en.wikipedia.org/wiki/Wikipedia:Administrators'_reading_list Reading list for administrators] at Wikipedia

Rule:Durnak wires

2024-03-20T15:10:08Z

Atavoidirc: fixing double redirect

#REDIRECT [[Rule:CoralLifeBalance]]

44P12.2

2024-03-20T15:09:47Z

Atavoidirc: fixing double redirect

#REDIRECT [[Eye of Sauron]]

134P39.1

2023-09-17T17:29:53Z

Atavoidirc:

{{Oscillator
|name = 134P39.1
|pname = 134p39.1
|c = 134
|bx = 25
|by = 29
|p = 39
|m = 39
|h = 33.1
|v = 0.46
|sv = 0.01
|discoverer = Noam Elkies
|discoverer2 = David Buckingham
|discoveryear = 2000
|rulemin = B3/S23
|rulemax = B38/S2378
|rulespecial = [[Conway's Game of Life|Conway's Life]]
|isorulemin = B3/S23
|isorulemax = B36c8/S234cer5-ijqr6aen78
|plaintext = true
|rle = true
|apgcode = xp39_y68kkm0mk13zy91011wgca6zw8e1f0brggy35dll552z355h0nni22q5ic0ccx123z32qj43wgd04bl553zy5dd11
|pentadecathlonid = 134P39.1
|animated = yes
|viewerconfig = #C [[ GPS 3 LOOP 39 THUMBSIZE 2 ZOOM 8 ]]
}}
'''134P39.1''' is an unnamed {{period|39}} [[oscillator]]. It was the first [[non-trivial]] period 39 oscillator to be found,<ref>{{CiteSummersPattern|name=jslife|accessdate=April 9, 2009}}</ref> all previously known period 39 oscillators being made up of disjoint period-3 and period-13 oscillators, and was discovered by [[Noam Elkies]] with the help of [[David Buckingham]] on July 24, {{year|2000}}.<ref>{{cite web|url=http://entropymine.com/jason/life/status.html |title=Game of Life Status page |accessdate=April 9, 2009}}</ref>

It features one of [[Stephen Silver]]'s modifications of [[eater 2]], a large unnamed period 3 oscillator, and a period {{period|13|brief}} oscillator based on [[Buckingham's p13]].

==See also==
*[[90P51]]

==References==
<references />

== External links ==
{{LinkCatagolue|xp39_y68kkm0mk13zy91011wgca6zw8e1f0brggy35dll552z355h0nni22q5ic0ccx123z32qj43wgd04bl553zy5dd11}}
{{LinkPentadecathlonObject|134P39.1}}

[[Category:Unnamed periodic objects]]
[[Category:Least-common-multiple oscillators]]

134P39.1

2023-09-17T17:28:21Z

Atavoidirc:

{{Oscillator
|name = 134P39.1
|pname = 134p39.1
|c = 134
|bx = 25
|by = 29
|p = 39
|m = 39
|h = 33.1
|v = 0.46
|sv = 0.01
|discoverer = Noam Elkies
|discoverer2 = David Buckingham
|discoveryear = 2000
|rulemin = B3/S23
|rulemax = B38/S2378
|rulespecial = [[Conway's Game of Life|Conway's Life]]
|isorulemin = B3/S23
|isorulemax = B36c8/S234cer5-ijqr6aen78
|plaintext = true
|rle = true
|apgcode = xp39_y68kkm0mk13zy91011wgca6zw8e1f0brggy35dll552z355h0nni22q5ic0ccx123z32qj43wgd04bl553zy5dd11
|pentadecathlonid = 134P39.1
|animated = yes
|viewerconfig = #C [[ GPS 3 LOOP 39 THUMBSIZE 2 ZOOM 8 ]]
}}
'''134P39.1''' is an unnamed {{period|39}} [[oscillator]]. It was the first [[non-trivial]] period 39 oscillator to be found,<ref>{{CiteSummersPattern|name=jslife|accessdate=April 9, 2009}}</ref> and was discovered by [[Noam Elkies]] with the help of [[David Buckingham]] on July 24, {{year|2000}}.<ref>{{cite web|url=http://entropymine.com/jason/life/status.html |title=Game of Life Status page |accessdate=April 9, 2009}}</ref>

It features one of [[Stephen Silver]]'s modifications of [[eater 2]], a large unnamed period 3 oscillator, and a period {{period|13|brief}} oscillator based on [[Buckingham's p13]].

==See also==
*[[90P51]]

==References==
<references />

== External links ==
{{LinkCatagolue|xp39_y68kkm0mk13zy91011wgca6zw8e1f0brggy35dll552z355h0nni22q5ic0ccx123z32qj43wgd04bl553zy5dd11}}
{{LinkPentadecathlonObject|134P39.1}}

[[Category:Unnamed periodic objects]]
[[Category:Least-common-multiple oscillators]]

Omniperiodic

2023-09-17T17:27:58Z

Atavoidirc: as p3, p13 and p17 had been discovered prior to 2000, trivial p39 and p51 oscillators could have been constructed

{{Glossary}}
A [[cellular automaton]] is said to be '''omniperiodic''' if it has [[oscillator]]s of all [[period]]s.

[[Conway's Game of Life]] is omniperiodic, since there are oscillators of every period, with the last found period being {{period|41|text=p41}} in July {{year|2023}}. The last periods to be found are as follows:

*{{period|39|text=p39}} (the first [[non-trivial]] example) in July {{year|2000}}
*{{period|27|text=p27}} in November {{year|2002}}
*{{period|51|text=p51}} (the first [[non-trivial]] example) in March {{year|2009}}
*{{period|37|text=p37}} in April {{year|2009}}
*{{period|31|text=p31}} in November {{year|2010}}
*{{period|43|text=p43}} and {{period|53|text=p53}} in April {{year|2013}}
*{{period|23|text=p23}} in November {{year|2019}}
*{{period|38|text=p38}} in January {{year|2022}}
*{{period|34|text=p34}} (the first [[non-trivial]] example) in July {{year|2022}}
*{{period|19|text=p19}} and {{period|41|text=p41}} in July {{year|2023}}

==Large-period oscillators==
In October {{year|1996}}, [[David Buckingham]] wrote the article ''My Experience with B-heptominos in Oscillators''<ref>{{LinkCallahan|patterns/bhept/bhept.html|patternname=Buckingham on B-heptomino/Herschel oscillators|nobullet=nobullet}}</ref> that describes his discovery of [[Herschel conduit]]s, including sufficient [[stable conduit]]s to enable, for the first time, the construction of [[period]] '''''n''''' [[oscillator]]s for every '''''n''''' ≥ 58, and true period '''''n''''' [[gun]]s for every '''''n''''' ≥ 62.

The discovery of the [[Snark]] by [[Mike Playle]] in April 2013 allowed the construction of oscillators of all periods greater than or equal to 43.

==Other rules==
By running [[Dean Hickerson]]'s [[drifter]] searcher to find signals that can be manipulated like Herschels, it is possible to prove that a variety of [[Life-like cellular automata]] are omniperiodic.<ref name="post2521" /><ref name="post139416" /> However, these signals are more like the [[2c/3 wire|2c/3 signal]], in that they operate on a dense background and can closely follow each other. There is a significant possibility that such a signal turner exists for Conway's Game of Life, but no explicit examples have been found.

==See also==
* [[Emu]]
* [[Herschel loop]]

==References==
<references>
<ref name="post2521">{{LinkForumThread
|format = ref
|p = 2521
|title = Re: B3/S234
|author = Matthias Merzenich
|date = June 4, 2010
}}</ref>
<ref name="post139416">{{LinkForumThread
|format = ref
|p = 139416
|title = Re: Suggested LifeWiki edits
|author = Dave Greene
|date = December 26, 2021
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_m.htm#myexperiencewithbheptominosinoscillators|patternname=My Experience with B-heptominos in Oscillators}}
* {{LinkLexicon|lex_o.htm#omniperiodic}}
* {{LinkGoLNews|2011/01/is_life_omniperiodic.html|title=Is Life omniperiodic?|date=January 16, 2011|author=Adam P. Goucher}}
* {{LinkForumThread|format=ref|f=11|t=1217|title=Which Life-like CA have been proven omniperiodic?}}

__NOTOC__

Omniperiodic

2023-09-17T17:26:08Z

Atavoidirc:

{{Glossary}}
A [[cellular automaton]] is said to be '''omniperiodic''' if it has [[oscillator]]s of all [[period]]s.

[[Conway's Game of Life]] is omniperiodic, since there are oscillators of every period, with the last found period being {{period|41|text=p41}} in July {{year|2023}}. The last periods to be found are as follows:

*{{period|39|text=p39}} in July {{year|2000}}
*{{period|27|text=p27}} in November {{year|2002}}
*{{period|51|text=p51}} in March {{year|2009}}
*{{period|37|text=p37}} in April {{year|2009}}
*{{period|31|text=p31}} in November {{year|2010}}
*{{period|43|text=p43}} and {{period|53|text=p53}} in April {{year|2013}}
*{{period|23|text=p23}} in November {{year|2019}}
*{{period|38|text=p38}} in January {{year|2022}}
*{{period|34|text=p34}} (the first [[non-trivial]] example) in July {{year|2022}}
*{{period|19|text=p19}} and {{period|41|text=p41}} in July {{year|2023}}

==Large-period oscillators==
In October {{year|1996}}, [[David Buckingham]] wrote the article ''My Experience with B-heptominos in Oscillators''<ref>{{LinkCallahan|patterns/bhept/bhept.html|patternname=Buckingham on B-heptomino/Herschel oscillators|nobullet=nobullet}}</ref> that describes his discovery of [[Herschel conduit]]s, including sufficient [[stable conduit]]s to enable, for the first time, the construction of [[period]] '''''n''''' [[oscillator]]s for every '''''n''''' ≥ 58, and true period '''''n''''' [[gun]]s for every '''''n''''' ≥ 62.

The discovery of the [[Snark]] by [[Mike Playle]] in April 2013 allowed the construction of oscillators of all periods greater than or equal to 43.

==Other rules==
By running [[Dean Hickerson]]'s [[drifter]] searcher to find signals that can be manipulated like Herschels, it is possible to prove that a variety of [[Life-like cellular automata]] are omniperiodic.<ref name="post2521" /><ref name="post139416" /> However, these signals are more like the [[2c/3 wire|2c/3 signal]], in that they operate on a dense background and can closely follow each other. There is a significant possibility that such a signal turner exists for Conway's Game of Life, but no explicit examples have been found.

==See also==
* [[Emu]]
* [[Herschel loop]]

==References==
<references>
<ref name="post2521">{{LinkForumThread
|format = ref
|p = 2521
|title = Re: B3/S234
|author = Matthias Merzenich
|date = June 4, 2010
}}</ref>
<ref name="post139416">{{LinkForumThread
|format = ref
|p = 139416
|title = Re: Suggested LifeWiki edits
|author = Dave Greene
|date = December 26, 2021
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_m.htm#myexperiencewithbheptominosinoscillators|patternname=My Experience with B-heptominos in Oscillators}}
* {{LinkLexicon|lex_o.htm#omniperiodic}}
* {{LinkGoLNews|2011/01/is_life_omniperiodic.html|title=Is Life omniperiodic?|date=January 16, 2011|author=Adam P. Goucher}}
* {{LinkForumThread|format=ref|f=11|t=1217|title=Which Life-like CA have been proven omniperiodic?}}

__NOTOC__

4-glider collision

2023-08-18T22:41:23Z

Atavoidirc:

{{Glossary}}{{stub}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|rle = x = 40, y = 27, rule = B3/S23
37b2o$36bo2bo$37b2o$o$b2o34b2o$2o34bo2bo$37b2o2$37b2o$36bo2bo$37b2o6$
11b3o$13bo$12bo13b2o$25b2o$27bo4$14b3o$16bo$15bo!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 HEIGHT 450 THEME Book AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 88 PAUSE 2 LOOP 89 ]]
|position = center
|caption = A four-glider synthesis of a [[pseudo still life|stack]] of three [[beehive]]s, found in April {{year|2023}}<ref group=c name="j4179541540" />
|apgcode = xs18_69606960696
}}
|-
|{{EmbedViewer
|rle = x = 33, y = 25, rule = B3/S23
15bo$14bo$14b3o3$30bo$29bobo$30bobo$31bo2$30bo$29bobo$30bo3$3o13b3o$2bo13bo$bo15bo5$28b3o$28bo$29bo!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 HEIGHT 450 THEME Book AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 4 T 32 PAUSE 1 T 69 PAUSE 3 LOOP 70 ]]
|position = center
|caption = A small stable constellation is constructed via a four-glider synthesis discovered in March 2023.<ref group=c name="j4003237887" /> Previously constructed with 5 gliders, this constellation is the result of the first step of an incremental synthesis of [[Negentropy]], reducing the glider cost of the oscillator from 90 to 89 gliders.<ref group=c name="c_negentropy" />
|apgcode = xs10_25204a52
}}
|}
A '''4-glider collision''' is a [[collision]] between four [[glider]]s. There are infinitely many distinct 4-glider collisions.

There are no known attempts of a systematic classification or description of all possible (families of) four-glider collisions.<ref name="post115310" /><ref name="post49067" /><ref name="post43893" /><ref name="post21948" /> In particular, it is unknown whether or not it is possible to find a four-glider [[reverse caber-tosser]]; there is no known way to rule out with certainty a four-glider synthesis for any given glider-constructible target pattern.<ref name="post151662" />

==See also==
* [[2-glider collision]], [[3-glider collision]]
* {{CategoryLink|Patterns that can be constructed with 4 gliders}}
* [[4g-to-5g reaction]]
* [[LifeWiki:Did you know/45]]

==References==
<references>
<ref name="post21948">{{LinkForumThread|format=ref|p=21948|title=Re: Searching algorithms|author=Adam P. Goucher|date=August 16, 2015}}</ref>
<ref name="post43893">{{LinkForumThread|format=ref|p=43893|title=Re: Enumerating Three-Glider Collisions|author=Dave Greene|date=May 30, 2017}}</ref>
<ref name="post49067">{{LinkForumThread|format=ref|p=49067|title=Re: Thread for basic questions|author=Dave Greene|date=August 17, 2017}}</ref>
<ref name="post115310">{{LinkForumThread|format=ref|p=115310|title=Re: Thread for basic questions|author=goldenratio|date=December 11, 2020}}</ref>
<ref name="post151662">{{LinkForumThread|format=ref|p=151662|title=Re: Unproven conjectures|author=Dave Greene|date=October 2, 2022}}</ref>
</references>

; Catagolue

<references group=c>
<ref name=c_negentropy>Syntheses of Negentropy on Catagolue: [https://web.archive.org/web/20210717121538/https://catagolue.hatsya.com/textsamples/xp2_gg0gba9jz1107ac87066zx3213/b3s23/synthesis 90-glider synthesis] (archived copy as of 2021-07-17), [https://web.archive.org/web/20230329054202/https://catagolue.hatsya.com/textsamples/xp2_gg0gba9jz1107ac87066zx3213/b3s23/synthesis 89-glider synthesis] (archived copy as of 2023-03-29)</ref>
<ref name="j4003237887">{{CiteCatagolueJob|job=4003237887|date=March 26, 2023}} [https://web.archive.org/web/20230326224706/https://catagolue.hatsya.com/textcensus/b3s23/synthesis-costs-2023-03-25/xs10 synthesis-costs-2023-03-25/xs10]</ref>
<ref name="j4179541540">{{CiteCatagolueJob|job=4179541540|date=April 26, 2023}}</ref>
</references>

==External links==
* {{LinkForumThread|f=2|t=1394|title=4 glider syntheses}}
* [https://github.com/dvgrn/glider-collisions glider-collisions code repository] by [[Dave Greene]] (contains collision database and search scripts)
* {{LinkForumThread|f=9|t=5782|title=New 4-glider collision database|author=Carson Cheng|date=August 24, 2022}}
* {{LinkNiemiec|objcost.htm#cost-g4|Objects buildable with 4 gliders}}
* [https://conwaylife.com/ref/DRH/syntheses.html 2, 3, and 4-glider syntheses] at [[Dean Hickerson]]'s Life page

[[Category:Patterns that can be constructed with 4 gliders| ]]
[[Category:Synthesis]]
[[Category:Collisions]]
__NOTOC__

3-glider collision

2023-08-18T22:41:19Z

Atavoidirc:

{{Glossary}}
{|style="float:right;margin-left:16px;margin-bottom:8px;width:300px;"
|{{EmbedViewer
|pname = pentadecathlonsynthesis
|viewerconfig = #C [[ THUMBSIZE 2 THEME Book AUTOSTART PAUSE 3 LOOP 60 GPS 12 ]]
|position = center
|caption = 3-glider [[pentadecathlon]] synthesis
}}
|-
|{{EmbedViewer
|pname = hwsssynthesis
|viewerconfig = #C [[ THUMBSIZE 2 THEME Book AUTOSTART PAUSE 3 LOOP 60 GPS 12 ]]
|position = center
|caption = 3-glider [[HWSS]] synthesis
}}
|}
A '''3-glider collision''' is a [[collision]] of three [[glider]]s. There are infinitely many distinct 3-glider collisions as some [[2-glider collision]]s generate output gliders, making it possible for another glider to collide with the output glider to form an arbitrarily faraway object or [[constellation]].

In late {{year|2017}}, an enumeration of 3G collisions was done by [[2718281828]], resulting in a database containing 464,746 entries.<ref group=note>The data can be found [https://conwaylife.com/forums/viewtopic.php?p=55572#p55572 in this forum post]. Obtaining an exact count of "essentially different" 3G collisions is complicated by a number of factors, such as existence of glider-producing [[2G collision]]s and [[Heisenburp]]-type [[reaction]]s, and the difference between counting distinct reactions and counting distinct outputs.</ref> Multiple scripts exist to search through the database to find 3-glider [[syntheses]] of stable constellations and unstable patterns.<ref group=note>For the use of these scripts, please see [[Tutorials/Glider syntheses#3-glider collision database|the tutorial section of the 3-glider database]]; see also [[octo3g database]].</ref>

The following single [[object]]s have known 3-glider syntheses:
* 11 still lifes: [[paperclip]], [[half-bakery]], [[bi-pond]], [[tub]], [[barge]], [[ship]], [[long boat]], [[long barge]], [[mango]], [[very long boat]], [[hat]]
* 4 oscillators: [[beacon]], [[toad]], [[pulsar]], [[pentadecathlon]]
* 3 spaceships: [[middleweight spaceship]], [[heavyweight spaceship]], [[lightweight spaceship]]

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

==See also==
* [[2-glider collision]], [[4-glider collision]]
* {{CategoryLink|Patterns that can be constructed with 3 gliders}}
* [[Ternary reaction]]

==External links==
* {{LinkForumThread|f=9|t=2833|title=Enumerating Three-Glider Collisions}}
* [https://github.com/dvgrn/glider-collisions glider-collisions code repository] by [[Dave Greene]] (contains collision database and search scripts)
* {{LinkNiemiec|glider-3.htm|Life Objects Buildable With 3 Gliders}}

[[Category:Patterns that can be constructed with 3 gliders| ]]
[[Category:Synthesis]]
[[Category:Collisions]]
__NOTOC__

2-glider collision

2023-08-18T22:41:13Z

Atavoidirc:

{{Glossary}}
A '''2-glider collision''' is a [[collision]] of two [[glider]]s at right angles or head-on.{{refn|group=note|The direction requirement is a necessary but not sufficient condition for the 2-glider collision to be ''valid''. Two gliders moving in the same direction either never interact or collapse in at most 4 ticks due to being very close. In the latter case, the gliders cannot [[Rewind|come from infinity]] and this "collision" is deemed invalid. Glider syntheses should avoid such glider pairs.<ref name="post16856" />}}

The gliders can react with each other in many different ways. A large number of the reactions cleanly destroy both gliders leaving nothing. Many of the remaining reactions cleanly create some [[common]] objects, and so are used as the first steps in [[Glider synthesis|glider syntheses]] or as part of constructing interesting objects using [[rake]]s. Only a small number of collisions can be considered [[dirty]] due to creating multiple objects or a mess.

== Results ==

<div class="mw-collapsible">
Below are tabulated possible results of a two-glider collision, along with how many distinct ways they can occur.
<div class="mw-collapsible-content">
{| class="sortable wikitable" style="margin-left:auto;margin-right:auto"
|-
! Result !! Right-angle !! Head-on
|-
| [[Vacuum (empty space)|''nothing'']] || 11 || 17
|-
| [[Beehive]] || 1 || 0
|-
| [[B-heptomino]] || 1 || 2
|-
| [[Bi-block]] || 1 || 0
|-
| [[Blinker]] || 2 || 1
|-
| [[Block]] || 3 || 3
|-
| [[Boat]] || 0 || 1
|-
| [[Eater 1]] || 1 || 0
|-
| [[Kickback|Glider]] || 1 || 1
|-
| [[Honey farm]] || 3 || 2
|-
| [[Interchange]] || 1 || 0
|-
| [[Loaf]] || 0 || 1
|-
| [[Lumps of muck]] || 1 || 0
|-
| [[Two-glider octomino]] || 0 || 1
|-
| [[Pi-heptomino]] || 2 || 1
|-
| [[Pond]] || 1 || 1
|-
| [[Teardrop]] || 1 || 0
|-
| [[Traffic light]] || 2 || 1
|-
| [[Four skewed blocks]] || 0 || 1
|-
| [[Dirty]] || 6 || 0
|}
</div></div>

The messiest of the two-glider collisions in the "dirty" category is [[2-glider mess]].

{{EmbedViewer
|pname = twoglidersyntheses
|position = center
|caption = All 71 distinct 2-glider collisions,<ref>{{citeLifeline|vol=5|pages= page 6}}</ref><ref name="post123750" /> arranged by what they synthesize in a pattern constructed by [[Jason Summers]]<ref>{{LinkGoLNews|2005/01/71_glider_collisions.html|title=71 Glider Collisions|date=January 29, 2005|author=Dave Greene}}</ref>
|viewerconfig = #C [[ WIDTH 800 HEIGHT 800 ZOOM 2 ]]
|style = width:300px;
}}

== Classification of the results ==

In {{year|1973}}, [[Everett Boyer]] et al. proposed a classification scheme for 90° two-glider collisions.<ref>{{CiteLifeline|vol=11|pages=page 10}}</ref> By considering the ''delay'' and ''parity'' of separation, a two-glider collision is labelled with a number and a plus/minus sign. For instance, in the collision that gives a bi-block, the paths of two gliders are separated by an odd number of cells (the effect can be seen clearly under {{rl|LifeHistory}}), and two gliders arrive simultaneously to the intersection point of two paths — therefore it is labelled "0-". Delaying any of the two gliders gives a "1-" reaction that synthesizes a B-heptomino.

The results are tabulated below. A pair of colliding gliders has the same [[parity]] with an even delay (or different with odd ones), and has the same [[color]] with an even parity of separation (or different with odd ones).

{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! rowspan="2" | Delay
! colspan="2" | Parity of separation
|-
! Even (+)
! Odd (-)
|-
| 0 || (0+) [[Interchange]]{{refn|group=note|The two gliders can be reflected by a block, as shown in the [[rephaser]] and [[glider-block cycle]] article.}} || (0-) [[Bi-block]]{{refn|group=note|This reaction can also be seen as a tagalong for a c/3 orthogonal dot sparker, as discovered by MathAndCode and wwei23.<ref name="post117181" />}}
|-
| 1 || (1+) 94-tick [[spark]] ([[Ghost Herschel]] / [[Banana spark|banana]] / [[domino]]) || (1-) [[B-heptomino]]
|-
| 2 || (2+) [[Honeyfarm]] || (2-) [[Blinker]]
|-
| 3 || (3+) [[Pond]] || (3-) 32-tick spark ([[Ghost Herschel]] / [[Banana spark|banana]] / [[domino]])
|-
| 4 || (4+) 4-tick spark ([[obo! spark]]) || (4-) [[Traffic light]] and [[glider]]
|-
| 5 || (5+) [[Honeyfarm]] || (5-) 6-tick spark
|-
| 6 || (6+) [[Honeyfarm]] || (6-) 13-tick spark ([[P-pentomino]] / [[V spark]] / [[domino]])
|-
| 7 || (7+) [[Teardrop]] || (7-) 10-tick spark ([[domino]])
|-
| 8 || (8+) [[Blinker]], [[loaf]], [[block]] and [[tub]]{{refn|group=note|name=xp2_xccy3252zgw8kicz3|[[Ash]] on {{LinkCatagolue|style=brief|xp2_xccy3252zgw8kicz3}}}}|| (8-) 8-tick spark (domino)
|-
| 9 || (9+) [[Eater 1]] || (9-) [[Lumps of muck]]
|-
| 10 || (10+) [[Block]] || (10-) [[Blinker]]
|-
| 11 || (11+) 4-tick spark (xp0_14) || (11-) [[Traffic light]]
|-
| 12 || (12+) [[Beehive]] || (12-) [[Block]]
|-
| 13 || (13+) [[Two-glider mess]] || (13-) 11-tick spark ([[P-pentomino]] / [[V spark]] / [[domino]])
|-
| 14 || (14+) [[Half-blockade]] || (14-) 13-tick spark ([[V spark]] / [[domino]])
|-
| 15 || (15+) [[House]] || (15-) 4-tick spark
|-
| 16 || (16+) [[Pi-heptomino]] || (16-) [[Traffic light]]
|-
| 17 || (17+) [[Block]] || (17-) [[Glider]] (90° [[kickback]])
|-
| 18 || (18+) [[Blinker]] and [[loaf]]{{refn|group=note|name=xp2_7zw6952|[[Ash]] on {{LinkCatagolue|style=brief|xp2_7zw6952}}}} || (18-) [[Blinker]] and [[loaf]]{{refn|group=note|name=xp2_7zw6952}}
|-
| ≥19 || colspan="2" style="text-align: center;" | No reaction onwards
|}

Another table of 180° collisions can be similarly made.

{| class="wikitable" style="margin-left:auto;margin-right:auto"
|-
! rowspan="2" | Lane offset
! colspan="5" | Time offset
|-
! 0
! 4
! 1
! 3
! 2
|-
| 0 || colspan="2" style="text-align: center;" | 4-tick spark (xp0_108) || colspan="2" style="text-align: center;" | 6-tick spark (xp0_106 / [[dot]]) || 6-tick spark ([[duoplet]])
|-
| 1 || 10-tick spark || [[Block]] || 5-tick spark ([[Banana spark|banana]] / [[domino]]) || [[Honey farm]] || [[Two-glider octomino]]
|-
| 2 || 5-tick spark || 4-tick spark (domino) || 4-tick spark (domino) || 5-tick spark (domino) || [[Loaf]] (from [[V-pentomino]] or [[W-pentomino]])
|-
| 3 || 4-tick spark (xp0_h) || 5-tick spark || [[Honey farm]] || [[Boat]] || [[Blinker]] (from [[Angel]])
|-
| 4 || 5-tick spark || 12-tick spark || [[Traffic light]] || [[B-heptomino]] || [[Pi-heptomino]]
|-
| 5 || 3-tick spark || 8-tick spark || [[Pond]] || [[Block]] || [[Glider]] (180° [[kickback]])
|-
| 6 || [[Four skewed blocks]] || 7-tick spark ([[domino]]) || [[Block]] || 12-tick spark ([[Banana spark|banana]] / [[domino]]) || [[B-heptaplet]]
|-
| ≥7 || colspan="5" style="text-align: center;" | No reaction onwards
|}

==See also==
* [[3-glider collision]]
* [[Collisions of a glider with common objects]]

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

==References==
<references>
<ref name="post16856">{{LinkForumThread
|p = 16856
|format = ref
|title = Errors of glider synthesis
|author = Bob Shemyakin
|date = February 15, 2015
}}</ref>
<ref name="post123750">{{LinkForumThread
|format = ref
|title = Re: Thread For Your Accidental Discoveries
|p = 123750
|author = Mark Niemiec
|date = February 25, 2021
}}</ref>
<ref name="post117181">{{LinkForumThread
|format = ref
|title = Re: Thread for your Trolls
|p = 117181
|author = wwei23
|date = December 29, 2020
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_1.htm#a-2glidercollision}}
* {{LinkNiemiec|glider-2.htm|Life Objects Buildable With 2 Gliders}}

[[Category:Patterns that can be constructed with 2 gliders| ]]
[[Category:Synthesis]]
[[Category:Collisions]]
__NOTOC__

File:Identify-map.png

2023-07-22T15:10:54Z

Atavoidirc:

Pattern is [[p96 Hans Leo hassler]]

File:Identify-map.png

2023-07-22T15:10:19Z

Atavoidirc:

Pattern is [[B-heptomino hasslers#p96]]

User:Atavoidirc

2023-07-07T23:58:58Z

Atavoidirc:

__NOTOC__
This is a hub page
[[User:Atavoidirc/Spaceship table]]
==[[User:GUYTU6J]]/Neighbourhood==
{{User:GUYTU6J/Neighbourhood}}
==Life wiki Pages==
* [[LifeWiki:Game of Life Status page]]
* [[LifeWiki:Spaceship Search Status Page]]
* [[LifeWiki:Smallest Spaceships Supporting Specific Speeds]]
* [[LifeWiki:Project OmniOsci/Overview]]
* [[LifeWiki:LifeViewer cheatsheet for LifeWiki articles]]
* [[LifeWiki:List of ongoing projects]]

==Other Pages==
* [[Table of oscillators by period]]

==Rules in Userspace==
* [[User:Carbon6/Gnarl]]
* [[User:Drc/GlideLife]]
* [[User:Prime Raptor21/Nothing (Rule)]]
* [[User:Evin/BiLife]]
* [[User:Moosey/eatsplosion]]
* [[User:Evin/Silverseeds]]
* [[User:Evin/OCA:E1]]
* [[User:Evin/Wlife]]
* [[User:GUYTU6J/OCA:Glimmering Garden]]
* [[User:Yujh/B34kz5e7c8/S23-a4ityz5k]]
* [[User:Cvojan/TubularTest]]
* [[User:Ultimium/OCA:LeapLife]]
* [[User:Cgoler2/rrlife]]
* [[User:Cgoler2/Clife]]
* [[User:Pzq Alex/BitLife]]

User:Atavoidirc

2023-07-07T23:50:33Z

Atavoidirc:

__NOTOC__
This is a hub page
[[User:Atavoidirc/Spaceship table]]

[[User:Atavoidirc/All Conduit Inputs and Outputs]]
==[[User:GUYTU6J]]/Neighbourhood==
{{User:GUYTU6J/Neighbourhood}}
==Life wiki Pages==
* [[LifeWiki:Game of Life Status page]]
* [[LifeWiki:Spaceship Search Status Page]]
* [[LifeWiki:Smallest Spaceships Supporting Specific Speeds]]
* [[LifeWiki:Project OmniOsci/Overview]]
* [[LifeWiki:LifeViewer cheatsheet for LifeWiki articles]]
* [[LifeWiki:List of ongoing projects]]

==Other Pages==
* [[Table of oscillators by period]]

==Rules in Userspace==
* [[User:Carbon6/Gnarl]]
* [[User:Drc/GlideLife]]
* [[User:Prime Raptor21/Nothing (Rule)]]
* [[User:Evin/BiLife]]
* [[User:Moosey/eatsplosion]]
* [[User:Evin/Silverseeds]]
* [[User:Evin/OCA:E1]]
* [[User:Evin/Wlife]]
* [[User:GUYTU6J/OCA:Glimmering Garden]]
* [[User:Yujh/B34kz5e7c8/S23-a4ityz5k]]
* [[User:Cvojan/TubularTest]]
* [[User:Ultimium/OCA:LeapLife]]
* [[User:Cgoler2/rrlife]]
* [[User:Cgoler2/Clife]]
* [[User:Pzq Alex/BitLife]]

Static symmetry

2023-06-27T09:56:10Z

Atavoidirc: /* On a square grid */

A '''static symmetry'''<ref name="post138823" /> refers to the combined rotational and reflectional symmetries of an arrangement of cells on a grid. Most isotropic rules preserve all such symmetries.

This page specifically only covers purely geometric symmetries. Other preserved attributes which are not necessarily geometrical symmetries, notably gutters, are compiled on the [[Minor static symmetries]] page. Symmetries which apply to periodic objects, such as still lifes, oscillators and spaceships, which also includes time symmetries, are listed on the [[Kinetic symmetry]] page.

== Basic theory ==
The Life transition rule, like that of any [[Isotropic non-totalistic cellular automaton|isotropic cellular automaton]], is invariant under valid reflections and rotations. That is, the change in state of a cell remains the same if its [[neighbourhood]] is rotated or reflected. This implies there are '''symmetries''' which if present in a pattern are present in all its successors. Note that the converse is not true: a pattern need not have the full symmetry of one of its successor states.

== On a square grid ==
[[File:Symmetries.png|center|frame|Overview of symmetries (excluding D8_2).]]

=== Rotational ===
<div class="mw-collapsible">
Rotational symmetries are prefixed with "C", referring to the cyclic groups.<ref>[https://en.wikipedia.org/wiki/Cyclic_group Cyclic group] on Wikipedia</ref>
<div class="mw-collapsible-content">

==== C1 ====
'''C1''': Symmetric under 360° rotation. This is essentially no symmetry at all. Example: [[Eater 1]]

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o!
|width = 160
|height = 160
|caption = C1 symmetry
}}</center>

==== C2 ====
'''C2''': Symmetric under 180° rotation. There are three possibilities:

* '''C2_1''': Rotation around the center of a cell. The bounding rectangle of a C2_1 pattern is odd by odd. Example: [[Long snake]]
* '''C2_2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd. Example: [[Aircraft carrier]]
* '''C2_4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Snake]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$31o
$15bo14bo$15bo14bo$15bo9b2o3bo$15bo8b4o2bo$15bo8b4o2bo$15bo2b10o2bo$
15bo14bo$15bo14bo$15bo3b2o4b2o3bo$15bo2bo2bo2bo2bo2bo$15bo2bo2bo2bo2bo
2bo$15bo3b2o4b2o3bo$15bo14bo$15bo14bo$15b16o!
|width = 320
|height = 320
|caption = C2_1 symmetry}}
| {{Sym-demo
|rle = x = 31, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$15b16o$15bo14bo$15bo14bo$15bo9b2o3bo$15bo8b4o2bo$15bo8b4o2bo$15bo2b
10o2bo$15bo14bo$15bo14bo$15bo3b2o4b2o3bo$15bo2bo2bo2bo2bo2bo$15bo2bo2b
o2bo2bo2bo$15bo3b2o4b2o3bo$15bo14bo$15bo14bo$15b16o!
|width = 320
|height = 320
|caption = C2_2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$16b16o$16bo14bo$16bo14bo$16bo9b2o3bo$16bo8b4o2bo$16bo8b4o2bo$16bo2b
10o2bo$16bo14bo$16bo14bo$16bo3b2o4b2o3bo$16bo2bo2bo2bo2bo2bo$16bo2bo2b
o2bo2bo2bo$16bo3b2o4b2o3bo$16bo14bo$16bo14bo$16b16o!
|width = 320
|height = 320
|caption = C2_4 symmetry}}
|}

==== C4 ====
'''C4''': Symmetric under 90° rotation. There are two possibilities:

* '''C4_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Shuriken]]
* '''C4_4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Quad]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o3b2o4b2o3bo3b3o3b2o3bo$o2bo2bo2bo2bo2bo2b4o2b
o2bo2bo$o2bo2bo2bo2bo2bo2b4o2bo2bo2bo$o3b2o4b2o3bo3b3o3b2o3bo$o14bo5bo
8bo$o14bo5bo8bo$o2b10o2bo5bo3b2o3bo$o2b4o8bo5bo2bo2bo2bo$o2b4o8bo5bo2b
o2bo2bo$o3b2o9bo5bo3b2o3bo$o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo
$o3b2o3bo5bo9b2o3bo$o2bo2bo2bo5bo8b4o2bo$o2bo2bo2bo5bo8b4o2bo$o3b2o3bo
5bo2b10o2bo$o8bo5bo14bo$o8bo5bo14bo$o3b2o3b3o3bo3b2o4b2o3bo$o2bo2bo2b
4o2bo2bo2bo2bo2bo2bo$o2bo2bo2b4o2bo2bo2bo2bo2bo2bo$o3b2o3b3o3bo3b2o4b
2o3bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = C4_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b3o3b2o3bo$o2bo2bo2bo2bo2b2o2b
4o2bo2bo2bo$o2bo2bo2bo2bo2b2o2b4o2bo2bo2bo$o3b2o4b2o3b2o3b3o3b2o3bo$o
14b2o5bo8bo$o14b2o5bo8bo$o2b10o2b2o5bo3b2o3bo$o2b4o8b2o5bo2bo2bo2bo$o
2b4o8b2o5bo2bo2bo2bo$o3b2o9b2o5bo3b2o3bo$o14b2o14bo$o14b2o14bo$32o$32o
$o14b2o14bo$o14b2o14bo$o3b2o3bo5b2o9b2o3bo$o2bo2bo2bo5b2o8b4o2bo$o2bo
2bo2bo5b2o8b4o2bo$o3b2o3bo5b2o2b10o2bo$o8bo5b2o14bo$o8bo5b2o14bo$o3b2o
3b3o3b2o3b2o4b2o3bo$o2bo2bo2b4o2b2o2bo2bo2bo2bo2bo$o2bo2bo2b4o2b2o2bo
2bo2bo2bo2bo$o3b2o3b3o3b2o3b2o4b2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = C4_4 symmetry}}
|}
</div></div>

C4 tends to produce record [[diehard]]s and [[megasized]] soups compared to other symmetries.

=== Reflectional ===
<div class="mw-collapsible">
Reflectional symmetries are prefixed with "D", referring to the dihedral groups.<ref>[https://en.wikipedia.org/wiki/Dihedral_group Dihedral group] on Wikipedia</ref>
<div class="mw-collapsible-content">

==== D2 ====
'''D2''': Symmetric under reflection through a line. There are two possibilities:

* '''D2_+''' The line is orthogonal. There are two sub-possibilities:
** '''D2_+1''' The line bisects a row of cells. The bounding rectangle is odd by any. Example: [[Hat]]
** '''D2_+2''' The line lies between two rows of cells. The bounding rectangle is even by any. Example: [[Frutterfly]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 16, y = 31, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$o14bo$o14bo$o3b2o9bo$o2b4o8bo$o2b4o8bo$o2b10o2bo$o14bo$o14bo$o3b2o4b
2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b2o3bo$o14bo$o14bo$16o!
|width = 160
|height = 320
|caption = D2_+1 symmetry}}
| {{Sym-demo
|rle = x = 16, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$16o$o14bo$o14bo$o3b2o9bo$o2b4o8bo$o2b4o8bo$o2b10o2bo$o14bo$o14bo$o3b
2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b2o3bo$o14bo$o14bo$
16o!
|width = 160
|height = 320
|caption = D2_+2 symmetry}}
|}

* '''D2_x''' The line is diagonal. Example: [[Elevener]]

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S012345678
16o$o14bo$o14bo$o7bo6bo$o6bobo5bo$o7bo3bo2bo$o11bo2bo$o3bo7bo2bo$o2bob
o6bo2bo$o3bo6bo3bo$o9bo4bo$o8bo5bo$o4b4o6bo$o14bo$o14bo$16o!
|width = 160
|height = 160
|caption = D2_x symmetry}}</center>

==== D4 ====
'''D4''': Symmetric under both reflection and 180° rotation. The reflection symmetry will be with respect to two lines. There are two possibilities:

* '''D4_+''': The lines are orthogonal. There are three sub-possibilities:
** '''D4_+1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Dead spark coil]]
** '''D4_+2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd. Example: [[Honeycomb]]
** '''D4_+4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[A for all]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o3b2o4b2o3bo3b2o4b2o3bo$o2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo$o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$o3b2o4b2o3bo3b2o4b2o3bo$o14b
o14bo$o14bo14bo$o2b10o2bo2b10o2bo$o2b4o8bo8b4o2bo$o2b4o8bo8b4o2bo$o3b
2o9bo9b2o3bo$o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo$o3b2o9bo9b2o
3bo$o2b4o8bo8b4o2bo$o2b4o8bo8b4o2bo$o2b10o2bo2b10o2bo$o14bo14bo$o14bo
14bo$o3b2o4b2o3bo3b2o4b2o3bo$o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo$o3b2o4b2o3bo3b2o4b2o3bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D4_+1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 31, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b2o2b
o2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b2o3b
o$o14b2o14bo$o14b2o14bo$o2b10o2b2o2b10o2bo$o2b4o8b2o8b4o2bo$o2b4o8b2o
8b4o2bo$o3b2o9b2o9b2o3bo$o14b2o14bo$o14b2o14bo$32o$o14b2o14bo$o14b2o
14bo$o3b2o9b2o9b2o3bo$o2b4o8b2o8b4o2bo$o2b4o8b2o8b4o2bo$o2b10o2b2o2b
10o2bo$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b
2o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b
2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D4_+2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b2o2b
o2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b2o3b
o$o14b2o14bo$o14b2o14bo$o2b10o2b2o2b10o2bo$o2b4o8b2o8b4o2bo$o2b4o8b2o
8b4o2bo$o3b2o9b2o9b2o3bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b
2o14bo$o3b2o9b2o9b2o3bo$o2b4o8b2o8b4o2bo$o2b4o8b2o8b4o2bo$o2b10o2b2o2b
10o2bo$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b
2o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b
2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D4_+4 symmetry}}
|}

* '''D4_x''' The lines are diagonal. There are two sub-possibilities:
** '''D4_x1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Loaf siamese loaf]]
** '''D4_x4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Long ship]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o7bo6bo5b3o6bo$o6bobo5bo5bobo6bo$o7bo3bo2bo2bo
2b3o6bo$o11bo2bo2b2o10bo$o3bo7bo2bo2b2o5b3o2bo$o2bobo6bo2bo2b3o4bobo2b
o$o3bo6bo3bo3b2o4b3o2bo$o9bo4bo3b4o7bo$o8bo5bo4b5o5bo$o4b4o6bo6b4o4bo$
o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo$o4b4o6bo6b4o4bo$o5b5o4bo5b
o8bo$o7b4o3bo4bo9bo$o2b3o4b2o3bo3bo6bo3bo$o2bobo4b3o2bo2bo6bobo2bo$o2b
3o5b2o2bo2bo7bo3bo$o10b2o2bo2bo11bo$o6b3o2bo2bo2bo3bo7bo$o6bobo5bo5bob
o6bo$o6b3o5bo6bo7bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D4_x1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o5b3o6bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo2b3o6bo$o11bo2b2o2b2o10bo$o3bo7bo2b2o2b2o5b3o2bo$o2bobo6bo2b2o2b
3o4bobo2bo$o3bo6bo3b2o3b2o4b3o2bo$o9bo4b2o3b4o7bo$o8bo5b2o4b5o5bo$o4b
4o6b2o6b4o4bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b2o14bo$o4b
4o6b2o6b4o4bo$o5b5o4b2o5bo8bo$o7b4o3b2o4bo9bo$o2b3o4b2o3b2o3bo6bo3bo$o
2bobo4b3o2b2o2bo6bobo2bo$o2b3o5b2o2b2o2bo7bo3bo$o10b2o2b2o2bo11bo$o6b
3o2bo2b2o2bo3bo7bo$o6bobo5b2o5bobo6bo$o6b3o5b2o6bo7bo$o14b2o14bo$o14b
2o14bo$32o!
|width = 320
|height = 320
|caption = D4_x4 symmetry}}
|}

==== D8 ====
'''D8''': Symmetric under both reflection and 90° rotation. The reflection symmetry will be with respect to horizontal, vertical, and diagonal lines. There are three possibilities:

* '''D8_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Pulsar]]
* '''D8_2''': Rotation around a edge of a cell. The bounding rectangle is even by odd. This symmetry is not preserved by Life (reverting to D4_+2), but is with most bilaterally symmetric rules.
* '''D8_4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Lake 2]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o7bo6bo6bo7bo$o6bobo5bo5bobo6bo$o7bo3bo2bo2bo
3bo7bo$o11bo2bo2bo11bo$o3bo7bo2bo2bo7bo3bo$o2bobo6bo2bo2bo6bobo2bo$o3b
o6bo3bo3bo6bo3bo$o9bo4bo4bo9bo$o8bo5bo5bo8bo$o4b4o6bo6b4o4bo$o14bo14bo
$o14bo14bo$31o$o14bo14bo$o14bo14bo$o4b4o6bo6b4o4bo$o8bo5bo5bo8bo$o9bo
4bo4bo9bo$o3bo6bo3bo3bo6bo3bo$o2bobo6bo2bo2bo6bobo2bo$o3bo7bo2bo2bo7bo
3bo$o11bo2bo2bo11bo$o7bo3bo2bo2bo3bo7bo$o6bobo5bo5bobo6bo$o7bo6bo6bo7b
o$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D8_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 31, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o6bo7bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo3bo7bo$o11bo2b2o2bo11bo$o3bo7bo2b2o2bo7bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo6bo3b2o3bo6bo3bo$o9bo4b2o4bo9bo$o8bo5b2o5bo8bo$o4b4o6b2o6b4o
4bo$o14b2o14bo$o14b2o14bo$32o$o14b2o14bo$o14b2o14bo$o4b4o6b2o6b4o4bo$o
8bo5b2o5bo8bo$o9bo4b2o4bo9bo$o3bo6bo3b2o3bo6bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo7bo2b2o2bo7bo3bo$o11bo2b2o2bo11bo$o7bo3bo2b2o2bo3bo7bo$o6bobo
5b2o5bobo6bo$o7bo6b2o6bo7bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D8_2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o6bo7bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo3bo7bo$o11bo2b2o2bo11bo$o3bo7bo2b2o2bo7bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo6bo3b2o3bo6bo3bo$o9bo4b2o4bo9bo$o8bo5b2o5bo8bo$o4b4o6b2o6b4o
4bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b2o14bo$o4b4o6b2o6b4o
4bo$o8bo5b2o5bo8bo$o9bo4b2o4bo9bo$o3bo6bo3b2o3bo6bo3bo$o2bobo6bo2b2o2b
o6bobo2bo$o3bo7bo2b2o2bo7bo3bo$o11bo2b2o2bo11bo$o7bo3bo2b2o2bo3bo7bo$o
6bobo5b2o5bobo6bo$o7bo6b2o6bo7bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D8_4 symmetry}}
|}

To preserve D8_2 symmetry, the following [[isotropic non-totalistic]] transitions must either all exist simultaneously with all other transitions in the same line or none should:<ref name="post143859" />

*B4i=B2a=B2i=B1e
*S6a=S7e=S4t=S6i
*S4c=S3y=S4q
*B1c=B2c=B4c
*S3a=S1e=S0
*S7c=S6c=S4e
*B5y=B4w=B4e
*B8=B7e=B5a
*B5e=B4n
*B4a=B5i
*B4t=B5r
*S5y=S5q
*S5e=S5j
*B6i=B3i
*B6c=B6k
*S4i=S3r
*B3j=B3e
*B3y=B3q
*S2k=S2c
*S4a=S3i
*S3e=S4r
*S5i=S2i
</div></div>

== On a hexagonal or triangular grid ==
[[Hexagonal neighbourhood|Hexagonal]] and [[triangular neighbourhood|triangular]] grids have the same set of admissible symmetries as each other (by planar<ref>[http://mathworld.wolfram.com/DualTessellation.html Dual tessellation] on mathworld.wolfram.com</ref> or polytopic duality<ref>[https://en.wikipedia.org/wiki/Dual_polyhedron#Dual_polytopes_and_tessellations Dual polyhedron] on Wikipedia</ref> - see also [[Schläfli symbol]]), but these are not the same symmetries as square grids. Due to how hexagonal and triangular grids are handled by programs such as [[Golly]] and [[LifeViewer]], they will also appear markedly different in these respects. C2, D2, and D4 symmetries are still compatible, but C4 symmetries become meaningless because the cells no longer have a side count that is perfectly divisible by 4. Other symmetries are exclusive to these alternative grids, as indicated below:

* C1
* C2_1
* C2_4
* C3_1
* C3_3 (unsupported by apgsearch)
* C6
* D2_xo
* D2_x
* D4_x1
* D4_x4
* D6_1
* D6_1o
* D6_3 (unsupported by apgsearch)
* D12

[[apgsearch]] currently supports most higher symmetries for hexagonal rules; the rest (C3_3 and D6_3) will be added in a future version.<ref name="post66638" />

Another type of rotational symmetry which may not have been accounted for in the above list, arising as an alternate form of C2_2, was described in November 2021. Whether this is an actually distinct type of symmetry, however, is unknown and needs investigation.<ref name="post137220" />

=== Rotational ===
<div class="mw-collapsible">
Click on "Expand" to the right to view a list of hexagonal/triangular rotational symmetries.
<div class="mw-collapsible-content">

==== C1 ====
'''C1''': Symmetric under 360° rotation. This is essentially no symmetry at all.

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S0123456H
16o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o6b2o6bo$o2b2o10bo$o2bobo9bo$o3b2o
4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o4bo$o8b2o4bo$o14bo$o14bo$16o!
|width = 200
|height = 200
|caption = C1 symmetry
}}</center>

==== C2 ====
'''C2''': Symmetric under 180° rotation. There are two possibilities:

* '''C2_1''': Rotation around the center of a cell.
* '''C2_2''': Rotation around the midpoint of a side of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
15b16o$15bo14bo$15bo14bo$15bo4b2o8bo$15bo4b3o7bo$15bo5b2o7bo$15bo4b2o
8bo$15bo3b2o4b2o3bo$15bo9bobo2bo$15bo10b2o2bo$15bo6b2o6bo$15bo6bobo5bo
$15bo7b2o5bo$15bo14bo$15bo14bo$31o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o6b
2o6bo$o2b2o10bo$o2bobo9bo$o3b2o4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o4bo$o8b
2o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = C2_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S0123456H
16b16o$16bo14bo$16bo14bo$16bo4b2o8bo$16bo4b3o7bo$16bo5b2o7bo$16bo4b2o
8bo$16bo3b2o4b2o3bo$16bo9bobo2bo$16bo10b2o2bo$16bo6b2o6bo$16bo6bobo5bo
$16bo7b2o5bo$16bo14bo$16bo14bo$16b16o$16o$o14bo$o14bo$o5b2o7bo$o5bobo
6bo$o6b2o6bo$o2b2o10bo$o2bobo9bo$o3b2o4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o
4bo$o8b2o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = C2_4(?) symmetry}}
|}

==== C3 ====
'''C3''': Symmetric under 120° rotation. There are two possibilities:

* '''C3_1''': Rotation around the center of a cell.
* '''C3_3''': Rotation around a corner of a cell. (unsupported by apgsearch)

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 46, y = 46, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o9bo$o6b2o2bo$o2b2o2bobo2b
o$o2b3o2b2o3bo$o3b2o8bo$o5bo8bo$bo4bo8bo$2bo4bo2b2o3bo$3bo3bo2bobo2bo$
4bo6b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo$
13bobo$14b2o$31o$o14b2o14bo$o14bobo14bo$o5b2o7bo2bo14bo$o5bobo6bo3bo7b
o6bo$o6b2o6bo4bo7b2ob2o2bo$o2b2o10bo5bo8b4o2bo$o2bobo9bo6bo3b2o4b2o3bo
$o3b2o4b2o3bo7bo2bobo9bo$o8b2o4bo8bo2b2o10bo$o7b2o5bo9bo6b2o6bo$o7b3o
4bo10bo5bobo6bo$o8b2o4bo11bo5b2o7bo$o14bo12bo14bo$o14bo13bo14bo$16o14b
16o!
|width = 400
|height = 400
|caption = C3_1 symmetry}}
| {{Sym-demo
|rle = x = 48, y = 48, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o9bo$o6b2o2bo$o2b2o2bobo2b
o$o2b3o2b2o3bo$o3b2o8bo$o5bo8bo$bo4bo8bo$2bo4bo2b2o3bo$3bo3bo2bobo2bo$
4bo6b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo$
13bobo$14b2o$15bo2$16ob16o$o14bo2bo14bo$o14bo3bo14bo$o5b2o7bo4bo14bo$o
5bobo6bo5bo7bo6bo$o6b2o6bo6bo7b2ob2o2bo$o2b2o10bo7bo8b4o2bo$o2bobo9bo
8bo3b2o4b2o3bo$o3b2o4b2o3bo9bo2bobo9bo$o8b2o4bo10bo2b2o10bo$o7b2o5bo
11bo6b2o6bo$o7b3o4bo12bo5bobo6bo$o8b2o4bo13bo5b2o7bo$o14bo14bo14bo$o
14bo15bo14bo$16o16b16o!
|width = 400
|height = 400
|caption = C3_3 symmetry}}
|}

==== C6 ====
'''C6''': Symmetric under 60° rotation.

<center>{{Sym-demo
|rle = x = 61, y = 61, rule = B/S0123456H
15bo$15b2o$15bobo$15bo2bo$15bo3bo$15bo4bo$15bo5bo$15bo6bo$15bo7bo$15bo
8bo$15bo9bo$15bo6b2o2bo$15bo2b2o2bobo2bo$15bo2b3o2b2o3bo$15bo3b2o8bo$
16o5bo8b16o$bo14bo4bo8bo14bo$2bo14bo4bo2b2o3bo14bo$3bo7b2o5bo3bo2bobo
2bo4b2o8bo$4bo6bobo5bo6b2o2bo4b3o7bo$5bo6b2o6bo9bo5b2o7bo$6bo10b2o2bo
8bo4b2o8bo$7bo9bobo2bo7bo3b2o4b2o3bo$8bo3b2o4b2o3bo6bo9bobo2bo$9bo2b4o
8bo5bo10b2o2bo$10bo2b2ob2o7bo4bo6b2o6bo$11bo6bo7bo3bo6bobo5bo$12bo14bo
2bo7b2o5bo$13bo14bobo14bo$14bo14b2o14bo$15b31o$15bo14b2o14bo$15bo14bob
o14bo$15bo5b2o7bo2bo14bo$15bo5bobo6bo3bo7bo6bo$15bo6b2o6bo4bo7b2ob2o2b
o$15bo2b2o10bo5bo8b4o2bo$15bo2bobo9bo6bo3b2o4b2o3bo$15bo3b2o4b2o3bo7bo
2bobo9bo$15bo8b2o4bo8bo2b2o10bo$15bo7b2o5bo9bo6b2o6bo$15bo7b3o4bo2b2o
6bo5bobo6bo$15bo8b2o4bo2bobo2bo3bo5b2o7bo$15bo14bo3b2o2bo4bo14bo$15bo
14bo8bo4bo14bo$15b16o8bo5b16o$31bo8b2o3bo$32bo3b2o2b3o2bo$33bo2bobo2b
2o2bo$34bo2b2o6bo$35bo9bo$36bo8bo$37bo7bo$38bo6bo$39bo5bo$40bo4bo$41bo
3bo$42bo2bo$43bobo$44b2o$45bo!
|width = 500
|height = 500
|caption = C6 symmetry}}</center>
</div></div>

=== Reflectional ===
<div class="mw-collapsible">
Click on "Expand" to the right to view a list of hexagonal/triangular reflectional symmetries.
<div class="mw-collapsible-content">

==== D2 ====
'''D2''': There is line symmetry. There are two possibilities:

* '''D2_x''': Through the vertices of a cell.
* '''D2_xo''': Through the edges of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 16, y = 16, rule = B/S0123456H
16o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o
2bo6bobo2bo$o3bo6b2o2bo$o4bo9bo$o5bo8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 300
|height = 300
|caption = D2_x symmetry}}
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
16o$bo14bo$2bo14bo$3bo8b2o4bo$4bo7b3o4bo$5bo7b2o5bo$6bo8b2o4bo$7bo3b2o
4b2o3bo$8bo2bobo9bo$9bo2b2o10bo$10bo6b2o6bo$11bo5bobo6bo$12bo5b2o7bo$
13bo14bo$14bo14bo$15b16o$15bo14bo$15bo14bo$15bo5b2o7bo$15bo5bobo6bo$15b
o6b2o6bo$15bo2b2o10bo$15bo2bobo9bo$15bo3b2o4b2o3bo$15bo8b2o4bo$15bo7b
2o5bo$15bo7b3o4bo$15bo8b2o4bo$15bo14bo$15bo14bo$15b16o!
|width = 300
|height = 300
|caption = D2_xo symmetry}}
|}

==== D4 ====
'''D4''': Symmetric under both reflection and 180° rotation. The reflection symmetry will be with respect to two lines. There are two possibilities:

* '''D4_x1''': Rotation around the center of a cell.
* '''D4_x4''': Rotation around the edges of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
15b16o$15bo14bo$15bo14bo$15bo4b4o6bo$15bo8bo5bo$15bo9bo4bo$15bo2b2o6bo
3bo$15bo2bobo6bo2bo$15bo3b2o6bo2bo$15bo11bo2bo$15bo6b2o3bo2bo$15bo6bob
o5bo$15bo7b2o5bo$15bo14bo$15bo14bo$31o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$
o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o2bo6bobo2bo$o3bo6b2o2bo$o4bo9bo$o5bo
8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = D4_x1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S0123456H
16b16o$16bo14bo$16bo14bo$16bo4b4o6bo$16bo8bo5bo$16bo9bo4bo$16bo2b2o6bo
3bo$16bo2bobo6bo2bo$16bo3b2o6bo2bo$16bo11bo2bo$16bo6b2o3bo2bo$16bo6bob
o5bo$16bo7b2o5bo$16bo14bo$16bo14bo$16b16o$16o$o14bo$o14bo$o5b2o7bo$o5b
obo6bo$o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o2bo6bobo2bo$o3bo6b2o2bo$o4bo
9bo$o5bo8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = D4_x4 symmetry}}
|}

==== D6 ====
'''D6''': Symmetric under both reflection and 120° rotation. The reflection symmetry will be with respect to three lines. There are three possibilities:

* '''D6_1''': Rotation around the center of a cell with lines going through the edges of cells.
* '''D6_1o''': Rotation around the center of a cell with lines going through the centers of cells.
* '''D6_3''': Rotation around the corner of a cell. (unsupported by apgsearch)

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 46, y = 46, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o2b5o2bo$o2bo4bo2bo$o2bo5b
o2bo$o2bo6bo2bo$o13bo$o14bo$bo13bo$2bo3b2o2b2o3bo$3bo2bobobobo2bo$4bo
2b2o2b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo
$13bobo$14b2o$31o$o14b2o14bo$o14bobo14bo$o5b2o7bo2bo7b2o5bo$o5bobo6bo
3bo6bobo5bo$o2bo3b2o6bo4bo6b2o3bo2bo$o2bo11bo5bo11bo2bo$o2bo6b2o3bo6bo
3b2o6bo2bo$o2bo6bobo2bo7bo2bobo6bo2bo$o3bo6b2o2bo8bo2b2o6bo3bo$o4bo9bo
9bo9bo4bo$o5bo8bo10bo8bo5bo$o6b4o4bo11bo4b4o6bo$o14bo12bo14bo$o14bo13b
o14bo$16o14b16o!
|width = 400
|height = 400
|caption = D6_1 symmetry}}
| {{Sym-demo
|rle = x = 31, y = 31, rule = B2/S34H
16o$2o14bo$obo14bo$o2bo4b5o5bo$o3bo8b2o4bo$o4bo9b2o3bo$o5bo3b2o5b2o2bo
$o6bo2bobo6bo2bo$o2bo4bo2b2o7bo2bo$o2bo5bo11bo2bo$o2bo2b2o2bo7b2o2bo2b
o$o2bo2bobo2bo6bobo5bo$o2bo3b2o3bo6b2o6bo$o3bo8bo14bo$o3bo9bo14bo$o4bo
9b16o$bo3bo9bo14bo$2bo3bo8bo14bo$3bo2bo3b2o3bo6b2o6bo$4bo2bo2bobo2bo6b
obo5bo$5bo2bo2b2o2bo7b2o2bo2bo$6bo2bo5bo11bo2bo$7bo2bo4bo2b2o7bo2bo$8b
o6bo2bobo6bo2bo$9bo5bo3b2o5b2o2bo$10bo4bo9b2o3bo$11bo3bo8b2o4bo$12bo2b
o4b5o5bo$13bobo14bo$14b2o14bo$15b16o!
|width = 400
|height = 400
|caption = D6_1o symmetry}}
| {{Sym-demo
|rle = x = 48, y = 48, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o2b5o2bo$o2bo4bo2bo$o2bo5b
o2bo$o2bo6bo2bo$o13bo$o14bo$bo13bo$2bo3b2o2b2o3bo$3bo2bobobobo2bo$4bo
2b2o2b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo
$13bobo$14b2o$15bo2$16ob16o$o14bo2bo14bo$o14bo3bo14bo$o5b2o7bo4bo7b2o
5bo$o5bobo6bo5bo6bobo5bo$o2bo3b2o6bo6bo6b2o3bo2bo$o2bo11bo7bo11bo2bo$o
2bo6b2o3bo8bo3b2o6bo2bo$o2bo6bobo2bo9bo2bobo6bo2bo$o3bo6b2o2bo10bo2b2o
6bo3bo$o4bo9bo11bo9bo4bo$o5bo8bo12bo8bo5bo$o6b4o4bo13bo4b4o6bo$o14bo
14bo14bo$o14bo15bo14bo$16o16b16o!
|width = 400
|height = 400
|caption = D6_3 symmetry}}
|}

==== D12 ====
'''D12''': Symmetric under both reflection and 60° rotation. The reflection symmetry will be with respect to six lines.

<center>{{Sym-demo
|rle = x = 61, y = 61, rule = B/S0123456H
15bo$15b2o$15bobo$15bo2bo$15bo3bo$15bo4bo$15bo5bo$15bo6bo$15bo7bo$15bo
8bo$15bo2b5o2bo$15bo2bo4bo2bo$15bo2bo5bo2bo$15bo2bo6bo2bo$15bo13bo$16o
14b16o$bo14bo13bo14bo$2bo14bo3b2o2b2o3bo14bo$3bo6b4o4bo2bobobobo2bo4b
4o6bo$4bo5bo8bo2b2o2b2o2bo8bo5bo$5bo4bo9bo9bo9bo4bo$6bo3bo6b2o2bo8bo2b
2o6bo3bo$7bo2bo6bobo2bo7bo2bobo6bo2bo$8bo2bo6b2o3bo6bo3b2o6bo2bo$9bo2b
o11bo5bo11bo2bo$10bo2bo3b2o6bo4bo6b2o3bo2bo$11bo5bobo6bo3bo6bobo5bo$
12bo5b2o7bo2bo7b2o5bo$13bo14bobo14bo$14bo14b2o14bo$15b31o$15bo14b2o14b
o$15bo14bobo14bo$15bo5b2o7bo2bo7b2o5bo$15bo5bobo6bo3bo6bobo5bo$15bo2bo
3b2o6bo4bo6b2o3bo2bo$15bo2bo11bo5bo11bo2bo$15bo2bo6b2o3bo6bo3b2o6bo2bo
$15bo2bo6bobo2bo7bo2bobo6bo2bo$15bo3bo6b2o2bo8bo2b2o6bo3bo$15bo4bo9bo
9bo9bo4bo$15bo5bo8bo2b2o2b2o2bo8bo5bo$15bo6b4o4bo2bobobobo2bo4b4o6bo$
15bo14bo3b2o2b2o3bo14bo$15bo14bo13bo14bo$15b16o14b16o$31bo13bo$32bo2bo
6bo2bo$33bo2bo5bo2bo$34bo2bo4bo2bo$35bo2b5o2bo$36bo8bo$37bo7bo$38bo6bo
$39bo5bo$40bo4bo$41bo3bo$42bo2bo$43bobo$44b2o$45bo!
|width = 500
|height = 500
|caption = D12 symmetry}}</center>
</div></div>

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
<ref name="post143859">{{LinkForumThread
|format = ref
|title = Re: Truly Bilateral Life-Like rules
|p = 143859
|author = LaundryPizza03
|date = April 6, 2022
}}</ref>
<ref name="post66638">{{LinkForumThread
|format = ref
|title = Re: apgsearch v4.0
|p = 66638
|author = Adam P. Goucher
|date = December 20, 2018
}}</ref>
<ref name="post137220">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 137220
|author = GUYTU6J
|date = November 2, 2021
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_s.htm#symmetric|name=Symmetric}}
* {{LinkForumThread|f=7|t=1898|title=Help with symmetries}}

[[Category:Everything else]]

User:Atavoidirc/Spaceship table

2023-06-25T00:15:38Z

Atavoidirc: WIP

The following table displays all known [[spaceship]] [[speed]]s and directions that are reasonably small (<1000 cells).

[[List of spaceships|Show all]]

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! [[Speed]]
! Smallest known
! Min. [[population]]
!  
! First found
! Discoverer
! Year found
|-
! style="background-color:#80ff80;" colspan="7" | [[Orthogonal]] speeds
|-
! style="background-color:#c6efce;" | [[c/2 orthogonal|c/2]]
| style="background-color:#c6efce;" | [[64P2H1V0]]
| style="background-color:#c6efce;" | {{cells|32}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[64P2H1V0]]{{refn|group=note|Although Hickerson does not remember which specific c/2 spaceship was discovered first, this was among the earliest.}}
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1971}}
|-
! style="background-color:#dfdfff;" | [[2c/4 orthogonal|2c/4]]
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | {{cells|9}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | [[John Conway]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#cfffff;" | [[8c/16 orthogonal|8/16]]
| style="background-color:#c6efce;" | [[Coe ship]]
| style="background-color:#c6efce;" | {{cells|28}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[Coe ship]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|1995}}
|-
! style="background-color:#c6efce;" | [[10c/20 orthogonal|10c/20]]
| style="background-color:#c6efce;" | [[Sidewinder]]
| style="background-color:#c6efce;" | {{cells|32}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[Ecologist]]
| style="background-color:#c6efce;" | [[Bill Gosper]]
| style="background-color:#c6efce;" | {{year|1971}}
|-
! style="background-color:#c6efce;" | [[3c/7 orthogonal|3c/7]]
| style="background-color:#c6efce;" | [[232P7H3V0]]
| style="background-color:#c6efce;" | {{cells|232}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[spaghetti monster]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|2016}}
|-
! style="background-color:#cfffff;" | [[2c/5 orthogonal|2c/5]]
| style="background-color:#c6efce;" | [[30P5H2V0]]
| style="background-color:#c6efce;" | {{cells|30}}
| style="background-color:#c6efce;" |
| style="background-color:#cfffff;" | [[44P5H2V0]]
| style="background-color:#cfffff;" | [[Dean Hickerson]]
| style="background-color:#cfffff;" | {{year|1991}}
|-
! style="background-color:#cfffff;" | [[c/3 orthogonal|c/3]]{{refn|group=note|Although neither the first nor the smallest known c/3 spaceships have appeared on [[Catagolue]], the speed as a whole is semi-natural, as on March 4, {{year|2022}}, a symmetric [[soup]] was found containing a [[dart]].<ref name="post142429" />}}
| style="background-color:#c6efce;" | [[25P3H1V0.1]], [[25P3H1V0.2]]
| style="background-color:#c6efce;" | {{cells|25}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[84P3H1V0.1]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[2c/7 orthogonal|2c/7]]
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | {{cells|36}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | [[David Eppstein]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/4 orthogonal|c/4]]
| style="background-color:#c6efce;" | [[37P4H1V0]]
| style="background-color:#c6efce;" | {{cells|37}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[119P4H1V0]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[c/5 orthogonal|c/5]]
| style="background-color:#c6efce;" | [[spider]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[snail]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|1996}}
|-
! style="background-color:#c6efce;" | [[c/6 orthogonal|c/6]]
| style="background-color:#c6efce;" | [[56P6H1V0]]
| style="background-color:#c6efce;" | {{cells|56}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[dragon]]
| style="background-color:#c6efce;" | [[Paul Tooke]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#dfdfff;" | [[c/7 orthogonal|c/7]]
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | {{cells|20}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | [[Josh Ball]]
| style="background-color:#dfdfff;" | {{year|2013}}
|-
! style="background-color:#cfffff;" | [[c/10 orthogonal|c/10]]
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | {{cells|28}}
| style="background-color:#cfffff;" |
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | [[zdr]]
| style="background-color:#cfffff;" | {{year|2016}}
|-
! style="background-color:#ffff80;" colspan="7" | [[Diagonal]] speeds
|-
! style="background-color:#dfdfff;" | [[c/4 diagonal|c/4]]
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | {{cells|5}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | [[Richard K. Guy]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[c/5 diagonal|c/5]]
| style="background-color:#c6efce;" | [[58P5H1V1]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[295P5H1V1]]
| style="background-color:#c6efce;" | [[Jason Summers]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/6 diagonal|c/6]]
| style="background-color:#c6efce;" | [[77P6H1V1]]
| style="background-color:#c6efce;" | {{cells|77}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[seal]]
| style="background-color:#c6efce;" | [[Nicolay Beluchenko]]
| style="background-color:#c6efce;" | {{year|2005}}
|-
! style="background-color:#c6efce;" | [[c/7 diagonal|c/7]]
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | {{cells|83}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | [[Matthias Merzenich]]
| style="background-color:#c6efce;" | {{year|2011}}
|-
! style="background-color:#c6efce;" | [[c/8 diagonal|c/8]]
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | {{cells|68}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]]
| style="background-color:#c6efce;" | {{year|2023}}
|-
! style="background-color:#c6efce;" | [[c/12 diagonal|c/12]]
| style="background-color:#c6efce;" | [[2-engine Cordership]]
| style="background-color:#c6efce;" | {{cells|100}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[13-engine Cordership]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1991}}
|-
! style="background-color:#ffa0a0;" colspan="7" | [[Knightship]]s ([[slope]] 2)
|-
! style="background-color:#c6efce;" | [[(2,1)c/6]]
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | {{cells|282}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]] and [[Tomas Rokicki]]
| style="background-color:#c6efce;" | {{year|2018}}
|}

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! style="background-color:#dfdfff;color:#0131b7;" | This spaceship has occurred from an asymmetric [[soup]].
|-
! style="background-color:#cfffff;color:#0180b7;" | This spaceship has occurred from a symmetric [[soup]].
|-
! style="background-color:#c6efce;color:#006100;" | This spaceship is an [[Spaceship#Elementary spaceships|elementary spaceship]].
|}

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

== References ==
<references>
<ref name="post142429">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 142429
|author = cvojan
|date = March 4, 2022
}}</ref>
</references>

User:Atavoidirc/Spaceship table

2023-06-25T00:08:10Z

Atavoidirc:

The following table displays all known [[spaceship]] [[speed]]s and directions that are reasonably small (<1000 cells).

[[List of spaceships|Show all]]

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! [[Speed]]
! Smallest known
! Min. [[population]]
!  
! First found
! Discoverer
! Year found
|-
! style="background-color:#80ff80;" colspan="7" | [[Orthogonal]] speeds
|-
! style="background-color:#dfdfff;" | [[c/2 orthogonal|c/2]]
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | {{cells|9}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | [[John Conway]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[3c/7 orthogonal|3c/7]]
| style="background-color:#c6efce;" | [[232P7H3V0]]
| style="background-color:#c6efce;" | {{cells|232}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[spaghetti monster]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|2016}}
|-
! style="background-color:#cfffff;" | [[2c/5 orthogonal|2c/5]]
| style="background-color:#c6efce;" | [[30P5H2V0]]
| style="background-color:#c6efce;" | {{cells|30}}
| style="background-color:#c6efce;" |
| style="background-color:#cfffff;" | [[44P5H2V0]]
| style="background-color:#cfffff;" | [[Dean Hickerson]]
| style="background-color:#cfffff;" | {{year|1991}}
|-
! style="background-color:#cfffff;" | [[c/3 orthogonal|c/3]]{{refn|group=note|Although neither the first nor the smallest known c/3 spaceships have appeared on [[Catagolue]], the speed as a whole is semi-natural, as on March 4, {{year|2022}}, a symmetric [[soup]] was found containing a [[dart]].<ref name="post142429" />}}
| style="background-color:#c6efce;" | [[25P3H1V0.1]], [[25P3H1V0.2]]
| style="background-color:#c6efce;" | {{cells|25}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[84P3H1V0.1]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[2c/7 orthogonal|2c/7]]
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | {{cells|36}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | [[David Eppstein]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/4 orthogonal|c/4]]
| style="background-color:#c6efce;" | [[37P4H1V0]]
| style="background-color:#c6efce;" | {{cells|37}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[119P4H1V0]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[c/5 orthogonal|c/5]]
| style="background-color:#c6efce;" | [[spider]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[snail]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|1996}}
|-
! style="background-color:#c6efce;" | [[c/6 orthogonal|c/6]]
| style="background-color:#c6efce;" | [[56P6H1V0]]
| style="background-color:#c6efce;" | {{cells|56}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[dragon]]
| style="background-color:#c6efce;" | [[Paul Tooke]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#dfdfff;" | [[c/7 orthogonal|c/7]]
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | {{cells|20}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | [[Josh Ball]]
| style="background-color:#dfdfff;" | {{year|2013}}
|-
! style="background-color:#cfffff;" | [[c/10 orthogonal|c/10]]
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | {{cells|28}}
| style="background-color:#cfffff;" |
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | [[zdr]]
| style="background-color:#cfffff;" | {{year|2016}}
|-
! style="background-color:#ffff80;" colspan="7" | [[Diagonal]] speeds
|-
! style="background-color:#dfdfff;" | [[c/4 diagonal|c/4]]
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | {{cells|5}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | [[Richard K. Guy]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[c/5 diagonal|c/5]]
| style="background-color:#c6efce;" | [[58P5H1V1]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[295P5H1V1]]
| style="background-color:#c6efce;" | [[Jason Summers]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/6 diagonal|c/6]]
| style="background-color:#c6efce;" | [[77P6H1V1]]
| style="background-color:#c6efce;" | {{cells|77}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[seal]]
| style="background-color:#c6efce;" | [[Nicolay Beluchenko]]
| style="background-color:#c6efce;" | {{year|2005}}
|-
! style="background-color:#c6efce;" | [[c/7 diagonal|c/7]]
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | {{cells|83}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | [[Matthias Merzenich]]
| style="background-color:#c6efce;" | {{year|2011}}
|-
! style="background-color:#c6efce;" | [[c/8 diagonal|c/8]]
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | {{cells|68}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]]
| style="background-color:#c6efce;" | {{year|2023}}
|-
! style="background-color:#c6efce;" | [[c/12 diagonal|c/12]]
| style="background-color:#c6efce;" | [[2-engine Cordership]]
| style="background-color:#c6efce;" | {{cells|100}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[13-engine Cordership]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1991}}
|-
! style="background-color:#ffa0a0;" colspan="7" | [[Knightship]]s ([[slope]] 2)
|-
! style="background-color:#c6efce;" | [[(2,1)c/6]]
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | {{cells|282}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]] and [[Tomas Rokicki]]
| style="background-color:#c6efce;" | {{year|2018}}
|}

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! style="background-color:#dfdfff;color:#0131b7;" | This spaceship has occurred from an asymmetric [[soup]].
|-
! style="background-color:#cfffff;color:#0180b7;" | This spaceship has occurred from a symmetric [[soup]].
|-
! style="background-color:#c6efce;color:#006100;" | This spaceship is an [[Spaceship#Elementary spaceships|elementary spaceship]].
|}

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

== References ==
<references>
<ref name="post142429">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 142429
|author = cvojan
|date = March 4, 2022
}}</ref>
</references>

[[Category:Lists of patterns]]

User:Atavoidirc/Spaceship table

2023-06-25T00:07:49Z

Atavoidirc: Created page with "The following table displays all known spaceship speeds and directions that are reasonably small (<1000 cells). Show all {| class="wikitable" style="margin-left:auto;margin-right:auto;" |- ! Speed ! Smallest known ! Min. population !   ! First found ! Discoverer ! Year found |- ! style="background-color:#80ff80;" colspan="7" | Orthogonal speeds |- ! style="background-color:#dfdfff;" | c/2 | style="back..."

The following table displays all known [[spaceship]] [[speed]]s and directions that are reasonably small (<1000 cells).

[[List of spaceships|Show all]]

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! [[Speed]]
! Smallest known
! Min. [[population]]
!  
! First found
! Discoverer
! Year found
|-
! style="background-color:#80ff80;" colspan="7" | [[Orthogonal]] speeds
|-
! style="background-color:#dfdfff;" | [[c/2 orthogonal|c/2]]
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | {{cells|9}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | [[John Conway]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[3c/7 orthogonal|3c/7]]
| style="background-color:#c6efce;" | [[232P7H3V0]]
| style="background-color:#c6efce;" | {{cells|232}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[spaghetti monster]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|2016}}
|-
! style="background-color:#cfffff;" | [[2c/5 orthogonal|2c/5]]
| style="background-color:#c6efce;" | [[30P5H2V0]]
| style="background-color:#c6efce;" | {{cells|30}}
| style="background-color:#c6efce;" |
| style="background-color:#cfffff;" | [[44P5H2V0]]
| style="background-color:#cfffff;" | [[Dean Hickerson]]
| style="background-color:#cfffff;" | {{year|1991}}
|-
! style="background-color:#ffffdd;" | [[17c/45 orthogonal|17c/45]]
| style="background-color:#ffffdd;" | [[caterpillar]]
| style="background-color:#ffffdd;" | {{cells|11,880,039}}<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1258&start=75#p32418|title=Re: Caterpillar's little brother research|author=Dave Greene|date=28 June 2016|accessdate=2 July 2016}}</ref>
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[caterpillar]]
| style="background-color:#ffffdd;" | [[Gabriel Nivasch]]
| style="background-color:#ffffdd;" | {{year|2004}}
|-
! style="background-color:#cfffff;" | [[c/3 orthogonal|c/3]]{{refn|group=note|Although neither the first nor the smallest known c/3 spaceships have appeared on [[Catagolue]], the speed as a whole is semi-natural, as on March 4, {{year|2022}}, a symmetric [[soup]] was found containing a [[dart]].<ref name="post142429" />}}
| style="background-color:#c6efce;" | [[25P3H1V0.1]], [[25P3H1V0.2]]
| style="background-color:#c6efce;" | {{cells|25}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[84P3H1V0.1]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[2c/7 orthogonal|2c/7]]
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | {{cells|36}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | [[David Eppstein]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/4 orthogonal|c/4]]
| style="background-color:#c6efce;" | [[37P4H1V0]]
| style="background-color:#c6efce;" | {{cells|37}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[119P4H1V0]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[c/5 orthogonal|c/5]]
| style="background-color:#c6efce;" | [[spider]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[snail]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|1996}}
|-
! style="background-color:#c6efce;" | [[c/6 orthogonal|c/6]]
| style="background-color:#c6efce;" | [[56P6H1V0]]
| style="background-color:#c6efce;" | {{cells|56}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[dragon]]
| style="background-color:#c6efce;" | [[Paul Tooke]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#dfdfff;" | [[c/7 orthogonal|c/7]]
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | {{cells|20}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | [[Josh Ball]]
| style="background-color:#dfdfff;" | {{year|2013}}
|-
! style="background-color:#cfffff;" | [[c/10 orthogonal|c/10]]
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | {{cells|28}}
| style="background-color:#cfffff;" |
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | [[zdr]]
| style="background-color:#cfffff;" | {{year|2016}}
|-
! style="background-color:#ffff80;" colspan="7" | [[Diagonal]] speeds
|-
! style="background-color:#dfdfff;" | [[c/4 diagonal|c/4]]
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | {{cells|5}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | [[Richard K. Guy]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[c/5 diagonal|c/5]]
| style="background-color:#c6efce;" | [[58P5H1V1]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[295P5H1V1]]
| style="background-color:#c6efce;" | [[Jason Summers]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/6 diagonal|c/6]]
| style="background-color:#c6efce;" | [[77P6H1V1]]
| style="background-color:#c6efce;" | {{cells|77}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[seal]]
| style="background-color:#c6efce;" | [[Nicolay Beluchenko]]
| style="background-color:#c6efce;" | {{year|2005}}
|-
! style="background-color:#c6efce;" | [[c/7 diagonal|c/7]]
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | {{cells|83}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | [[Matthias Merzenich]]
| style="background-color:#c6efce;" | {{year|2011}}
|-
! style="background-color:#c6efce;" | [[c/8 diagonal|c/8]]
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | {{cells|68}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]]
| style="background-color:#c6efce;" | {{year|2023}}
|-
! style="background-color:#c6efce;" | [[c/12 diagonal|c/12]]
| style="background-color:#c6efce;" | [[2-engine Cordership]]
| style="background-color:#c6efce;" | {{cells|100}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[13-engine Cordership]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1991}}
|-
! style="background-color:#ffa0a0;" colspan="7" | [[Knightship]]s ([[slope]] 2)
|-
! style="background-color:#c6efce;" | [[(2,1)c/6]]
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | {{cells|282}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]] and [[Tomas Rokicki]]
| style="background-color:#c6efce;" | {{year|2018}}
|}

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! style="background-color:#dfdfff;color:#0131b7;" | This spaceship has occurred from an asymmetric [[soup]].
|-
! style="background-color:#cfffff;color:#0180b7;" | This spaceship has occurred from a symmetric [[soup]].
|-
! style="background-color:#c6efce;color:#006100;" | This spaceship is an [[Spaceship#Elementary spaceships|elementary spaceship]].
|}

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

== References ==
<references>
<ref name="post142429">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 142429
|author = cvojan
|date = March 4, 2022
}}</ref>
</references>

[[Category:Lists of patterns]]

User:Atavoidirc

2023-06-25T00:06:01Z

Atavoidirc:

__NOTOC__
This is a hub page
[[User:Atavoidirc/Spaceship table]]
==[[User:GUYTU6J]]/Neighbourhood==
{{User:GUYTU6J/Neighbourhood}}
==Life wiki Pages==
* [[LifeWiki:Game of Life Status page]]
* [[LifeWiki:Spaceship Search Status Page]]
* [[LifeWiki:Smallest Spaceships Supporting Specific Speeds]]
* [[LifeWiki:Project OmniOsci/Overview]]
* [[LifeWiki:LifeViewer cheatsheet for LifeWiki articles]]
* [[LifeWiki:List of ongoing projects]]

==Other Pages==
* [[Table of oscillators by period]]

==Rules in Userspace==
* [[User:Carbon6/Gnarl]]
* [[User:Drc/GlideLife]]
* [[User:Prime Raptor21/Nothing (Rule)]]
* [[User:Evin/BiLife]]
* [[User:Moosey/eatsplosion]]
* [[User:Evin/Silverseeds]]
* [[User:Evin/OCA:E1]]
* [[User:Evin/Wlife]]
* [[User:GUYTU6J/OCA:Glimmering Garden]]
* [[User:Yujh/B34kz5e7c8/S23-a4ityz5k]]
* [[User:Cvojan/TubularTest]]
* [[User:Ultimium/OCA:LeapLife]]
* [[User:Cgoler2/rrlife]]
* [[User:Cgoler2/Clife]]
* [[User:Pzq Alex/BitLife]]

User:Atavoidirc/Sandbox

2023-06-22T23:23:01Z

Atavoidirc: Atavoidirc changed the content model of the page User:Atavoidirc/Sandbox from "wikitext" to "CSS"

riwjwuejugwunehhnshdfynhsvdndhvnvhfaniapsnjanovinshid svvaf-->{{InfoboxStart
|typename = Spaceship
|defaultconfig = spaceship
|viewerconfig = {{{viewerconfig|}}}
|name = {{{name|}}}
|zip = {{{zip|}}}
|mc = {{{mc|}}}
|life105 = {{{life105|}}}
|life106 = {{{life106|}}}
|plaintext = {{{plaintext|}}}
|rle = {{{rle|}}}
|nofile = {{{nofile|}}}
|pname = {{{pname|}}}
|animated = {{{animated|}}}
}}<tr>
<th valign="top"> Pattern type </th>
<td> {{#if: {{{type|}}} | [[{{{type|}}}]]<br /> }}[[Spaceship]] </td></tr>
{{#if: {{{family|}}} |
<tr>
<th> Family </th>
<td> [[:Category:{{{family}}} variants|{{{family}}}]] </td></tr>
}}{{PatternPopulationAndBoundingBox
|c = {{{c|}}}
|bx = {{{bx|}}}
|by = {{{by|}}}
|fc = {{{fc|}}}
|catextra = Spaceships
|periodic = true
}}{{InfoboxDivider}}
<tr>
<th> [[Direction]] </th>
<td> {{#if: {{{dir|}}} | [[:Category:{{{dir}}} spaceships|{{{dir}}}]] | Unknown }} </td></tr>
{{#if: {{{slope|}}} |
<tr>
<th> [[Slope]] </th>
<td> [[:Category:Spaceships with slope {{{slope}}}|{{{slope}}}]] </td></tr>
}}
<tr>
<th> [[Period#Spaceships|Period]] </th>
<td> {{#if: {{{p|}}} | [[:Category:Spaceships with period {{{p}}}|{{{p}}}]] | Unknown }} </td></tr>
<tr>
<th> [[Mod]] </th>
<td> {{#if: {{{m|}}} | [[:Category:Spaceships with mod {{{m}}}|{{{m}}}]] | Unknown }} </td></tr>
<tr>
<th> [[Speed]] </th>
<td> {{#if: {{{s|}}} | [[:Category:Spaceships with speed {{{s}}}|{{{s}}}]] | Unknown }} </td></tr>
<tr>
<th> [[Speed]] (unsimplified) </th>
<td> {{#if: {{{z|}}} | [[:Category:Spaceships with unsimplified speed {{{z}}}|{{{z}}}]] | Unknown }} </td></tr>
<tr>
<th> [[Heat]] </th>
<td> {{#if: {{{h|}}} | {{#iferror: {{#expr: floor({{{h}}})}} | {{{h}}} | [[:Category:Spaceships with heat {{CellsCategoryName|{{#expr: floor({{{h}}})}}}}|{{{h}}}]] }} | Unknown }} </td></tr>{{InfoboxDivider}}{{PatternDiscovery
|discoverer = {{{discoverer|}}}
|discoverer2 = {{{discoverer2|}}}
|discoverer3 = {{{discoverer3|}}}
|discoverer4 = {{{discoverer4|}}}
|discoverer5 = {{{discoverer5|}}}
|discoveryear = {{{discoveryear|}}}
}}{{PatternDownload
|synthesis = {{{synthesis|}}}
|synthesis2 = {{{synthesis2|}}}
|synthesisRLE = {{{synthesisRLE|}}}
|apgcode = {{{apgcode|}}}
|apgcode2 = {{{apgcode2|}}}
|life105 = {{{life105|}}}
|life106 = {{{life106|}}}
|plaintext = {{{plaintext|}}}
|zip = {{{zip|}}}
|mc = {{{mc|}}}
|rle = {{{rle|}}}
|pname = {{{pname|}}}
|rulespecial = {{{rulespecial|}}}
|rulemax = {{{rulemax|}}}
|rulemin = {{{rulemin|}}}
|isorulemax = {{{isorulemax|}}}
|isorulemin = {{{isorulemin|}}}
}}{{PatternIdentifiers
|apgcode = {{{apgcode|}}}
|apgcode2 = {{{apgcode2|}}}
|niemiecid = {{{niemiecid|}}}
|pentadecathlonid = {{{pentadecathlonid|}}}
|eppsteinid = {{{eppsteinid|}}}
}}

User:Atavoidirc/Sandbox

2023-06-22T23:22:54Z

Atavoidirc:

W-pentomino

2023-06-22T23:17:58Z

Atavoidirc: Atavoidirc changed the content model of the page W-pentomino from "JavaScript" to "wikitext": yeah i don't think i should be able to do this

#REDIRECT [[Polyomino#Pentominoes]]
[[Category:Patterns]]
[[Category:Patterns_with_5_cells]]
[[Category:Patterns_with_bilateral_diagonal_symmetry]]
[[Category:Patterns that can be constructed with 2 gliders]]

W-pentomino

2023-06-22T23:17:27Z

Atavoidirc: Atavoidirc changed the content model of the page W-pentomino from "wikitext" to "JavaScript"

2-engine Cordership

2023-06-22T23:16:35Z

Atavoidirc: fixing template error

{{Spaceship
|name = 2-engine Cordership
|pname = 2enginecordership
|family = Cordership
|c = 100
|bx = 41
|by = 48
|dir = Diagonal
|p = 96
|m = 96
|s = c/12
|z = 8c/96
|h = 110.4
|discoverer = praosylen
|discoveryear = 2017
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B3/S23
|synthesis = 9
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xq96_y8573w8aegvzys33zwg8gyvoozsvv0338gy2442cia049uo239e4z037e8x1z08464ogzy011zy3oozyf51guozyd2451032
|viewerconfig = #C [[ TRACK 1/12 1/12 THUMBSIZE 2 GPS 48 HEIGHT 480 WIDTH 480 ]]
}}
The '''2-engine Cordership''' is a [[c/12 diagonal]] [[spaceship]] that was discovered by praosylen on December 31, {{year|2017}}.<ref name="post54444" /> It is the [[Cordership]] that uses the fewest number of [[switch engine]]s known to be possible (ahead of the [[3-engine Cordership]]) as well as the smallest Cordership in terms of population (ahead of a variant of the [[4-engine Cordership]]) and the smallest engineered spaceship.{{refn|group=note|Status as engineered is debated.}}

The {{POTY|year=2017|rank=1}}

==Reactions==
[[Dave Greene]] noted that the 2-engine Cordership, like its [[3-engine Cordership|3-engine]] counterpart, can be stopped by a single [[glider]] from behind without releasing any [[glider]]s or other [[spaceship]]s,<ref name="post54470" /> and updated [[Martin Grant]]'s [[Model D Heisenburp|Model D]] [[Heisenburp device]] for the 2-engine Cordership.<ref name="post54470" />

[[Dave Greene]], [[BlinkerSpawn]] and [[Matthias Merzenich]] noted that the 2-engine Cordership can be eaten by a constellation of two [[eater]]s and three [[block]]s:<ref name="post54470" />

{{EmbedViewer
|pname = 2eceater
|caption = 2-engine Cordership eater
|position = center
|viewerconfig = #C [[ THEME 6 THUMBNAIL THUMBSIZE 2 ZOOM 6 HEIGHT 600 WIDTH 600 ]]
|style = width:360px;
}}

[[gmc_nxtman]] pointed out that the 2-engine Cordership can reflect a glider 180 degrees, while preserving its mod-4 timing, resulting in an updated version of [[glider loop]].<ref name="post54583" />

==Synthesis and seeds==
[[Dave Greene]] found a {{gliders|13}} [[synthesis]] of the 2-engine Cordership on the day of its discovery,<ref name="post54450" /> which [[Luka Okanishi]] improved to {{gliders|9|text=9 gliders}}.<ref name="post54453" />

Two-glider [[seed]]s using as few as 9 still lifes and [[one-glider seed]]s using 15 still lifes are known.<ref name="post54492" /><ref name="post57674" />

{{EmbedViewer
|pname = 2enginecordershipslowsalvo
|caption = [[Slow salvo]] construction of a one-glider seed
|position = center
|viewerconfig = #C [[ THEME 6 THUMBNAIL THUMBSIZE 2 AUTOSTART X -375 Y -375 ZOOM 6 LOOP 5000 ]]
#C [[ PAUSE 2 LINEAR ZOOM WIDTH 600 HEIGHT 600 ]]
#C [[ T 500 ]]
#C [[ T 1000 X -200 Y -200 Z -1 STEP 5 ]]
#C [[ T 3000 X -350 Y -350 Z 4 LINEAR ZOOM ]]
#C [[ T 3200 X -380 Y -380 Z 8 LINEAR ZOOM ]]
#C [[ T 4000 X -425 Y -425 ]]
|style = width:360px;
}}

==Uses==
[[David Bell]] built a [[log(t) growth]] from four 2-engine Corderships,<ref name="post54585" /> and a 4-engine Cordership [[rake]] from two adjacent 2-engine Corderships,<ref name="post54628" /> both on January 3rd, {{year|2018}}. [[2718281828]], [[Dave Greene]] and [[Chris Cain]] posted glider syntheses for this rake on January 7th, allowing for the construction of [[breeder]]s.<ref name="post54798" /><ref name="post54801" /><ref name="post54808" />

Bell further built two different period-96 c/12 forward rakes, one using the 4-engine rake, along with the 2-engine Cordership and an older 3-engine block [[puffer]],<ref name="post54784" /> the other using a new Cordership [[boat]] and [[block]] puffer, two 2-engine Corderships, and a sideways rake, both on January 6th, 2018.<ref name="post54784" /> He also built a different Cordership made from a two-engine boat puffer and a 2-engine Cordership that contains a glider which can escape if the [[boat]] is deleted by a sideways or forward glider.<ref name="post54784" />

[[Chris Cain]] updated the [[infinite glider hotel]] to use the 2-engine Cordership on January 3rd, 2018.<ref name="post54590" />

[[Entity Valkyrie]] built an {{times|714|501}} 2-engine Cordership gun on January 6, 2018, using [[Luka Okanishi]]'s 9-glider synthesis;<ref name="post54750" /> [[BlinkerSpawn]] noted that this gun could be compacted to {{times|385|253}} using the [[quadri-Snark]].<ref name="post54753" /> [[Dave Greene]] built an unrelated period-556 2-engine Cordership gun on January 7.<ref name="post54814" /><ref name="post54815" /> Entity Valkyrie built a different gun using a [[boat]] [[keeper]] reaction on January 10.<ref name="post54928" /> On August 29 that year, [[Nathaniel Johnston]] completed a stable glider to 2-engine Cordership [[converter]],<ref name="post63153" /> which converts an input glider to a 2-engine Cordership at [[repeat time]] 556 ticks, thus allowing for arbitrary high-period guns to be built. The following is an improved design by Dave Greene:
{{EmbedViewer
|pname = gliderto2ec
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM -1.5 GPS 60 STEP 6 Y 36 AUTOSTART LOOP 4146 HEIGHT 480 ]]
|caption = Converts an input glider to a 2-engine Cordership
|style = width:360px;
}}

Using a variant of the same script used to discover it, [[praosylen]] combined the 2-engine Cordership with an additional switch engine to obtain various puffers.<ref name="post54816" />


Toward the end of 2018, Adam P. Goucher added a "0-degree" slow-salvo synthesis of a 2-engine Cordership to [[slmake]], to allow more efficient long [[elbow]] pushes to be automatically compiled in [[self-constructing]] [[spaceship]] [[recipe]]s.<ref name="post63956" />

==See also==
* {{CategoryLink|Corderships}}

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

==References==
<references>
<ref name="post54444">{{LinkForumThread
|p = 54444
|format = ref
|title = Re: Spaceship Discussion Thread
|author = praosylen
|accessdate = January 4, 2018
|date = December 31, 2017
}}</ref>
<ref name="post54450">{{LinkForumThread
|p = 54450
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 4, 2018
|date = December 31, 2017
}}</ref>
<ref name="post54453">{{LinkForumThread
|p = 54453
|format = ref
|title = Re: Spaceship Discussion Thread
|author = [[Luka Okanishi]] (AbhpzTa)
|accessdate = January 4, 2018
|date = December 31, 2017
}}</ref>
<ref name="post54470">{{LinkForumThread
|p = 54470
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 3, 2018
}}</ref>
<ref name="post54492">{{LinkForumThread
|p = 54492
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 1, 2018
}}</ref>
<ref name="post54583">{{LinkForumThread
|p = 54583
|format = ref
|title = Re: Spaceship Discussion Thread
|author = gmc_nxtman
|accessdate = January 8, 2018
|date = January 3, 2018
}}</ref>
<ref name="post54585">{{LinkForumThread
|p = 54585
|format = ref
|title = Re: Spaceship Discussion Thread
|author = David Bell
|accessdate = August 10, 2019
|date = January 3, 2018
}}</ref>
<ref name="post54590">{{LinkForumThread
|p = 54590
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Chris Cain
|accessdate = January 8, 2018
|date = January 3, 2018
}}</ref>
<ref name="post54628">{{LinkForumThread
|p = 54628
|format = ref
|title = Re: Spaceship Discussion Thread
|author = David Bell
|accessdate = January 4, 2018
|date = January 3, 2018
}}</ref>
<ref name="post54750">{{LinkForumThread
|p = 54750
|format = ref
|title = Guns Discussion Thread
|author = Entity Valkyrie
|accessdate = January 8, 2018
|date = January 6, 2018
}}</ref>
<ref name="post54753">{{LinkForumThread
|p = 54753
|format = ref
|title = Re: Guns Discussion Thread
|author = BlinkerSpawn
|accessdate = January 8, 2018
|date = January 6, 2018
}}</ref>
<ref name="post54784">{{LinkForumThread
|p = 54784
|format = ref
|title = Re: Spaceship Discussion Thread
|author = David Bell
|accessdate = January 8, 2018
|date = January 6, 2018
}}</ref>
<ref name="post54798">{{LinkForumThread
|p = 54798
|format = ref
|title = Re: Spaceship Discussion Thread
|author = 2718281828
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54801">{{LinkForumThread
|p = 54801
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54808">{{LinkForumThread
|p = 54808
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Chris Cain
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54814">{{LinkForumThread
|p = 54814
|format = ref
|title = Re: Guns Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54815">{{LinkForumThread
|p = 54815
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54816">{{LinkForumThread
|p = 54816
|format = ref
|title = Re: Spaceship Discussion Thread
|author = praosylen
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54928">{{LinkForumThread
|p = 54928
|format = ref
|title = Re: Small Spaceship Syntheses
|author = Entity Valkyrie
|accessdate = January 10, 2018
|date = January 10, 2018
}}</ref>
<ref name="post57674">{{LinkForumThread
|p = 57674
|format = ref
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Dave Greene
|accessdate = March 11, 2018
|date = March 10, 2018
}}</ref>
<ref name="post63956">{{LinkForumThread
|p = 63956
|format = ref
|title = Re: Slow-salvo recipes
|author = Adam P. Goucher
|accessdate = December 31, 2018
|date = September 23, 2018
}}</ref>
<ref name="post63153">{{LinkForumThread
|author = Nathaniel Johnston
|title = Re: Stable Signal Converters
|format = ref
|p = 63153
|date = August 29, 2018
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_1.htm#a-2enginecordership}}
* {{LinkCatagolue|xq96_y8573w8aegvzys33zwg8gyvoozsvv0338gy2442cia049uo239e4z037e8x1z08464ogzy011zy3oozyf51guozyd2451032|format=extended}}

[[Category:Engineered spaceships]]
[[Category:Non-monotonic spaceships]]
[[Category:Patterns involving switch engines]]

2-engine Cordership

2023-06-22T23:15:25Z

Atavoidirc:

{{Spaceship
|name = 2-engine Cordership
|pname = 2enginecordership
|family = Cordership
|c = 100
|bx = 41
|by = 48
|dir = Diagonal
|p = 96
|m = 96
|s = c/12
|z = 8c/96
|h = 110.4
|discoverer = praosylen
|discoveryear = 2017
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B3/S23
|synthesis = 9
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xq96_y8573w8aegvzys33zwg8gyvoozsvv0338gy2442cia049uo239e4z037e8x1z08464ogzy011zy3oozyf51guozyd2451032
|viewerconfig = #C [[ TRACK 1/12 1/12 THUMBSIZE 2 GPS 48 HEIGHT 480 WIDTH 480 ]]
}}
The '''2-engine Cordership''' is a [[c/12 diagonal]] [[spaceship]] that was discovered by praosylen on December 31, {{year|2017}}.<ref name="post54444" /> It is the [[Cordership]] that uses the fewest number of [[switch engine]]s known to be possible (ahead of the [[3-engine Cordership]]) as well as the smallest Cordership in terms of population (ahead of a variant of the [[4-engine Cordership]]) and the smallest engineered spaceship.{{refn|group=note|Status as engineered is debated.}}

The {{POTY|year=2017|rank=1}}

==Reactions==
[[Dave Greene]] noted that the 2-engine Cordership, like its [[3-engine Cordership|3-engine]] counterpart, can be stopped by a single [[glider]] from behind without releasing any [[glider]]s or other [[spaceship]]s,<ref name="post54470" /> and updated [[Martin Grant]]'s [[Model D Heisenburp|Model D]] [[Heisenburp device]] for the 2-engine Cordership.<ref name="post54470" />

[[Dave Greene]], [[BlinkerSpawn]] and [[Matthias Merzenich]] noted that the 2-engine Cordership can be eaten by a constellation of two [[eater]]s and three [[block]]s:<ref name="post54470" />

{{EmbedViewer
|pname = 2eceater
|caption = 2-engine Cordership eater
|position = center
|viewerconfig = #C [[ THEME 6 THUMBNAIL THUMBSIZE 2 ZOOM 6 HEIGHT 600 WIDTH 600 ]]
|style = width:360px;
}}

[[gmc_nxtman]] pointed out that the 2-engine Cordership can reflect a glider 180 degrees, while preserving its mod-4 timing, resulting in an updated version of [[glider loop]].<ref name="post54583" />

==Synthesis and seeds==
[[Dave Greene]] found a {{gliders|13}} [[synthesis]] of the 2-engine Cordership on the day of its discovery,<ref name="post54450" /> which [[Luka Okanishi]] improved to {{gliders|9|text=9 gliders}}.<ref name="post54453" />

Two-glider [[seed]]s using as few as 9 still lifes and [[one-glider seed]]s using 15 still lifes are known.<ref name="post54492" /><ref name="post57674" />

{{EmbedViewer
|pname = 2enginecordershipslowsalvo
|caption = [[Slow salvo]] construction of a one-glider seed
|position = center
|viewerconfig = #C [[ THEME 6 THUMBNAIL THUMBSIZE 2 AUTOSTART X -375 Y -375 ZOOM 6 LOOP 5000 ]]
#C [[ PAUSE 2 LINEAR ZOOM WIDTH 600 HEIGHT 600 ]]
#C [[ T 500 ]]
#C [[ T 1000 X -200 Y -200 Z -1 STEP 5 ]]
#C [[ T 3000 X -350 Y -350 Z 4 LINEAR ZOOM ]]
#C [[ T 3200 X -380 Y -380 Z 8 LINEAR ZOOM ]]
#C [[ T 4000 X -425 Y -425 ]]
|style = width:360px;
}}

==Uses==
[[David Bell]] built a [[log(t) growth]] from four 2-engine Corderships,<ref name="post54585" /> and a 4-engine Cordership [[rake]] from two adjacent 2-engine Corderships,<ref name="post54628" /> both on January 3rd, {{year|2018}}. [[2718281828]], [[Dave Greene]] and [[Chris Cain]] posted glider syntheses for this rake on January 7th, allowing for the construction of [[breeder]]s.<ref name="post54798" /><ref name="post54801" /><ref name="post54808" />

Bell further built two different period-96 c/12 forward rakes, one using the 4-engine rake, along with the 2-engine Cordership and an older 3-engine block [[puffer]],<ref name="post54784" /> the other using a new Cordership [[boat]] and [[block]] puffer, two 2-engine Corderships, and a sideways rake, both on January 6th, 2018.<ref name="post54784" /> He also built a different Cordership made from a two-engine boat puffer and a 2-engine Cordership that contains a glider which can escape if the [[boat]] is deleted by a sideways or forward glider.<ref name="post54784" />

[[Chris Cain]] updated the [[infinite glider hotel]] to use the 2-engine Cordership on January 3rd, 2018.<ref name="post54590" />

[[Entity Valkyrie]] built an {{times|714|501}} 2-engine Cordership gun on January 6, 2018, using [[Luka Okanishi]]'s 9-glider synthesis;<ref name="post54750" /> [[BlinkerSpawn]] noted that this gun could be compacted to {{times|385|253}} using the [[quadri-Snark]].<ref name="post54753" /> [[Dave Greene]] built an unrelated period-556 2-engine Cordership gun on January 7.<ref name="post54814" /><ref name="post54815" /> Entity Valkyrie built a different gun using a [[boat]] [[keeper]] reaction on January 10.<ref name="post54928" /> On August 29 that year, [[Nathaniel Johnston]] completed a stable glider to 2-engine Cordership [[converter]],<ref name="post63153" /> which converts an input glider to a 2-engine Cordership at [[repeat time]] 556 ticks, thus allowing for arbitrary high-period guns to be built. The following is an improved design by Dave Greene:
{{EmbedViewer
|pname = gliderto2ec
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM -1.5 GPS 60 STEP 6 Y 36 AUTOSTART LOOP 4146 HEIGHT 480 ]]
|caption = Converts an input glider to a 2-engine Cordership
|style = width:360px;
}}

Using a variant of the same script used to discover it, [[praosylen]] combined the 2-engine Cordership with an additional switch engine to obtain various puffers.<ref name="post54816" />


Toward the end of 2018, Adam P. Goucher added a "0-degree" slow-salvo synthesis of a 2-engine Cordership to [[slmake]], to allow more efficient long [[elbow]] pushes to be automatically compiled in [[self-constructing]] [[spaceship]] [[recipe]]s.<ref name="post63956" />

==See also==
* {{CategoryLink|Corderships}}

==References==
<references>
<ref name="post54444">{{LinkForumThread
|p = 54444
|format = ref
|title = Re: Spaceship Discussion Thread
|author = praosylen
|accessdate = January 4, 2018
|date = December 31, 2017
}}</ref>
<ref name="post54450">{{LinkForumThread
|p = 54450
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 4, 2018
|date = December 31, 2017
}}</ref>
<ref name="post54453">{{LinkForumThread
|p = 54453
|format = ref
|title = Re: Spaceship Discussion Thread
|author = [[Luka Okanishi]] (AbhpzTa)
|accessdate = January 4, 2018
|date = December 31, 2017
}}</ref>
<ref name="post54470">{{LinkForumThread
|p = 54470
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 3, 2018
}}</ref>
<ref name="post54492">{{LinkForumThread
|p = 54492
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 1, 2018
}}</ref>
<ref name="post54583">{{LinkForumThread
|p = 54583
|format = ref
|title = Re: Spaceship Discussion Thread
|author = gmc_nxtman
|accessdate = January 8, 2018
|date = January 3, 2018
}}</ref>
<ref name="post54585">{{LinkForumThread
|p = 54585
|format = ref
|title = Re: Spaceship Discussion Thread
|author = David Bell
|accessdate = August 10, 2019
|date = January 3, 2018
}}</ref>
<ref name="post54590">{{LinkForumThread
|p = 54590
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Chris Cain
|accessdate = January 8, 2018
|date = January 3, 2018
}}</ref>
<ref name="post54628">{{LinkForumThread
|p = 54628
|format = ref
|title = Re: Spaceship Discussion Thread
|author = David Bell
|accessdate = January 4, 2018
|date = January 3, 2018
}}</ref>
<ref name="post54750">{{LinkForumThread
|p = 54750
|format = ref
|title = Guns Discussion Thread
|author = Entity Valkyrie
|accessdate = January 8, 2018
|date = January 6, 2018
}}</ref>
<ref name="post54753">{{LinkForumThread
|p = 54753
|format = ref
|title = Re: Guns Discussion Thread
|author = BlinkerSpawn
|accessdate = January 8, 2018
|date = January 6, 2018
}}</ref>
<ref name="post54784">{{LinkForumThread
|p = 54784
|format = ref
|title = Re: Spaceship Discussion Thread
|author = David Bell
|accessdate = January 8, 2018
|date = January 6, 2018
}}</ref>
<ref name="post54798">{{LinkForumThread
|p = 54798
|format = ref
|title = Re: Spaceship Discussion Thread
|author = 2718281828
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54801">{{LinkForumThread
|p = 54801
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54808">{{LinkForumThread
|p = 54808
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Chris Cain
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54814">{{LinkForumThread
|p = 54814
|format = ref
|title = Re: Guns Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54815">{{LinkForumThread
|p = 54815
|format = ref
|title = Re: Spaceship Discussion Thread
|author = Dave Greene
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54816">{{LinkForumThread
|p = 54816
|format = ref
|title = Re: Spaceship Discussion Thread
|author = praosylen
|accessdate = January 8, 2018
|date = January 7, 2018
}}</ref>
<ref name="post54928">{{LinkForumThread
|p = 54928
|format = ref
|title = Re: Small Spaceship Syntheses
|author = Entity Valkyrie
|accessdate = January 10, 2018
|date = January 10, 2018
}}</ref>
<ref name="post57674">{{LinkForumThread
|p = 57674
|format = ref
|title = Re: Thread For Synthesisable Spaceship Guns
|author = Dave Greene
|accessdate = March 11, 2018
|date = March 10, 2018
}}</ref>
<ref name="post63956">{{LinkForumThread
|p = 63956
|format = ref
|title = Re: Slow-salvo recipes
|author = Adam P. Goucher
|accessdate = December 31, 2018
|date = September 23, 2018
}}</ref>
<ref name="post63153">{{LinkForumThread
|author = Nathaniel Johnston
|title = Re: Stable Signal Converters
|format = ref
|p = 63153
|date = August 29, 2018
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_1.htm#a-2enginecordership}}
* {{LinkCatagolue|xq96_y8573w8aegvzys33zwg8gyvoozsvv0338gy2442cia049uo239e4z037e8x1z08464ogzy011zy3oozyf51guozyd2451032|format=extended}}

[[Category:Engineered spaceships]]
[[Category:Non-monotonic spaceships]]
[[Category:Patterns involving switch engines]]

List of spaceships/noadjustable

2023-06-22T23:12:32Z

Atavoidirc:

The following table displays all known [[spaceship]] [[speed]]s and directions that do not rely on [[Spaceship#Adjustable spaceships|adjustable ships]].

[[List of spaceships|Show all]]

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! [[Speed]]
! Smallest known
! Min. [[population]]
!  
! First found
! Discoverer
! Year found
|-
! style="background-color:#80ff80;" colspan="7" | [[Orthogonal]] speeds
|-
! style="background-color:#dfdfff;" | [[c/2 orthogonal|c/2]]
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | {{cells|9}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | [[John Conway]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[3c/7 orthogonal|3c/7]]
| style="background-color:#c6efce;" | [[232P7H3V0]]
| style="background-color:#c6efce;" | {{cells|232}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[spaghetti monster]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|2016}}
|-
! style="background-color:#cfffff;" | [[2c/5 orthogonal|2c/5]]
| style="background-color:#c6efce;" | [[30P5H2V0]]
| style="background-color:#c6efce;" | {{cells|30}}
| style="background-color:#c6efce;" |
| style="background-color:#cfffff;" | [[44P5H2V0]]
| style="background-color:#cfffff;" | [[Dean Hickerson]]
| style="background-color:#cfffff;" | {{year|1991}}
|-
! style="background-color:#ffffdd;" | [[17c/45 orthogonal|17c/45]]
| style="background-color:#ffffdd;" | [[caterpillar]]
| style="background-color:#ffffdd;" | {{cells|11,880,039}}<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1258&start=75#p32418|title=Re: Caterpillar's little brother research|author=Dave Greene|date=28 June 2016|accessdate=2 July 2016}}</ref>
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[caterpillar]]
| style="background-color:#ffffdd;" | [[Gabriel Nivasch]]
| style="background-color:#ffffdd;" | {{year|2004}}
|-
! style="background-color:#cfffff;" | [[c/3 orthogonal|c/3]]{{refn|group=note|Although neither the first nor the smallest known c/3 spaceships have appeared on [[Catagolue]], the speed as a whole is semi-natural, as on March 4, {{year|2022}}, a symmetric [[soup]] was found containing a [[dart]].<ref name="post142429" />}}
| style="background-color:#c6efce;" | [[25P3H1V0.1]], [[25P3H1V0.2]]
| style="background-color:#c6efce;" | {{cells|25}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[84P3H1V0.1]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[2c/7 orthogonal|2c/7]]
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | {{cells|36}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | [[David Eppstein]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/4 orthogonal|c/4]]
| style="background-color:#c6efce;" | [[37P4H1V0]]
| style="background-color:#c6efce;" | {{cells|37}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[119P4H1V0]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[c/5 orthogonal|c/5]]
| style="background-color:#c6efce;" | [[spider]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[snail]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|1996}}
|-
! style="background-color:#c6efce;" | [[c/6 orthogonal|c/6]]
| style="background-color:#c6efce;" | [[56P6H1V0]]
| style="background-color:#c6efce;" | {{cells|56}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[dragon]]
| style="background-color:#c6efce;" | [[Paul Tooke]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#dfdfff;" | [[c/7 orthogonal|c/7]]
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | {{cells|20}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | [[Josh Ball]]
| style="background-color:#dfdfff;" | {{year|2013}}
|-
! style="background-color:#ffffdd;" | [[31c/240 orthogonal|31c/240]]
| style="background-color:#ffffdd;" | [[silverfish]]
| style="background-color:#ffffdd;" | {{cells|210,108}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[shield bug]]
| style="background-color:#ffffdd;" | [[Dave Greene]]
| style="background-color:#ffffdd;" | {{year|2014}}
|-
! style="background-color:#cfffff;" | [[c/10 orthogonal|c/10]]
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | {{cells|28}}
| style="background-color:#cfffff;" |
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | [[zdr]]
| style="background-color:#cfffff;" | {{year|2016}}
|-
! style="background-color:#ffff80;" colspan="7" | [[Diagonal]] speeds
|-
! style="background-color:#dfdfff;" | [[c/4 diagonal|c/4]]
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | {{cells|5}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | [[Richard K. Guy]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[c/5 diagonal|c/5]]
| style="background-color:#c6efce;" | [[58P5H1V1]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[295P5H1V1]]
| style="background-color:#c6efce;" | [[Jason Summers]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/6 diagonal|c/6]]
| style="background-color:#c6efce;" | [[77P6H1V1]]
| style="background-color:#c6efce;" | {{cells|77}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[seal]]
| style="background-color:#c6efce;" | [[Nicolay Beluchenko]]
| style="background-color:#c6efce;" | {{year|2005}}
|-
! style="background-color:#c6efce;" | [[c/7 diagonal|c/7]]
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | {{cells|83}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | [[Matthias Merzenich]]
| style="background-color:#c6efce;" | {{year|2011}}
|-
! style="background-color:#c6efce;" | [[c/8 diagonal|c/8]]
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | {{cells|68}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]]
| style="background-color:#c6efce;" | {{year|2023}}
|-
! style="background-color:#c6efce;" | [[c/12 diagonal|c/12]]
| style="background-color:#c6efce;" | [[2-engine Cordership]]
| style="background-color:#c6efce;" | {{cells|100}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[13-engine Cordership]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1991}}
|-
! style="background-color:#ffa0a0;" colspan="7" | [[Knightship]]s ([[slope]] 2)
|-
! style="background-color:#c6efce;" | [[(2,1)c/6]]
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | {{cells|282}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]] and [[Tomas Rokicki]]
| style="background-color:#c6efce;" | {{year|2018}}
|-
! style="background-color:#57aadd;" colspan="7" | Slope 34/7
|-
! style="background-color:#ffffdd;" | [[:Category:Spaceships with speed (34,7)c/156|(34,7)c/156]]
| style="background-color:#ffffdd;" | [[Unnamed (34,7)c/156 spaceship]]
| style="background-color:#ffffdd;" | {{cells|25,013,268}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[Unnamed (34,7)c/156 spaceship]]
| style="background-color:#ffffdd;" | [[Luka Okanishi]]
| style="background-color:#ffffdd;" | {{year|2023}}
|-
! style="background-color:#ffa0a0;" colspan="7" | Slope 23/5
|-
! style="background-color:#ffffdd;" | [[:Category:Spaceships with speed (23,5)c/79|(23,5)c/79]]
| style="background-color:#ffffdd;" | [[waterbear]]
| style="background-color:#ffffdd;" | {{cells|197,896}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[waterbear]]
| style="background-color:#ffffdd;" | [[Brett Berger]]
| style="background-color:#ffffdd;" | {{year|2014}}
|-
|}

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! style="background-color:#dfdfff;color:#0131b7;" | This spaceship has occurred from an asymmetric [[soup]].
|-
! style="background-color:#cfffff;color:#0180b7;" | This spaceship has occurred from a symmetric [[soup]].
|-
! style="background-color:#c6efce;color:#006100;" | This spaceship is an [[Spaceship#Elementary spaceships|elementary spaceship]].
|-
! style="background-color:#ffffdd;color:#8a7600;" | This spaceship is an [[Spaceship#Engineered spaceships|engineered spaceship]].
|}

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

== References ==
<references>
<ref name="post142429">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 142429
|author = cvojan
|date = March 4, 2022
}}</ref>
</references>

[[Category:Lists of patterns]]

List of spaceships

2023-06-22T23:10:13Z

Atavoidirc: added missing column

The following table displays '''all''' known [[spaceship]] [[speed]]s and directions.

[[List of spaceships/noadjustable|Hide adjustable spaceships]]

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! [[Speed]]
! Smallest known
! Min. [[population]]
! |  
! First found
! Discoverer
! Year found
|-
! style="background-color:#80ff80;" colspan="7" | [[Orthogonal]] speeds ([[slope]] 0)
|-
! style="background-color:#dfdfff;" | [[c/2 orthogonal|c/2]]
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | {{cells|9}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | [[John Conway]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[3c/7 orthogonal|3c/7]]
| style="background-color:#c6efce;" | [[232P7H3V0]]
| style="background-color:#c6efce;" | {{cells|232}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[spaghetti monster]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|2016}}
|-
! style="background-color:#cfffff;" | [[2c/5 orthogonal|2c/5]]
| style="background-color:#c6efce;" | [[30P5H2V0]]
| style="background-color:#c6efce;" | {{cells|30}}
| style="background-color:#c6efce;" |
| style="background-color:#cfffff;" | [[44P5H2V0]]
| style="background-color:#cfffff;" | [[Dean Hickerson]]
| style="background-color:#cfffff;" | {{year|1991}}
|-
! style="background-color:#ffffdd;" | [[17c/45 orthogonal|17c/45]]
| style="background-color:#ffffdd;" | [[caterpillar]]
| style="background-color:#ffffdd;" | {{cells|11,880,039}}<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1258&start=75#p32418|title=Re: Caterpillar's little brother research|author=Dave Greene|date=28 June 2016|accessdate=2 July 2016}}</ref>
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[caterpillar]]
| style="background-color:#ffffdd;" | [[Gabriel Nivasch]]
| style="background-color:#ffffdd;" | {{year|2004}}
|-
! style="background-color:#cfffff;" | [[c/3 orthogonal|c/3]]{{refn|group=note|Although neither the first nor the smallest known c/3 spaceships have appeared on [[Catagolue]], the speed as a whole is semi-natural, as on March 4, {{year|2022}}, a symmetric [[soup]] was found containing a [[dart]].<ref name="post142429" />}}
| style="background-color:#c6efce;" | [[25P3H1V0.1]]
| style="background-color:#c6efce;" | {{cells|25}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[84P3H1V0.1]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[2c/7 orthogonal|2c/7]]
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | {{cells|36}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | [[David Eppstein]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/4 orthogonal|c/4]]
| style="background-color:#c6efce;" | [[37P4H1V0]]
| style="background-color:#c6efce;" | {{cells|37}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[119P4H1V0]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#ffc7ce;" | 5c/21
| style="background-color:#ffc7ce;" | [[Caterloopillar|5c/21 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|915,290}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|5c/21 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 4c/17
| style="background-color:#ffc7ce;" | [[Caterloopillar|4c/17 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|801,673}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|4c/17 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/13
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/13 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|658,860}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/13 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/9
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/9 caterloopillar]]<ref name=MoreLoops>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=50#p30060|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=16 April 2016|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|545,843}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/9 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 4c/19
| style="background-color:#ffc7ce;" | [[Caterloopillar|4c/19 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|407,817}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|4c/19 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#c6efce;" | [[c/5 orthogonal|c/5]]
| style="background-color:#c6efce;" | [[spider]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[snail]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|1996}}
|-
! style="background-color:#ffc7ce;" | 4c/21
| style="background-color:#ffc7ce;" | [[Caterloopillar|4c/21 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|319,572}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|4c/21 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/16
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/16 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|307,754}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/16 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/11
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/11 caterloopillar]]<ref name=MoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|279,482}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/11 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/17
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/17 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|265,261}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/17 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#c6efce;" | [[c/6 orthogonal|c/6]]
| style="background-color:#c6efce;" | [[56P6H1V0]]
| style="background-color:#c6efce;" | {{cells|56}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[dragon]]
| style="background-color:#c6efce;" | [[Paul Tooke]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#ffc7ce;" | 11c/67
| style="background-color:#ffc7ce;" | [[Caterloopillar|11c/67 caterloopillar]]
| style="background-color:#ffc7ce;" | {{cells|359,218}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|11c/67 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/19
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/19 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|228,196}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/19 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/13
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/13 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|218,478}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/13 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/20
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/20 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|203,690}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/20 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#dfdfff;" | [[c/7 orthogonal|c/7]]
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | {{cells|20}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | [[Josh Ball]]
| style="background-color:#dfdfff;" | {{year|2013}}
|-
! style="background-color:#ffc7ce;" | 2c/15
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/15 caterloopillar]]<ref name=EMoreLoops>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=50#p30105|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=16 April 2016|accessdate=4 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|188,470}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/15 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffffdd;" | [[31c/240 orthogonal|31c/240]]
| style="background-color:#ffffdd;" | [[silverfish]]
| style="background-color:#ffffdd;" | {{cells|210,108}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[shield bug]]
| style="background-color:#ffffdd;" | [[Dave Greene]]
| style="background-color:#ffffdd;" | {{year|2014}}
|-
! style="background-color:#ffc7ce;" | [[c/8 orthogonal|c/8]]
| style="background-color:#ffc7ce;" | [[Caterloopillar|Original caterloopillar]]
| style="background-color:#ffc7ce;" | {{cells|232,815}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|Original caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/17
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/17 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|171,658}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/17 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | [[c/9 orthogonal|c/9]]
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/9 caterloopillar]]<ref name=NineEleven>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=50#p30046|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=15 April 2016|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|169,476}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/9 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 49c/456
| style="background-color:#ffc7ce;" | [[Caterloopillar|49c/456 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|433,416}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|49c/456 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/19
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/19 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|153,619}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/19 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#cfffff;" | [[c/10 orthogonal|c/10]]
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | {{cells|28}}
| style="background-color:#cfffff;" |
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | [[zdr]]
| style="background-color:#cfffff;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/21
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/21 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|144,020}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/21 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/11
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/11 caterloopillar]]<ref name=NineEleven/>
| style="background-color:#ffc7ce;" | {{cells|149,061}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/11 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/12
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/12 caterloopillar]]<ref name=MoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|125,427}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/12 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/13
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/13 caterloopillar]]
| style="background-color:#ffc7ce;" | {{cells|117,090}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/13 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/15
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/15 caterloopillar]]<ref name=EMoreLoops>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=50#p30105|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=16 April 2016|accessdate=4 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|108,728}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/15 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/16
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/16 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|106,262}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/16 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/17
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/17 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|98,621}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/17 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/19
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/19 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|93,555}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/19 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/20
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/20 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|93,497}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/20 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/21
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/21 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|88,972}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/21 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/24
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/24 caterloopillar]]<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=75#p30110|title=Re: Caterloopillar WIP (all speeds < c/4)|author=thunk|date=17 April 2016|accessdate=4 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|83,722}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/24 caterloopillar]]
| style="background-color:#ffc7ce;" | [[thunk]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/25
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/25 caterloopillar]]<ref name=YMoreLoops>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=75#p30134|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=17 April 2016|accessdate=4 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|84,876}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/25 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/27
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/27 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|84,154}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/27 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/28
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/28 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|83,516}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/28 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/29
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/29 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|81,582}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/29 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/31
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/31 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|77,445}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/31 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/32
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/32 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|77,591}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/32 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/33
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/33 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|77,143}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/33 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/35
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/35 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|74,769}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/35 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/67
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/67 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|63,135}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/67 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/87
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/87 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|62,343}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/87 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffff80;" colspan="7" | [[Diagonal]] speeds ([[slope]] 1)
|-
! style="background-color:#dfdfff;" | [[c/4 diagonal|c/4]]
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | {{cells|5}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | [[Richard K. Guy]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[c/5 diagonal|c/5]]
| style="background-color:#c6efce;" | [[58P5H1V1]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[295P5H1V1]]
| style="background-color:#c6efce;" | [[Jason Summers]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#ffc7ce;" | 1746011c/8916896
| style="background-color:#ffc7ce;" | [[Speed Demonoid]] Version 1
| style="background-color:#ffc7ce;" | {{cells|1,021,124}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Speed Demonoid]] Version 1
| style="background-color:#ffc7ce;" | [[Pavel Grankovskiy]]
| style="background-color:#ffc7ce;" | {{year|2020}}
|-
! style="background-color:#ffc7ce;" | 436513c/2215479
| style="background-color:#ffc7ce;" | lowest-period [[Speed Demonoid]] Version 1
| style="background-color:#ffc7ce;" | {{cells|1,021,124}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | lowest-period [[Speed Demonoid]] Version 1
| style="background-color:#ffc7ce;" | [[Pavel Grankovskiy]]
| style="background-color:#ffc7ce;" | {{year|2020}}
|-
! style="background-color:#ffc7ce;" | 1642811c/8246964
| style="background-color:#ffc7ce;" | smallest bounding box [[Speed Demonoid]] Version 2
| style="background-color:#ffc7ce;" | {{cells|426,464}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | smallest bounding box [[Speed Demonoid]] Version 2
| style="background-color:#ffc7ce;" | [[Pavel Grankovskiy]]
| style="background-color:#ffc7ce;" | {{year|2020}}
|-
! style="background-color:#c6efce;" | [[c/6 diagonal|c/6]]
| style="background-color:#c6efce;" | [[77P6H1V1]]
| style="background-color:#c6efce;" | {{cells|77}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[seal]]
| style="background-color:#c6efce;" | [[Nicolay Beluchenko]]
| style="background-color:#c6efce;" | {{year|2005}}
|-
! style="background-color:#c6efce;" | [[c/7 diagonal|c/7]]
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | {{cells|83}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | [[Matthias Merzenich]]
| style="background-color:#c6efce;" | {{year|2011}}
|-
! style="background-color:#c6efce;" | [[c/8 diagonal|c/8]]
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | {{cells|68}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]]
| style="background-color:#c6efce;" | {{year|2023}}
|-
! style="background-color:#c6efce;" | [[c/12 diagonal|c/12]]
| style="background-color:#c6efce;" | [[2-engine Cordership]]
| style="background-color:#c6efce;" | {{cells|100}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[13-engine Cordership]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1991}}
|-
! style="background-color:#ffc7ce;" | 65c/438852
| style="background-color:#ffc7ce;" | [[Demonoid|0hd Demonoid]]
| style="background-color:#ffc7ce;" | {{cells|27,250}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Demonoid|0hd Demonoid]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2015}}
|-
! style="background-color:#ffc7ce;" | 13c/96228
| style="background-color:#ffc7ce;" | [[Demonoid|0hd Demonoid]]
| style="background-color:#ffc7ce;" | [[:Category:Patterns with (number) cells|?]]
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Demonoid|0hd Demonoid]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2015}}
|-
! style="background-color:#ffc7ce;" | 65c/818356
| style="background-color:#ffc7ce;" | [[Demonoid|10hd Demonoid]]
| style="background-color:#ffc7ce;" | {{cells|47,701}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Demonoid|10hd Demonoid]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2015}}
|-
! style="background-color:#ffc7ce;" | c/12700<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1469&start=150#p25401|title=Re: Demonoid (diagonal Geminoid) completed!|author=Dave Greene|date=26 November 2015|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | [[Demonoid|10hd Demonoid]]
| style="background-color:#ffc7ce;" | [[:Category:Patterns with (number) cells|?]]
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Demonoid|10hd Demonoid]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2015}}
|-
! style="background-color:#ffa0a0;" colspan="7" | [[Knightship]]s (slope 2)
|-
! style="background-color:#c6efce;" | (2,1)c/6
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | {{cells|282}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]] and [[Tomas Rokicki]]
| style="background-color:#c6efce;" | {{year|2018}}
|-
! style="background-color:#ffc7ce;" | (4096,2048)c/17783745
| style="background-color:#ffc7ce;" | [[Gemini|Gemini 2]]<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=406&start=25#p2578|title=Re: Shrinking Gemini: Four Ideas|author=Dave Greene|date=13 June 2010|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | [[:Category:Patterns with between 100,000 and 999,999 cells|≤ 872,252]]
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Gemini|Gemini 2]]
| style="background-color:#ffc7ce;" | [[Dave Greene]]
| style="background-color:#ffc7ce;" | {{year|2010}}
|-
! style="background-color:#ffc7ce;" | (6,3)c/245912
| style="background-color:#ffc7ce;" | [[Parallel HBK]]
| style="background-color:#ffc7ce;" | {{cells|132,945}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Parallel HBK]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2014}}
|-
! style="background-color:#ffc7ce;" | (6,3)c/2621440
| style="background-color:#ffc7ce;" | [[Half-baked knightship]]
| style="background-color:#ffc7ce;" | {{cells|1,049,395}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Half-baked knightship]]
| style="background-color:#ffc7ce;" | [[Adam P. Goucher]]
| style="background-color:#ffc7ce;" | {{year|2014}}
|-
! style="background-color:#5dcc5d;" colspan="7" | [[Camelship]]s (slope 3)
|-
! style="background-color:#ffc7ce;" | (3072,1024)c/36000001
| style="background-color:#ffc7ce;" | [[Gemini|Gemini 3]]<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=406&start=25#p2590|title=Re: Shrinking Gemini: Four Ideas|author=Dave Greene|date=14 June 2010|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | [[:Category:Patterns with between 100,000 and 999,999 cells|≤ 850,932]]
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Gemini|Gemini 3]]
| style="background-color:#ffc7ce;" | [[Dave Greene]]
| style="background-color:#ffc7ce;" | {{year|2010}}
|-
! style="background-color:#ffc7ce;" | (3,1)c/3948264
| style="background-color:#ffc7ce;" | [[Camelship]]
| style="background-color:#ffc7ce;" | {{cells|239,822}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Camelship]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2018}}
|-
! style="background-color:#fdce5e;" colspan="7" | [[Giraffeship]]s (slope 4)
|-
| style="background-color:#ff8888;" colspan="7" align="center" | none found
|-
! style="background-color:#ff5757;" colspan="7" | Slope 23/5
|-
! style="background-color:#ffffdd;" | [[:Category:Spaceships with speed (23,5)c/79|(23,5)c/79]]
| style="background-color:#ffffdd;" | [[waterbear]]
| style="background-color:#ffffdd;" | {{cells|197,896}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[waterbear]]
| style="background-color:#ffffdd;" | [[Brett Berger]]
| style="background-color:#ffffdd;" | {{year|2014}}
|-
! style="background-color:#57aadd;" colspan="7" | Slope 34/7
|-
! style="background-color:#ffffdd;" | [[:Category:Spaceships with speed (34,7)c/156|(34,7)c/156]]
| style="background-color:#ffffdd;" | [[Unnamed (34,7)c/156 spaceship]]
| style="background-color:#ffffdd;" | {{cells|25,013,268}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[Unnamed (34,7)c/156 spaceship]]
| style="background-color:#ffffdd;" | [[Luka Okanishi]]
| style="background-color:#ffffdd;" | {{year|2023}}
|-
! style="background-color:#fa8072;" colspan="7" | [[Ibisship]]s (slope 5)
|-
! style="background-color:#ffc7ce;" | (5120,1024)c/16849793
| style="background-color:#ffc7ce;" | [[Gemini]]
| style="background-color:#ffc7ce;" | {{cells|846,278}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Gemini]]
| style="background-color:#ffc7ce;" | [[Andrew J. Wade]]
| style="background-color:#ffc7ce;" | {{year|2010}}
|-
|}

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! style="background-color:#dfdfff;color:#0131b7;" | This spaceship has occurred from an asymmetric [[soup]].
|-
! style="background-color:#cfffff;color:#0180b7;" | This spaceship has occurred from a symmetric [[soup]].
|-
! style="background-color:#c6efce;color:#006100;" | This spaceship is an [[Spaceship#Elementary spaceships|elementary spaceship]].
|-
! style="background-color:#ffffdd;color:#8a7600;" | This spaceship is an [[Spaceship#Engineered spaceships|engineered spaceship]].
|-
! style="background-color:#ffc7ce;color:#9c0006;" | This spaceship is an [[Spaceship#Adjustable spaceships|adjustable spaceship]].
|}

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

== References ==
<references>
<ref name="post142429">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 142429
|author = cvojan
|date = March 4, 2022
}}</ref>
</references>

[[Category:Lists of patterns]]

List of spaceships

2023-06-22T23:07:51Z

Atavoidirc: added (34,7)c/156 ship

The following table displays '''all''' known [[spaceship]] [[speed]]s and directions.

[[List of spaceships/noadjustable|Hide adjustable spaceships]]

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! [[Speed]]
! Smallest known
! Min. [[population]]
! style="background-color:white;border-top-color:white;" |  
! First found
! Discoverer
! Year found
|-
! style="background-color:#80ff80;" colspan="7" | [[Orthogonal]] speeds ([[slope]] 0)
|-
! style="background-color:#dfdfff;" | [[c/2 orthogonal|c/2]]
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | {{cells|9}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[lightweight spaceship]]
| style="background-color:#dfdfff;" | [[John Conway]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[3c/7 orthogonal|3c/7]]
| style="background-color:#c6efce;" | [[232P7H3V0]]
| style="background-color:#c6efce;" | {{cells|232}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[spaghetti monster]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|2016}}
|-
! style="background-color:#cfffff;" | [[2c/5 orthogonal|2c/5]]
| style="background-color:#c6efce;" | [[30P5H2V0]]
| style="background-color:#c6efce;" | {{cells|30}}
| style="background-color:#c6efce;" |
| style="background-color:#cfffff;" | [[44P5H2V0]]
| style="background-color:#cfffff;" | [[Dean Hickerson]]
| style="background-color:#cfffff;" | {{year|1991}}
|-
! style="background-color:#ffffdd;" | [[17c/45 orthogonal|17c/45]]
| style="background-color:#ffffdd;" | [[caterpillar]]
| style="background-color:#ffffdd;" | {{cells|11,880,039}}<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1258&start=75#p32418|title=Re: Caterpillar's little brother research|author=Dave Greene|date=28 June 2016|accessdate=2 July 2016}}</ref>
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[caterpillar]]
| style="background-color:#ffffdd;" | [[Gabriel Nivasch]]
| style="background-color:#ffffdd;" | {{year|2004}}
|-
! style="background-color:#cfffff;" | [[c/3 orthogonal|c/3]]{{refn|group=note|Although neither the first nor the smallest known c/3 spaceships have appeared on [[Catagolue]], the speed as a whole is semi-natural, as on March 4, {{year|2022}}, a symmetric [[soup]] was found containing a [[dart]].<ref name="post142429" />}}
| style="background-color:#c6efce;" | [[25P3H1V0.1]]
| style="background-color:#c6efce;" | {{cells|25}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[84P3H1V0.1]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#c6efce;" | [[2c/7 orthogonal|2c/7]]
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | {{cells|36}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[weekender]]
| style="background-color:#c6efce;" | [[David Eppstein]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#c6efce;" | [[c/4 orthogonal|c/4]]
| style="background-color:#c6efce;" | [[37P4H1V0]]
| style="background-color:#c6efce;" | {{cells|37}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[119P4H1V0]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1989}}
|-
! style="background-color:#ffc7ce;" | 5c/21
| style="background-color:#ffc7ce;" | [[Caterloopillar|5c/21 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|915,290}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|5c/21 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 4c/17
| style="background-color:#ffc7ce;" | [[Caterloopillar|4c/17 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|801,673}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|4c/17 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/13
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/13 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|658,860}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/13 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/9
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/9 caterloopillar]]<ref name=MoreLoops>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=50#p30060|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=16 April 2016|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|545,843}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/9 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 4c/19
| style="background-color:#ffc7ce;" | [[Caterloopillar|4c/19 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|407,817}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|4c/19 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#c6efce;" | [[c/5 orthogonal|c/5]]
| style="background-color:#c6efce;" | [[spider]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[snail]]
| style="background-color:#c6efce;" | [[Tim Coe]]
| style="background-color:#c6efce;" | {{year|1996}}
|-
! style="background-color:#ffc7ce;" | 4c/21
| style="background-color:#ffc7ce;" | [[Caterloopillar|4c/21 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|319,572}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|4c/21 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/16
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/16 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|307,754}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/16 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/11
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/11 caterloopillar]]<ref name=MoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|279,482}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/11 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/17
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/17 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|265,261}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/17 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#c6efce;" | [[c/6 orthogonal|c/6]]
| style="background-color:#c6efce;" | [[56P6H1V0]]
| style="background-color:#c6efce;" | {{cells|56}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[dragon]]
| style="background-color:#c6efce;" | [[Paul Tooke]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#ffc7ce;" | 11c/67
| style="background-color:#ffc7ce;" | [[Caterloopillar|11c/67 caterloopillar]]
| style="background-color:#ffc7ce;" | {{cells|359,218}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|11c/67 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/19
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/19 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|228,196}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/19 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/13
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/13 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|218,478}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/13 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 3c/20
| style="background-color:#ffc7ce;" | [[Caterloopillar|3c/20 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|203,690}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|3c/20 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#dfdfff;" | [[c/7 orthogonal|c/7]]
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | {{cells|20}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[loafer]]
| style="background-color:#dfdfff;" | [[Josh Ball]]
| style="background-color:#dfdfff;" | {{year|2013}}
|-
! style="background-color:#ffc7ce;" | 2c/15
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/15 caterloopillar]]<ref name=EMoreLoops>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=50#p30105|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=16 April 2016|accessdate=4 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|188,470}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/15 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffffdd;" | [[31c/240 orthogonal|31c/240]]
| style="background-color:#ffffdd;" | [[silverfish]]
| style="background-color:#ffffdd;" | {{cells|210,108}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[shield bug]]
| style="background-color:#ffffdd;" | [[Dave Greene]]
| style="background-color:#ffffdd;" | {{year|2014}}
|-
! style="background-color:#ffc7ce;" | [[c/8 orthogonal|c/8]]
| style="background-color:#ffc7ce;" | [[Caterloopillar|Original caterloopillar]]
| style="background-color:#ffc7ce;" | {{cells|232,815}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|Original caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/17
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/17 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|171,658}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/17 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | [[c/9 orthogonal|c/9]]
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/9 caterloopillar]]<ref name=NineEleven>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=50#p30046|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=15 April 2016|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|169,476}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/9 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 49c/456
| style="background-color:#ffc7ce;" | [[Caterloopillar|49c/456 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|433,416}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|49c/456 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/19
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/19 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|153,619}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/19 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#cfffff;" | [[c/10 orthogonal|c/10]]
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | {{cells|28}}
| style="background-color:#cfffff;" |
| style="background-color:#cfffff;" | [[copperhead]]
| style="background-color:#cfffff;" | [[zdr]]
| style="background-color:#cfffff;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | 2c/21
| style="background-color:#ffc7ce;" | [[Caterloopillar|2c/21 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|144,020}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|2c/21 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/11
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/11 caterloopillar]]<ref name=NineEleven/>
| style="background-color:#ffc7ce;" | {{cells|149,061}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/11 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/12
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/12 caterloopillar]]<ref name=MoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|125,427}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/12 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/13
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/13 caterloopillar]]
| style="background-color:#ffc7ce;" | {{cells|117,090}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/13 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/15
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/15 caterloopillar]]<ref name=EMoreLoops>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=50#p30105|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=16 April 2016|accessdate=4 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|108,728}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/15 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/16
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/16 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|106,262}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/16 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/17
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/17 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|98,621}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/17 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/19
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/19 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|93,555}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/19 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/20
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/20 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|93,497}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/20 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/21
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/21 caterloopillar]]<ref name=EMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|88,972}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/21 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/24
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/24 caterloopillar]]<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=75#p30110|title=Re: Caterloopillar WIP (all speeds < c/4)|author=thunk|date=17 April 2016|accessdate=4 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|83,722}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/24 caterloopillar]]
| style="background-color:#ffc7ce;" | [[thunk]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/25
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/25 caterloopillar]]<ref name=YMoreLoops>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=2151&start=75#p30134|title=Re: Caterloopillar WIP (all speeds < c/4)|author=Michael Simkin|date=17 April 2016|accessdate=4 July 2016}}</ref>
| style="background-color:#ffc7ce;" | {{cells|84,876}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/25 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/27
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/27 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|84,154}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/27 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/28
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/28 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|83,516}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/28 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/29
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/29 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|81,582}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/29 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/31
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/31 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|77,445}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/31 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/32
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/32 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|77,591}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/32 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/33
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/33 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|77,143}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/33 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/35
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/35 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|74,769}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/35 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/67
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/67 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|63,135}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/67 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffc7ce;" | c/87
| style="background-color:#ffc7ce;" | [[Caterloopillar|c/87 caterloopillar]]<ref name=YMoreLoops/>
| style="background-color:#ffc7ce;" | {{cells|62,343}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[caterloopillar|c/87 caterloopillar]]
| style="background-color:#ffc7ce;" | [[Michael Simkin]]
| style="background-color:#ffc7ce;" | {{year|2016}}
|-
! style="background-color:#ffff80;" colspan="7" | [[Diagonal]] speeds ([[slope]] 1)
|-
! style="background-color:#dfdfff;" | [[c/4 diagonal|c/4]]
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | {{cells|5}}
| style="background-color:#dfdfff;" |
| style="background-color:#dfdfff;" | [[glider]]
| style="background-color:#dfdfff;" | [[Richard K. Guy]]
| style="background-color:#dfdfff;" | {{year|1970}}
|-
! style="background-color:#c6efce;" | [[c/5 diagonal|c/5]]
| style="background-color:#c6efce;" | [[58P5H1V1]]
| style="background-color:#c6efce;" | {{cells|58}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[295P5H1V1]]
| style="background-color:#c6efce;" | [[Jason Summers]]
| style="background-color:#c6efce;" | {{year|2000}}
|-
! style="background-color:#ffc7ce;" | 1746011c/8916896
| style="background-color:#ffc7ce;" | [[Speed Demonoid]] Version 1
| style="background-color:#ffc7ce;" | {{cells|1,021,124}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Speed Demonoid]] Version 1
| style="background-color:#ffc7ce;" | [[Pavel Grankovskiy]]
| style="background-color:#ffc7ce;" | {{year|2020}}
|-
! style="background-color:#ffc7ce;" | 436513c/2215479
| style="background-color:#ffc7ce;" | lowest-period [[Speed Demonoid]] Version 1
| style="background-color:#ffc7ce;" | {{cells|1,021,124}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | lowest-period [[Speed Demonoid]] Version 1
| style="background-color:#ffc7ce;" | [[Pavel Grankovskiy]]
| style="background-color:#ffc7ce;" | {{year|2020}}
|-
! style="background-color:#ffc7ce;" | 1642811c/8246964
| style="background-color:#ffc7ce;" | smallest bounding box [[Speed Demonoid]] Version 2
| style="background-color:#ffc7ce;" | {{cells|426,464}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | smallest bounding box [[Speed Demonoid]] Version 2
| style="background-color:#ffc7ce;" | [[Pavel Grankovskiy]]
| style="background-color:#ffc7ce;" | {{year|2020}}
|-
! style="background-color:#c6efce;" | [[c/6 diagonal|c/6]]
| style="background-color:#c6efce;" | [[77P6H1V1]]
| style="background-color:#c6efce;" | {{cells|77}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[seal]]
| style="background-color:#c6efce;" | [[Nicolay Beluchenko]]
| style="background-color:#c6efce;" | {{year|2005}}
|-
! style="background-color:#c6efce;" | [[c/7 diagonal|c/7]]
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | {{cells|83}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[lobster (spaceship)|lobster]]
| style="background-color:#c6efce;" | [[Matthias Merzenich]]
| style="background-color:#c6efce;" | {{year|2011}}
|-
! style="background-color:#c6efce;" | [[c/8 diagonal|c/8]]
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | {{cells|68}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[walrus]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]]
| style="background-color:#c6efce;" | {{year|2023}}
|-
! style="background-color:#c6efce;" | [[c/12 diagonal|c/12]]
| style="background-color:#c6efce;" | [[2-engine Cordership]]
| style="background-color:#c6efce;" | {{cells|100}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[13-engine Cordership]]
| style="background-color:#c6efce;" | [[Dean Hickerson]]
| style="background-color:#c6efce;" | {{year|1991}}
|-
! style="background-color:#ffc7ce;" | 65c/438852
| style="background-color:#ffc7ce;" | [[Demonoid|0hd Demonoid]]
| style="background-color:#ffc7ce;" | {{cells|27,250}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Demonoid|0hd Demonoid]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2015}}
|-
! style="background-color:#ffc7ce;" | 13c/96228
| style="background-color:#ffc7ce;" | [[Demonoid|0hd Demonoid]]
| style="background-color:#ffc7ce;" | [[:Category:Patterns with (number) cells|?]]
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Demonoid|0hd Demonoid]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2015}}
|-
! style="background-color:#ffc7ce;" | 65c/818356
| style="background-color:#ffc7ce;" | [[Demonoid|10hd Demonoid]]
| style="background-color:#ffc7ce;" | {{cells|47,701}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Demonoid|10hd Demonoid]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2015}}
|-
! style="background-color:#ffc7ce;" | c/12700<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=1469&start=150#p25401|title=Re: Demonoid (diagonal Geminoid) completed!|author=Dave Greene|date=26 November 2015|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | [[Demonoid|10hd Demonoid]]
| style="background-color:#ffc7ce;" | [[:Category:Patterns with (number) cells|?]]
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Demonoid|10hd Demonoid]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2015}}
|-
! style="background-color:#ffa0a0;" colspan="7" | [[Knightship]]s (slope 2)
|-
! style="background-color:#c6efce;" | (2,1)c/6
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | {{cells|282}}
| style="background-color:#c6efce;" |
| style="background-color:#c6efce;" | [[Sir Robin]]
| style="background-color:#c6efce;" | [[Adam P. Goucher]] and [[Tomas Rokicki]]
| style="background-color:#c6efce;" | {{year|2018}}
|-
! style="background-color:#ffc7ce;" | (4096,2048)c/17783745
| style="background-color:#ffc7ce;" | [[Gemini|Gemini 2]]<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=406&start=25#p2578|title=Re: Shrinking Gemini: Four Ideas|author=Dave Greene|date=13 June 2010|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | [[:Category:Patterns with between 100,000 and 999,999 cells|≤ 872,252]]
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Gemini|Gemini 2]]
| style="background-color:#ffc7ce;" | [[Dave Greene]]
| style="background-color:#ffc7ce;" | {{year|2010}}
|-
! style="background-color:#ffc7ce;" | (6,3)c/245912
| style="background-color:#ffc7ce;" | [[Parallel HBK]]
| style="background-color:#ffc7ce;" | {{cells|132,945}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Parallel HBK]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2014}}
|-
! style="background-color:#ffc7ce;" | (6,3)c/2621440
| style="background-color:#ffc7ce;" | [[Half-baked knightship]]
| style="background-color:#ffc7ce;" | {{cells|1,049,395}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Half-baked knightship]]
| style="background-color:#ffc7ce;" | [[Adam P. Goucher]]
| style="background-color:#ffc7ce;" | {{year|2014}}
|-
! style="background-color:#5dcc5d;" colspan="7" | [[Camelship]]s (slope 3)
|-
! style="background-color:#ffc7ce;" | (3072,1024)c/36000001
| style="background-color:#ffc7ce;" | [[Gemini|Gemini 3]]<ref>{{cite web|url=https://conwaylife.com/forums/viewtopic.php?f=2&t=406&start=25#p2590|title=Re: Shrinking Gemini: Four Ideas|author=Dave Greene|date=14 June 2010|accessdate=2 July 2016}}</ref>
| style="background-color:#ffc7ce;" | [[:Category:Patterns with between 100,000 and 999,999 cells|≤ 850,932]]
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Gemini|Gemini 3]]
| style="background-color:#ffc7ce;" | [[Dave Greene]]
| style="background-color:#ffc7ce;" | {{year|2010}}
|-
! style="background-color:#ffc7ce;" | (3,1)c/3948264
| style="background-color:#ffc7ce;" | [[Camelship]]
| style="background-color:#ffc7ce;" | {{cells|239,822}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Camelship]]
| style="background-color:#ffc7ce;" | [[Chris Cain]]
| style="background-color:#ffc7ce;" | {{year|2018}}
|-
! style="background-color:#fdce5e;" colspan="7" | [[Giraffeship]]s (slope 4)
|-
| style="background-color:#ff8888;" colspan="7" align="center" | none found
|-
! style="background-color:#ff5757;" colspan="7" | Slope 23/5
|-
! style="background-color:#ffffdd;" | [[:Category:Spaceships with speed (23,5)c/79|(23,5)c/79]]
| style="background-color:#ffffdd;" | [[waterbear]]
| style="background-color:#ffffdd;" | {{cells|197,896}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[waterbear]]
| style="background-color:#ffffdd;" | [[Brett Berger]]
| style="background-color:#ffffdd;" | {{year|2014}}
|-
! style="background-color:#57aadd;" colspan="7" | Slope 34/7
|-
! style="background-color:#ffffdd;" | [[:Category:Spaceships with speed (34,7)c/156|(34,7)c/156]]
| style="background-color:#ffffdd;" | [[Unnamed (34,7)c/156 spaceship]]
| style="background-color:#ffffdd;" | {{cells|25,013,268}}
| style="background-color:#ffffdd;" |
| style="background-color:#ffffdd;" | [[Unnamed (34,7)c/156 spaceship]]
| style="background-color:#ffffdd;" | [[Luka Okanishi]]
| style="background-color:#ffffdd;" | {{year|2023}}
|-
! style="background-color:#fa8072;" colspan="7" | [[Ibisship]]s (slope 5)
|-
! style="background-color:#ffc7ce;" | (5120,1024)c/16849793
| style="background-color:#ffc7ce;" | [[Gemini]]
| style="background-color:#ffc7ce;" | {{cells|846,278}}
| style="background-color:#ffc7ce;" |
| style="background-color:#ffc7ce;" | [[Gemini]]
| style="background-color:#ffc7ce;" | [[Andrew J. Wade]]
| style="background-color:#ffc7ce;" | {{year|2010}}
|-
|}

{| class="wikitable" style="margin-left:auto;margin-right:auto;"
|-
! style="background-color:#dfdfff;color:#0131b7;" | This spaceship has occurred from an asymmetric [[soup]].
|-
! style="background-color:#cfffff;color:#0180b7;" | This spaceship has occurred from a symmetric [[soup]].
|-
! style="background-color:#c6efce;color:#006100;" | This spaceship is an [[Spaceship#Elementary spaceships|elementary spaceship]].
|-
! style="background-color:#ffffdd;color:#8a7600;" | This spaceship is an [[Spaceship#Engineered spaceships|engineered spaceship]].
|-
! style="background-color:#ffc7ce;color:#9c0006;" | This spaceship is an [[Spaceship#Adjustable spaceships|adjustable spaceship]].
|}

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

== References ==
<references>
<ref name="post142429">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 142429
|author = cvojan
|date = March 4, 2022
}}</ref>
</references>

[[Category:Lists of patterns]]

Ss

2023-06-21T13:18:10Z

Atavoidirc: Changed redirect target from Salvo to Salvo#Classification

#REDIRECT [[Salvo#Classification]]

Ss

2023-06-21T13:17:35Z

Atavoidirc: Changed redirect target from Slow Salvo to Salvo

#REDIRECT [[Salvo]]

Ss

2023-06-21T13:17:26Z

Atavoidirc: Redirected page to Slow Salvo

#REDIRECT [[Slow Salvo]]

Static symmetry

2023-06-20T16:05:51Z

Atavoidirc: /* On a square grid */ adding examples for reflectional symmetry (note: examples are not the smallest with each symmetry, but objects that i believe illustrate the symmetry well)

A '''static symmetry'''<ref name="post138823" /> refers to the combined rotational and reflectional symmetries of an arrangement of cells on a grid. Most isotropic rules preserve all such symmetries.

This page specifically only covers purely geometric symmetries. Other preserved attributes which are not necessarily geometrical symmetries, notably gutters, are compiled on the [[Minor static symmetries]] page. Symmetries which apply to periodic objects, such as still lifes, oscillators and spaceships, which also includes time symmetries, are listed on the [[Kinetic symmetry]] page.

== Basic theory ==
The Life transition rule, like that of any [[Isotropic non-totalistic cellular automaton|isotropic cellular automaton]], is invariant under valid reflections and rotations. That is, the change in state of a cell remains the same if its [[neighbourhood]] is rotated or reflected. This implies there are '''symmetries''' which if present in a pattern are present in all its successors. Note that the converse is not true: a pattern need not have the full symmetry of one of its successor states.

== On a square grid ==
[[File:Symmetries.png|center|frame|Overview of symmetries (excluding D8_2).]]

=== Rotational ===
<div class="mw-collapsible mw-collapsed">
Rotational symmetries are prefixed with "C", referring to the [https://en.wikipedia.org/wiki/Cyclic_group cyclic groups]. Click on "Expand" to the right to view a list of them.
<div class="mw-collapsible-content">

==== C1 ====
'''C1''': Symmetric under 360° rotation. This is essentially no symmetry at all. Example: [[Eater 1]]

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o!
|width = 160
|height = 160
|caption = C1 symmetry
}}</center>

==== C2 ====
'''C2''': Symmetric under 180° rotation. There are three possibilities:

* '''C2_1''': Rotation around the center of a cell. The bounding rectangle of a C2_1 pattern is odd by odd. Example: [[Long snake]]
* '''C2_2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd. Example: [[Aircraft carrier]]
* '''C2_4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Snake]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$31o
$15bo14bo$15bo14bo$15bo9b2o3bo$15bo8b4o2bo$15bo8b4o2bo$15bo2b10o2bo$
15bo14bo$15bo14bo$15bo3b2o4b2o3bo$15bo2bo2bo2bo2bo2bo$15bo2bo2bo2bo2bo
2bo$15bo3b2o4b2o3bo$15bo14bo$15bo14bo$15b16o!
|width = 320
|height = 320
|caption = C2_1 symmetry}}
| {{Sym-demo
|rle = x = 31, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$15b16o$15bo14bo$15bo14bo$15bo9b2o3bo$15bo8b4o2bo$15bo8b4o2bo$15bo2b
10o2bo$15bo14bo$15bo14bo$15bo3b2o4b2o3bo$15bo2bo2bo2bo2bo2bo$15bo2bo2b
o2bo2bo2bo$15bo3b2o4b2o3bo$15bo14bo$15bo14bo$15b16o!
|width = 320
|height = 320
|caption = C2_2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$16b16o$16bo14bo$16bo14bo$16bo9b2o3bo$16bo8b4o2bo$16bo8b4o2bo$16bo2b
10o2bo$16bo14bo$16bo14bo$16bo3b2o4b2o3bo$16bo2bo2bo2bo2bo2bo$16bo2bo2b
o2bo2bo2bo$16bo3b2o4b2o3bo$16bo14bo$16bo14bo$16b16o!
|width = 320
|height = 320
|caption = C2_4 symmetry}}
|}

==== C4 ====
'''C4''': Symmetric under 90° rotation. There are two possibilities:

* '''C4_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Shuriken]]
* '''C4_4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Quad]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o3b2o4b2o3bo3b3o3b2o3bo$o2bo2bo2bo2bo2bo2b4o2b
o2bo2bo$o2bo2bo2bo2bo2bo2b4o2bo2bo2bo$o3b2o4b2o3bo3b3o3b2o3bo$o14bo5bo
8bo$o14bo5bo8bo$o2b10o2bo5bo3b2o3bo$o2b4o8bo5bo2bo2bo2bo$o2b4o8bo5bo2b
o2bo2bo$o3b2o9bo5bo3b2o3bo$o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo
$o3b2o3bo5bo9b2o3bo$o2bo2bo2bo5bo8b4o2bo$o2bo2bo2bo5bo8b4o2bo$o3b2o3bo
5bo2b10o2bo$o8bo5bo14bo$o8bo5bo14bo$o3b2o3b3o3bo3b2o4b2o3bo$o2bo2bo2b
4o2bo2bo2bo2bo2bo2bo$o2bo2bo2b4o2bo2bo2bo2bo2bo2bo$o3b2o3b3o3bo3b2o4b
2o3bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = C4_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b3o3b2o3bo$o2bo2bo2bo2bo2b2o2b
4o2bo2bo2bo$o2bo2bo2bo2bo2b2o2b4o2bo2bo2bo$o3b2o4b2o3b2o3b3o3b2o3bo$o
14b2o5bo8bo$o14b2o5bo8bo$o2b10o2b2o5bo3b2o3bo$o2b4o8b2o5bo2bo2bo2bo$o
2b4o8b2o5bo2bo2bo2bo$o3b2o9b2o5bo3b2o3bo$o14b2o14bo$o14b2o14bo$32o$32o
$o14b2o14bo$o14b2o14bo$o3b2o3bo5b2o9b2o3bo$o2bo2bo2bo5b2o8b4o2bo$o2bo
2bo2bo5b2o8b4o2bo$o3b2o3bo5b2o2b10o2bo$o8bo5b2o14bo$o8bo5b2o14bo$o3b2o
3b3o3b2o3b2o4b2o3bo$o2bo2bo2b4o2b2o2bo2bo2bo2bo2bo$o2bo2bo2b4o2b2o2bo
2bo2bo2bo2bo$o3b2o3b3o3b2o3b2o4b2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = C4_4 symmetry}}
|}
</div></div>

C4 tends to produce record [[diehard]]s and [[megasized]] soups compared to other symmetries.

=== Reflectional ===
<div class="mw-collapsible mw-collapsed">
Reflectional symmetries are prefixed with "D", referring to the [https://en.wikipedia.org/wiki/Dihedral_group dihedral groups]. Click on "Expand" to the right to view a list of them.
<div class="mw-collapsible-content">

==== D2 ====
'''D2''': Symmetric under reflection through a line. There are two possibilities:

* '''D2_+''' The line is orthogonal. There are two sub-possibilities:
** '''D2_+1''' The line bisects a row of cells. The bounding rectangle is odd by any. Example: [[Hat]]
** '''D2_+2''' The line lies between two rows of cells. The bounding rectangle is even by any. Example: [[Frutterfly]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 16, y = 31, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$o14bo$o14bo$o3b2o9bo$o2b4o8bo$o2b4o8bo$o2b10o2bo$o14bo$o14bo$o3b2o4b
2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b2o3bo$o14bo$o14bo$16o!
|width = 160
|height = 320
|caption = D2_+1 symmetry}}
| {{Sym-demo
|rle = x = 16, y = 32, rule = B/S012345678
16o$o14bo$o14bo$o3b2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b
2o3bo$o14bo$o14bo$o2b10o2bo$o2b4o8bo$o2b4o8bo$o3b2o9bo$o14bo$o14bo$16o
$16o$o14bo$o14bo$o3b2o9bo$o2b4o8bo$o2b4o8bo$o2b10o2bo$o14bo$o14bo$o3b
2o4b2o3bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$o3b2o4b2o3bo$o14bo$o14bo$
16o!
|width = 160
|height = 320
|caption = D2_+2 symmetry}}
|}

* '''D2_x''' The line is diagonal. Example: [[Elevener]]

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S012345678
16o$o14bo$o14bo$o7bo6bo$o6bobo5bo$o7bo3bo2bo$o11bo2bo$o3bo7bo2bo$o2bob
o6bo2bo$o3bo6bo3bo$o9bo4bo$o8bo5bo$o4b4o6bo$o14bo$o14bo$16o!
|width = 160
|height = 160
|caption = D2_x symmetry}}</center>

==== D4 ====
'''D4''': Symmetric under both reflection and 180° rotation. The reflection symmetry will be with respect to two lines. There are two possibilities:

* '''D4_+''': The lines are orthogonal. There are three sub-possibilities:
** '''D4_+1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Dead spark coil]]
** '''D4_+2''': Rotation around the midpoint of a side of a cell. The bounding rectangle is even by odd. Example: [[Honeycomb]]
** '''D4_+4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[A for all]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o3b2o4b2o3bo3b2o4b2o3bo$o2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo$o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$o3b2o4b2o3bo3b2o4b2o3bo$o14b
o14bo$o14bo14bo$o2b10o2bo2b10o2bo$o2b4o8bo8b4o2bo$o2b4o8bo8b4o2bo$o3b
2o9bo9b2o3bo$o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo$o3b2o9bo9b2o
3bo$o2b4o8bo8b4o2bo$o2b4o8bo8b4o2bo$o2b10o2bo2b10o2bo$o14bo14bo$o14bo
14bo$o3b2o4b2o3bo3b2o4b2o3bo$o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo$o3b2o4b2o3bo3b2o4b2o3bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D4_+1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 31, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b2o2b
o2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b2o3b
o$o14b2o14bo$o14b2o14bo$o2b10o2b2o2b10o2bo$o2b4o8b2o8b4o2bo$o2b4o8b2o
8b4o2bo$o3b2o9b2o9b2o3bo$o14b2o14bo$o14b2o14bo$32o$o14b2o14bo$o14b2o
14bo$o3b2o9b2o9b2o3bo$o2b4o8b2o8b4o2bo$o2b4o8b2o8b4o2bo$o2b10o2b2o2b
10o2bo$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b
2o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b
2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D4_+2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b2o2b
o2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b2o3b
o$o14b2o14bo$o14b2o14bo$o2b10o2b2o2b10o2bo$o2b4o8b2o8b4o2bo$o2b4o8b2o
8b4o2bo$o3b2o9b2o9b2o3bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b
2o14bo$o3b2o9b2o9b2o3bo$o2b4o8b2o8b4o2bo$o2b4o8b2o8b4o2bo$o2b10o2b2o2b
10o2bo$o14b2o14bo$o14b2o14bo$o3b2o4b2o3b2o3b2o4b2o3bo$o2bo2bo2bo2bo2b
2o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2b2o2bo2bo2bo2bo2bo$o3b2o4b2o3b2o3b2o4b
2o3bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D4_+4 symmetry}}
|}

* '''D4_x''' The lines are diagonal. There are two sub-possibilities:
** '''D4_x1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Loaf siamese loaf]]
** '''D4_x4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Long ship]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o7bo6bo5b3o6bo$o6bobo5bo5bobo6bo$o7bo3bo2bo2bo
2b3o6bo$o11bo2bo2b2o10bo$o3bo7bo2bo2b2o5b3o2bo$o2bobo6bo2bo2b3o4bobo2b
o$o3bo6bo3bo3b2o4b3o2bo$o9bo4bo3b4o7bo$o8bo5bo4b5o5bo$o4b4o6bo6b4o4bo$
o14bo14bo$o14bo14bo$31o$o14bo14bo$o14bo14bo$o4b4o6bo6b4o4bo$o5b5o4bo5b
o8bo$o7b4o3bo4bo9bo$o2b3o4b2o3bo3bo6bo3bo$o2bobo4b3o2bo2bo6bobo2bo$o2b
3o5b2o2bo2bo7bo3bo$o10b2o2bo2bo11bo$o6b3o2bo2bo2bo3bo7bo$o6bobo5bo5bob
o6bo$o6b3o5bo6bo7bo$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D4_x1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o5b3o6bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo2b3o6bo$o11bo2b2o2b2o10bo$o3bo7bo2b2o2b2o5b3o2bo$o2bobo6bo2b2o2b
3o4bobo2bo$o3bo6bo3b2o3b2o4b3o2bo$o9bo4b2o3b4o7bo$o8bo5b2o4b5o5bo$o4b
4o6b2o6b4o4bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b2o14bo$o4b
4o6b2o6b4o4bo$o5b5o4b2o5bo8bo$o7b4o3b2o4bo9bo$o2b3o4b2o3b2o3bo6bo3bo$o
2bobo4b3o2b2o2bo6bobo2bo$o2b3o5b2o2b2o2bo7bo3bo$o10b2o2b2o2bo11bo$o6b
3o2bo2b2o2bo3bo7bo$o6bobo5b2o5bobo6bo$o6b3o5b2o6bo7bo$o14b2o14bo$o14b
2o14bo$32o!
|width = 320
|height = 320
|caption = D4_x4 symmetry}}
|}

==== D8 ====
'''D8''': Symmetric under both reflection and 90° rotation. The reflection symmetry will be with respect to horizontal, vertical, and diagonal lines. There are three possibilities:

* '''D8_1''': Rotation around the center of a cell. The bounding rectangle is odd by odd. Example: [[Pulsar]]
* '''D8_2''': Rotation around a edge of a cell. The bounding rectangle is even by odd. This symmetry is not preserved by Life (reverting to D4_+2), but is with most bilaterally symmetric rules.
* '''D8_4''': Rotation around a corner of a cell. The bounding rectangle is even by even. Example: [[Lake 2]]

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S012345678
31o$o14bo14bo$o14bo14bo$o7bo6bo6bo7bo$o6bobo5bo5bobo6bo$o7bo3bo2bo2bo
3bo7bo$o11bo2bo2bo11bo$o3bo7bo2bo2bo7bo3bo$o2bobo6bo2bo2bo6bobo2bo$o3b
o6bo3bo3bo6bo3bo$o9bo4bo4bo9bo$o8bo5bo5bo8bo$o4b4o6bo6b4o4bo$o14bo14bo
$o14bo14bo$31o$o14bo14bo$o14bo14bo$o4b4o6bo6b4o4bo$o8bo5bo5bo8bo$o9bo
4bo4bo9bo$o3bo6bo3bo3bo6bo3bo$o2bobo6bo2bo2bo6bobo2bo$o3bo7bo2bo2bo7bo
3bo$o11bo2bo2bo11bo$o7bo3bo2bo2bo3bo7bo$o6bobo5bo5bobo6bo$o7bo6bo6bo7b
o$o14bo14bo$o14bo14bo$31o!
|width = 320
|height = 320
|caption = D8_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 31, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o6bo7bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo3bo7bo$o11bo2b2o2bo11bo$o3bo7bo2b2o2bo7bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo6bo3b2o3bo6bo3bo$o9bo4b2o4bo9bo$o8bo5b2o5bo8bo$o4b4o6b2o6b4o
4bo$o14b2o14bo$o14b2o14bo$32o$o14b2o14bo$o14b2o14bo$o4b4o6b2o6b4o4bo$o
8bo5b2o5bo8bo$o9bo4b2o4bo9bo$o3bo6bo3b2o3bo6bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo7bo2b2o2bo7bo3bo$o11bo2b2o2bo11bo$o7bo3bo2b2o2bo3bo7bo$o6bobo
5b2o5bobo6bo$o7bo6b2o6bo7bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D8_2 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S012345678
32o$o14b2o14bo$o14b2o14bo$o7bo6b2o6bo7bo$o6bobo5b2o5bobo6bo$o7bo3bo2b
2o2bo3bo7bo$o11bo2b2o2bo11bo$o3bo7bo2b2o2bo7bo3bo$o2bobo6bo2b2o2bo6bob
o2bo$o3bo6bo3b2o3bo6bo3bo$o9bo4b2o4bo9bo$o8bo5b2o5bo8bo$o4b4o6b2o6b4o
4bo$o14b2o14bo$o14b2o14bo$32o$32o$o14b2o14bo$o14b2o14bo$o4b4o6b2o6b4o
4bo$o8bo5b2o5bo8bo$o9bo4b2o4bo9bo$o3bo6bo3b2o3bo6bo3bo$o2bobo6bo2b2o2b
o6bobo2bo$o3bo7bo2b2o2bo7bo3bo$o11bo2b2o2bo11bo$o7bo3bo2b2o2bo3bo7bo$o
6bobo5b2o5bobo6bo$o7bo6b2o6bo7bo$o14b2o14bo$o14b2o14bo$32o!
|width = 320
|height = 320
|caption = D8_4 symmetry}}
|}

To preserve D8_2 symmetry, the following [[isotropic non-totalistic]] transitions must either all exist simultaneously with all other transitions in the same line or none should:<ref name="post143859" />

*B4i=B2a=B2i=B1e
*S6a=S7e=S4t=S6i
*S4c=S3y=S4q
*B1c=B2c=B4c
*S3a=S1e=S0
*S7c=S6c=S4e
*B5y=B4w=B4e
*B8=B7e=B5a
*B5e=B4n
*B4a=B5i
*B4t=B5r
*S5y=S5q
*S5e=S5j
*B6i=B3i
*B6c=B6k
*S4i=S3r
*B3j=B3e
*B3y=B3q
*S2k=S2c
*S4a=S3i
*S3e=S4r
*S5i=S2i
</div></div>

== On a hexagonal or triangular grid ==
[[Hexagonal neighbourhood|Hexagonal]] and [[triangular neighbourhood|triangular]] grids have the same set of admissible symmetries as each other (by [http://mathworld.wolfram.com/DualTessellation.html planar] or [https://en.wikipedia.org/wiki/Dual_polyhedron#Dual_polytopes_and_tessellations polytopic duality] - see also [[Schläfli symbol]]), but these are not the same symmetries as square grids. Due to how hexagonal and triangular grids are handled by programs such as [[Golly]] and [[LifeViewer]], they will also appear markedly different in these respects. C2, D2, and D4 symmetries are still compatible, but C4 symmetries become meaningless because the cells no longer have a side count that is perfectly divisible by 4. Other symmetries are exclusive to these alternative grids, as indicated below:

* C1
* C2_1
* C2_4
* C3_1
* C3_3 (unsupported by apgsearch)
* C6
* D2_xo
* D2_x
* D4_x1
* D4_x4
* D6_1
* D6_1o
* D6_3 (unsupported by apgsearch)
* D12

[[apgsearch]] currently supports most higher symmetries for hexagonal rules; the rest (C3_3 and D6_3) will be added in a future version.<ref name="post66638" />

Another type of rotational symmetry which may not have been accounted for in the above list, arising as an alternate form of C2_2, was described in November 2021. Whether this is an actually distinct type of symmetry, however, is unknown and needs investigation.<ref name="post137220" />

=== Rotational ===
<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view a list of hexagonal/triangular rotational symmetries.
<div class="mw-collapsible-content">

==== C1 ====
'''C1''': Symmetric under 360° rotation. This is essentially no symmetry at all.

<center>{{Sym-demo
|rle = x = 16, y = 16, rule = B/S0123456H
16o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o6b2o6bo$o2b2o10bo$o2bobo9bo$o3b2o
4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o4bo$o8b2o4bo$o14bo$o14bo$16o!
|width = 200
|height = 200
|caption = C1 symmetry
}}</center>

==== C2 ====
'''C2''': Symmetric under 180° rotation. There are two possibilities:

* '''C2_1''': Rotation around the center of a cell.
* '''C2_2''': Rotation around the midpoint of a side of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
15b16o$15bo14bo$15bo14bo$15bo4b2o8bo$15bo4b3o7bo$15bo5b2o7bo$15bo4b2o
8bo$15bo3b2o4b2o3bo$15bo9bobo2bo$15bo10b2o2bo$15bo6b2o6bo$15bo6bobo5bo
$15bo7b2o5bo$15bo14bo$15bo14bo$31o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o6b
2o6bo$o2b2o10bo$o2bobo9bo$o3b2o4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o4bo$o8b
2o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = C2_1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S0123456H
16b16o$16bo14bo$16bo14bo$16bo4b2o8bo$16bo4b3o7bo$16bo5b2o7bo$16bo4b2o
8bo$16bo3b2o4b2o3bo$16bo9bobo2bo$16bo10b2o2bo$16bo6b2o6bo$16bo6bobo5bo
$16bo7b2o5bo$16bo14bo$16bo14bo$16b16o$16o$o14bo$o14bo$o5b2o7bo$o5bobo
6bo$o6b2o6bo$o2b2o10bo$o2bobo9bo$o3b2o4b2o3bo$o8b2o4bo$o7b2o5bo$o7b3o
4bo$o8b2o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = C2_4(?) symmetry}}
|}

==== C3 ====
'''C3''': Symmetric under 120° rotation. There are two possibilities:

* '''C3_1''': Rotation around the center of a cell.
* '''C3_3''': Rotation around a corner of a cell. (unsupported by apgsearch)

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 46, y = 46, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o9bo$o6b2o2bo$o2b2o2bobo2b
o$o2b3o2b2o3bo$o3b2o8bo$o5bo8bo$bo4bo8bo$2bo4bo2b2o3bo$3bo3bo2bobo2bo$
4bo6b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo$
13bobo$14b2o$31o$o14b2o14bo$o14bobo14bo$o5b2o7bo2bo14bo$o5bobo6bo3bo7b
o6bo$o6b2o6bo4bo7b2ob2o2bo$o2b2o10bo5bo8b4o2bo$o2bobo9bo6bo3b2o4b2o3bo
$o3b2o4b2o3bo7bo2bobo9bo$o8b2o4bo8bo2b2o10bo$o7b2o5bo9bo6b2o6bo$o7b3o
4bo10bo5bobo6bo$o8b2o4bo11bo5b2o7bo$o14bo12bo14bo$o14bo13bo14bo$16o14b
16o!
|width = 400
|height = 400
|caption = C3_1 symmetry}}
| {{Sym-demo
|rle = x = 48, y = 48, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o9bo$o6b2o2bo$o2b2o2bobo2b
o$o2b3o2b2o3bo$o3b2o8bo$o5bo8bo$bo4bo8bo$2bo4bo2b2o3bo$3bo3bo2bobo2bo$
4bo6b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo$
13bobo$14b2o$15bo2$16ob16o$o14bo2bo14bo$o14bo3bo14bo$o5b2o7bo4bo14bo$o
5bobo6bo5bo7bo6bo$o6b2o6bo6bo7b2ob2o2bo$o2b2o10bo7bo8b4o2bo$o2bobo9bo
8bo3b2o4b2o3bo$o3b2o4b2o3bo9bo2bobo9bo$o8b2o4bo10bo2b2o10bo$o7b2o5bo
11bo6b2o6bo$o7b3o4bo12bo5bobo6bo$o8b2o4bo13bo5b2o7bo$o14bo14bo14bo$o
14bo15bo14bo$16o16b16o!
|width = 400
|height = 400
|caption = C3_3 symmetry}}
|}

==== C6 ====
'''C6''': Symmetric under 60° rotation.

<center>{{Sym-demo
|rle = x = 61, y = 61, rule = B/S0123456H
15bo$15b2o$15bobo$15bo2bo$15bo3bo$15bo4bo$15bo5bo$15bo6bo$15bo7bo$15bo
8bo$15bo9bo$15bo6b2o2bo$15bo2b2o2bobo2bo$15bo2b3o2b2o3bo$15bo3b2o8bo$
16o5bo8b16o$bo14bo4bo8bo14bo$2bo14bo4bo2b2o3bo14bo$3bo7b2o5bo3bo2bobo
2bo4b2o8bo$4bo6bobo5bo6b2o2bo4b3o7bo$5bo6b2o6bo9bo5b2o7bo$6bo10b2o2bo
8bo4b2o8bo$7bo9bobo2bo7bo3b2o4b2o3bo$8bo3b2o4b2o3bo6bo9bobo2bo$9bo2b4o
8bo5bo10b2o2bo$10bo2b2ob2o7bo4bo6b2o6bo$11bo6bo7bo3bo6bobo5bo$12bo14bo
2bo7b2o5bo$13bo14bobo14bo$14bo14b2o14bo$15b31o$15bo14b2o14bo$15bo14bob
o14bo$15bo5b2o7bo2bo14bo$15bo5bobo6bo3bo7bo6bo$15bo6b2o6bo4bo7b2ob2o2b
o$15bo2b2o10bo5bo8b4o2bo$15bo2bobo9bo6bo3b2o4b2o3bo$15bo3b2o4b2o3bo7bo
2bobo9bo$15bo8b2o4bo8bo2b2o10bo$15bo7b2o5bo9bo6b2o6bo$15bo7b3o4bo2b2o
6bo5bobo6bo$15bo8b2o4bo2bobo2bo3bo5b2o7bo$15bo14bo3b2o2bo4bo14bo$15bo
14bo8bo4bo14bo$15b16o8bo5b16o$31bo8b2o3bo$32bo3b2o2b3o2bo$33bo2bobo2b
2o2bo$34bo2b2o6bo$35bo9bo$36bo8bo$37bo7bo$38bo6bo$39bo5bo$40bo4bo$41bo
3bo$42bo2bo$43bobo$44b2o$45bo!
|width = 500
|height = 500
|caption = C6 symmetry}}</center>
</div></div>

=== Reflectional ===
<div class="mw-collapsible mw-collapsed">
Click on "Expand" to the right to view a list of hexagonal/triangular reflectional symmetries.
<div class="mw-collapsible-content">

==== D2 ====
'''D2''': There is line symmetry. There are two possibilities:

* '''D2_x''': Through the vertices of a cell.
* '''D2_xo''': Through the edges of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 16, y = 16, rule = B/S0123456H
16o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o
2bo6bobo2bo$o3bo6b2o2bo$o4bo9bo$o5bo8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 300
|height = 300
|caption = D2_x symmetry}}
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
16o$bo14bo$2bo14bo$3bo8b2o4bo$4bo7b3o4bo$5bo7b2o5bo$6bo8b2o4bo$7bo3b2o
4b2o3bo$8bo2bobo9bo$9bo2b2o10bo$10bo6b2o6bo$11bo5bobo6bo$12bo5b2o7bo$
13bo14bo$14bo14bo$15b16o$15bo14bo$15bo14bo$15bo5b2o7bo$15bo5bobo6bo$15b
o6b2o6bo$15bo2b2o10bo$15bo2bobo9bo$15bo3b2o4b2o3bo$15bo8b2o4bo$15bo7b
2o5bo$15bo7b3o4bo$15bo8b2o4bo$15bo14bo$15bo14bo$15b16o!
|width = 300
|height = 300
|caption = D2_xo symmetry}}
|}

==== D4 ====
'''D4''': Symmetric under both reflection and 180° rotation. The reflection symmetry will be with respect to two lines. There are two possibilities:

* '''D4_x1''': Rotation around the center of a cell.
* '''D4_x4''': Rotation around the edges of a cell.

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 31, y = 31, rule = B/S0123456H
15b16o$15bo14bo$15bo14bo$15bo4b4o6bo$15bo8bo5bo$15bo9bo4bo$15bo2b2o6bo
3bo$15bo2bobo6bo2bo$15bo3b2o6bo2bo$15bo11bo2bo$15bo6b2o3bo2bo$15bo6bob
o5bo$15bo7b2o5bo$15bo14bo$15bo14bo$31o$o14bo$o14bo$o5b2o7bo$o5bobo6bo$
o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o2bo6bobo2bo$o3bo6b2o2bo$o4bo9bo$o5bo
8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = D4_x1 symmetry}}
| {{Sym-demo
|rle = x = 32, y = 32, rule = B/S0123456H
16b16o$16bo14bo$16bo14bo$16bo4b4o6bo$16bo8bo5bo$16bo9bo4bo$16bo2b2o6bo
3bo$16bo2bobo6bo2bo$16bo3b2o6bo2bo$16bo11bo2bo$16bo6b2o3bo2bo$16bo6bob
o5bo$16bo7b2o5bo$16bo14bo$16bo14bo$16b16o$16o$o14bo$o14bo$o5b2o7bo$o5b
obo6bo$o2bo3b2o6bo$o2bo11bo$o2bo6b2o3bo$o2bo6bobo2bo$o3bo6b2o2bo$o4bo
9bo$o5bo8bo$o6b4o4bo$o14bo$o14bo$16o!
|width = 400
|height = 400
|caption = D4_x4 symmetry}}
|}

==== D6 ====
'''D6''': Symmetric under both reflection and 120° rotation. The reflection symmetry will be with respect to three lines. There are three possibilities:

* '''D6_1''': Rotation around the center of a cell with lines going through the edges of cells.
* '''D6_1o''': Rotation around the center of a cell with lines going through the centers of cells.
* '''D6_3''': Rotation around the corner of a cell. (unsupported by apgsearch)

{| style="margin-left: auto; margin-right: auto"
|-
| {{Sym-demo
|rle = x = 46, y = 46, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o2b5o2bo$o2bo4bo2bo$o2bo5b
o2bo$o2bo6bo2bo$o13bo$o14bo$bo13bo$2bo3b2o2b2o3bo$3bo2bobobobo2bo$4bo
2b2o2b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo
$13bobo$14b2o$31o$o14b2o14bo$o14bobo14bo$o5b2o7bo2bo7b2o5bo$o5bobo6bo
3bo6bobo5bo$o2bo3b2o6bo4bo6b2o3bo2bo$o2bo11bo5bo11bo2bo$o2bo6b2o3bo6bo
3b2o6bo2bo$o2bo6bobo2bo7bo2bobo6bo2bo$o3bo6b2o2bo8bo2b2o6bo3bo$o4bo9bo
9bo9bo4bo$o5bo8bo10bo8bo5bo$o6b4o4bo11bo4b4o6bo$o14bo12bo14bo$o14bo13b
o14bo$16o14b16o!
|width = 400
|height = 400
|caption = D6_1 symmetry}}
| {{Sym-demo
|rle = x = 31, y = 31, rule = B2/S34H
16o$2o14bo$obo14bo$o2bo4b5o5bo$o3bo8b2o4bo$o4bo9b2o3bo$o5bo3b2o5b2o2bo
$o6bo2bobo6bo2bo$o2bo4bo2b2o7bo2bo$o2bo5bo11bo2bo$o2bo2b2o2bo7b2o2bo2b
o$o2bo2bobo2bo6bobo5bo$o2bo3b2o3bo6b2o6bo$o3bo8bo14bo$o3bo9bo14bo$o4bo
9b16o$bo3bo9bo14bo$2bo3bo8bo14bo$3bo2bo3b2o3bo6b2o6bo$4bo2bo2bobo2bo6b
obo5bo$5bo2bo2b2o2bo7b2o2bo2bo$6bo2bo5bo11bo2bo$7bo2bo4bo2b2o7bo2bo$8b
o6bo2bobo6bo2bo$9bo5bo3b2o5b2o2bo$10bo4bo9b2o3bo$11bo3bo8b2o4bo$12bo2b
o4b5o5bo$13bobo14bo$14b2o14bo$15b16o!
|width = 400
|height = 400
|caption = D6_1o symmetry}}
| {{Sym-demo
|rle = x = 48, y = 48, rule = B/S0123456H
o$2o$obo$o2bo$o3bo$o4bo$o5bo$o6bo$o7bo$o8bo$o2b5o2bo$o2bo4bo2bo$o2bo5b
o2bo$o2bo6bo2bo$o13bo$o14bo$bo13bo$2bo3b2o2b2o3bo$3bo2bobobobo2bo$4bo
2b2o2b2o2bo$5bo9bo$6bo8bo$7bo7bo$8bo6bo$9bo5bo$10bo4bo$11bo3bo$12bo2bo
$13bobo$14b2o$15bo2$16ob16o$o14bo2bo14bo$o14bo3bo14bo$o5b2o7bo4bo7b2o
5bo$o5bobo6bo5bo6bobo5bo$o2bo3b2o6bo6bo6b2o3bo2bo$o2bo11bo7bo11bo2bo$o
2bo6b2o3bo8bo3b2o6bo2bo$o2bo6bobo2bo9bo2bobo6bo2bo$o3bo6b2o2bo10bo2b2o
6bo3bo$o4bo9bo11bo9bo4bo$o5bo8bo12bo8bo5bo$o6b4o4bo13bo4b4o6bo$o14bo
14bo14bo$o14bo15bo14bo$16o16b16o!
|width = 400
|height = 400
|caption = D6_3 symmetry}}
|}

==== D12 ====
'''D12''': Symmetric under both reflection and 60° rotation. The reflection symmetry will be with respect to six lines.

<center>{{Sym-demo
|rle = x = 61, y = 61, rule = B/S0123456H
15bo$15b2o$15bobo$15bo2bo$15bo3bo$15bo4bo$15bo5bo$15bo6bo$15bo7bo$15bo
8bo$15bo2b5o2bo$15bo2bo4bo2bo$15bo2bo5bo2bo$15bo2bo6bo2bo$15bo13bo$16o
14b16o$bo14bo13bo14bo$2bo14bo3b2o2b2o3bo14bo$3bo6b4o4bo2bobobobo2bo4b
4o6bo$4bo5bo8bo2b2o2b2o2bo8bo5bo$5bo4bo9bo9bo9bo4bo$6bo3bo6b2o2bo8bo2b
2o6bo3bo$7bo2bo6bobo2bo7bo2bobo6bo2bo$8bo2bo6b2o3bo6bo3b2o6bo2bo$9bo2b
o11bo5bo11bo2bo$10bo2bo3b2o6bo4bo6b2o3bo2bo$11bo5bobo6bo3bo6bobo5bo$
12bo5b2o7bo2bo7b2o5bo$13bo14bobo14bo$14bo14b2o14bo$15b31o$15bo14b2o14b
o$15bo14bobo14bo$15bo5b2o7bo2bo7b2o5bo$15bo5bobo6bo3bo6bobo5bo$15bo2bo
3b2o6bo4bo6b2o3bo2bo$15bo2bo11bo5bo11bo2bo$15bo2bo6b2o3bo6bo3b2o6bo2bo
$15bo2bo6bobo2bo7bo2bobo6bo2bo$15bo3bo6b2o2bo8bo2b2o6bo3bo$15bo4bo9bo
9bo9bo4bo$15bo5bo8bo2b2o2b2o2bo8bo5bo$15bo6b4o4bo2bobobobo2bo4b4o6bo$
15bo14bo3b2o2b2o3bo14bo$15bo14bo13bo14bo$15b16o14b16o$31bo13bo$32bo2bo
6bo2bo$33bo2bo5bo2bo$34bo2bo4bo2bo$35bo2b5o2bo$36bo8bo$37bo7bo$38bo6bo
$39bo5bo$40bo4bo$41bo3bo$42bo2bo$43bobo$44b2o$45bo!
|width = 500
|height = 500
|caption = D12 symmetry}}</center>
</div></div>

== References ==
<references>
<ref name="post138823">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 138823
|author = GUYTU6J
|date = December 13, 2021
}}</ref>
<ref name="post143859">{{LinkForumThread
|format = ref
|title = Re: Truly Bilateral Life-Like rules
|p = 143859
|author = LaundryPizza03
|date = April 6, 2022
}}</ref>
<ref name="post66638">{{LinkForumThread
|format = ref
|title = Re: apgsearch v4.0
|p = 66638
|author = Adam P. Goucher
|date = December 20, 2018
}}</ref>
<ref name="post137220">{{LinkForumThread
|format = ref
|title = Re: Help with symmetries
|p = 137220
|author = GUYTU6J
|date = November 2, 2021
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_s.htm#symmetric|name=Symmetric}}
* {{LinkForumThread|f=7|t=1898|title=Help with symmetries}}

[[Category:Everything else]]

Frutterfly

2023-06-20T15:59:39Z

Atavoidirc: fixed bounding box

{{Oscillator
|name = Frutterfly
|pname = frutterfly
|c = 22
|bx = 12
|by = 6
|p = 4
|m = 4
|h = 18
|v = 0.86
|sv = 0.86
|rulemin = B3/S23
|rulemax = B3678/S02378
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B3-ckqy/S2-n3ar
|isorulemax = B2in34cejqrw5-ajr678/S0234-arz5-i6-a78
|synthesis = 8
|plaintext = true
|rle = true
|apgcode = xp4_199aaooaa991
|viewerconfig = #C [[ GPS 4 THUMBSIZE 2 ]]
}}
'''Frutterfly'''<ref>suggested name in the comments of object's Catagolue page</ref> is a {{period|4}} [[oscillator]], and is among the smallest true-period-4 oscillators not based on [[mold]].

It can nontrivially interact with one or two appropriate still lifes, such as a [[tub]], [[beehive]], [[loaf]] or [[mango]], and is {{LinkCatagolue|code=xp4_199aaooaaaa33aaiig|style=raw|patternname=arbitrarily extensible}}.

== Occurrences in Catagolue ==
Frutterfly has occurred in asymmetric [[soup]]s in B37e/S23-q,<ref> [https://catagolue.hatsya.com/hashsoup/C1/k_UvbxAAtEYEn22021/b37es23-q The occurrence in question], with two noninteracting copies</ref> but not in Life. However, it has occurred semi-naturally once in the [[Static_symmetry#C2|C2_2]] census, which is no more conducive to reflectionally-symmetrical occurrences than C1.<ref name="post147838" />

== See also ==
* [[20P4]]
* [[Pond-bound keys]]

== References ==
<references>
<ref name="post147838">{{LinkForumThread
|format = ref
|title = Re: Synthesising Oscillators
|p = 147838
|author = DroneBetter
|date = July 3, 2022
}}</ref>
</references>

== External links ==
{{LinkCatagolue|xp4_199aaooaa991}}
{{LinkCatagolue|xp4_6952giiaa33aaiig2596|patternname=Frutterfly with two loaves}}

{{symmetry|orthogonal2}}
[[Category:Semi-natural periodic objects]]
__NOTOC__

Alternating rule

2023-06-20T00:36:21Z

Atavoidirc: /* External links */

{{Glossary}}
'''Alternating rules''' are a generalisation of [[Life-like cellular automata]] in which cells behaving as one rule change into cells behaving as another rule in the next generation, and then either back to the original rule or onto yet another rule, creating loops.

By contrast, a rule containing different cell states net simulate different rules without alternating with each other is called a [[mashup rule]].

== Terminology ==
In an alternating rule, each of the non-alternating components (e.g. B2/S2 and B3/S2 in the rule B2/S2|B3/S2) are called subrules. The number of subrules in an alternating rule is called the step count. When a rule is not true orthodox, the way to calculate the practical period of an object is to divide the discrete period by the step count. The discrete period is the period of an object when ignoring the fact that it is an alternating rule. For true orthodox rules, the practical period is the same as the discrete.

The orthodoxy of an alternating rule is the measure of how much the rule behaves like non-alternating rules. An alternating rule is considered true orthodox if it contains at least one periodic object of period >1 which has the exact same evolution regardless of which subrule of the alternating rule it starts on, an example of such an object would be the [[blinker]] in {{nowrap|<nowiki>B3/S23|B36/S235</nowiki>}}, in which it will maintain the same [[phase]] sequence regardless of which subrule is in effect when the blinker is placed.

== Examples ==
{|style="margin:auto;width:300px;"
|{{EmbedViewer
|rle = x = 16, y = 10, rule = <nowiki>B3678/S23678|B3/S23</nowiki>
b2o10b3o$o2b2o7bo$ob6o5bobo$bo3b2obo5bo$5bo$4bo3bo$b3o$o2bo$o2bobo2bo$bo4b3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 160 PAUSE 1 T 320 PAUSE 3 LOOP 321 ]]
|position = center
|caption = A p160 [[RRO]] in {{nowrap|<nowiki>B3678/S23678|B3/S23</nowiki>}}<ref name="post70112" />
}}
|{{EmbedViewer
|rle = x = 9, y = 9, rule = <nowiki>B2/S35|B3/S1</nowiki>
2b2ob2o$3bobo$o2b3o$4obo$2bo2bo$5obobo$o4bo2$5bo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 15 HEIGHT 600 X -6 Y -6 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 230 PAUSE 3 LOOP 231 ]]
|position = center
|caption = A 16c/230 diagonal spaceship in {{nowrap|<nowiki>B2/S35|B3/S1</nowiki>}}<ref name="post88650" />
}}
|-
|{{EmbedViewer
|rle = x = 48, y = 48, rule = <nowiki>B3/S23|B35/S23</nowiki>:T48
12$17b2o$17b2o2$13b3o$13bobo$13b2o3$29b2o$29b2o3$32b2o$31b2o5$24b2o$23b
2o3$26b2o$26b2o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 30 THEME Book AUTOSTART T 0 PAUSE 1 T 648 PAUSE 3 LOOP 649 ]]
|position = center
|caption = A 8c/44 diagonal spaceship and a p216 oscillator in {{nowrap|<nowiki>B3/S23|B35/S23</nowiki>}}<ref name="post50997" />
}}
|{{EmbedViewer
|rle = x = 3, y = 3, rule = <nowiki>B2a4/S02|B3/S1c23-a</nowiki>:T48
2o$obo$obo!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 12 HEIGHT 600 GPS 20 THEME Book AUTOSTART T 0 PAUSE 1 T 384 PAUSE 3 LOOP 385 ]]
|position = center
|caption = A natural (16,4)c/32 [[giraffeship]] in {{nowrap|<nowiki>B2a4/S02|B3/S1c23-a</nowiki>}}<ref name="post154760" />
}}
|-
|{{EmbedViewer
|rle = x = 3, y = 5, rule = <nowiki>B1/S012345678|B/S578</nowiki>
o2$2bo2$o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 3 ZOOM 21 HEIGHT 600 GPS 2 AUTOSTART TRACKLOOP 4 1/4 0/4 ]]
|position = center
|caption = A natural spaceship in {{nowrap|<nowiki>B1/S012345678|B/S578</nowiki>}}<ref name="post5025" />
}}
|}

== Support ==
[[Golly]] supports a strict class subclass of alternating rules, which are used in simulating [[Birth on zero neighbours|B0 rules]] to avoid [[strobing]], using the process described in Golly's documentation.<ref>[http://golly.sourceforge.net/Help/Algorithms/QuickLife.html {{filename|Help/Algorithms/QuickLife}}]</ref>

[[LifeViewer]] supports alternating rules from build 292 onwards, with a few restrictions.

== Extensions ==
It is possible to extend such rules to [[von Neumann neighbourhood|von Neumann]] and [[hexagonal neighbourhood]]s, [[Larger than Life|extended neighbourhoods]], and [[isotropic non-totalistic|non-totalistic]] and [[non-isotropic]] rules, and can even alternate between combinations of these.

== References ==
<references>
<ref name="post5025">{{LinkForumThread
|format = ref
|p = 5025
|title = Alternating rules
|author = Tropylium
|date = August 21, 2011
}}</ref>
<ref name="post50997">{{LinkForumThread
|format = ref
|p = 50997
|title = Alternating rules
|author = Saka
|date = September 16, 2017
}}</ref>
<ref name="post70112">{{LinkForumThread
|format = ref
|p = 70112
|title = Re: Alternating rules
|author = muzik
|date = February 8, 2019
}}</ref>
<ref name="post88650">{{LinkForumThread
|format = ref
|p = 88650
|title = Re: Alternating rules
|author = nolovoto
|date = February 1, 2020
}}</ref>
<ref name="post154760">{{LinkForumThread
|format = ref
|p = 154760
|title = Re: Alternating rules
|author = May13
|date = December 12, 2022
}}</ref>
</references>

== External links ==
* {{LinkForumThread|f=11|t=719|title=Alternating rules}} (Started 2011)
* {{LinkForumThread|f=11|t=3096|title=Alternating rules}} (Started 2017)

[[Category:Algorithms]]
[[Category:Cellular automata]]
[[Category:Multistate rules]]

Rule:Hybrid2

2023-06-20T00:32:16Z

Atavoidirc: adding color

@RULE hybrid2

https://conwaylife.com/forums/viewtopic.php?p=13929#p13980

@TREE

num_states=4
num_neighbors=8
num_nodes=161
1 0 0 0 0
1 0 0 2 0
1 0 1 2 3
2 0 1 2 1
1 0 1 2 0
1 0 1 0 3
2 1 2 4 5
1 0 0 2 3
2 2 4 2 7
2 1 5 7 2
3 3 6 8 9
1 1 1 2 3
1 3 1 0 0
1 2 1 0 0
2 2 11 12 13
2 4 12 12 0
2 5 13 0 13
3 6 14 15 16
1 2 1 0 3
1 1 0 0 0
2 2 12 18 19
2 7 0 19 19
3 8 15 20 21
1 3 1 2 0
2 2 13 19 23
3 9 16 21 24
4 10 17 22 25
1 0 0 0 3
2 11 7 0 27
2 12 0 0 0
2 13 27 0 27
3 14 28 29 30
2 0 0 0 0
3 15 29 29 32
3 16 30 32 30
4 17 31 33 34
2 18 0 5 27
2 19 0 27 27
3 20 29 36 37
3 21 32 37 37
4 22 33 38 39
2 23 27 27 2
3 24 30 37 41
4 25 34 39 42
5 26 35 40 43
2 7 7 1 27
2 0 1 1 0
2 27 27 0 27
3 28 45 46 47
3 29 46 46 32
3 30 47 32 47
4 31 48 49 50
3 32 32 32 32
4 33 49 49 52
4 34 50 52 50
5 35 51 53 54
2 5 1 2 7
2 27 0 7 7
3 36 46 56 57
3 37 32 57 57
4 38 49 58 59
4 39 52 59 59
5 40 53 60 61
2 2 27 7 2
3 41 47 57 63
4 42 50 59 64
5 43 54 61 65
6 44 55 62 66
2 7 7 0 0
2 1 0 0 0
2 27 0 0 0
3 45 68 69 70
3 46 69 69 32
3 47 70 32 70
4 48 71 72 73
4 49 72 72 52
4 50 73 52 73
5 51 74 75 76
4 52 52 52 52
5 53 75 75 78
5 54 76 78 76
6 55 77 79 80
2 2 0 18 0
2 7 0 0 0
3 56 69 82 83
3 57 32 83 83
4 58 72 84 85
4 59 52 85 85
5 60 75 86 87
5 61 78 87 87
6 62 79 88 89
2 2 0 0 23
3 63 70 83 91
4 64 73 85 92
5 65 76 87 93
6 66 80 89 94
7 67 81 90 95
3 68 68 32 32
3 69 32 32 32
3 70 32 32 32
4 71 97 98 99
4 72 98 98 52
4 73 99 52 99
5 74 100 101 102
5 75 101 101 78
5 76 102 78 102
6 77 103 104 105
5 78 78 78 78
6 79 104 104 107
6 80 105 107 105
7 81 106 108 109
2 18 0 5 0
3 82 32 111 32
3 83 32 32 32
4 84 98 112 113
4 85 52 113 113
5 86 101 114 115
5 87 78 115 115
6 88 104 116 117
6 89 107 117 117
7 90 108 118 119
2 23 0 0 4
3 91 32 32 121
4 92 99 113 122
5 93 102 115 123
6 94 105 117 124
7 95 109 119 125
8 96 110 120 126
4 97 97 52 52
4 98 52 52 52
4 99 52 52 52
5 100 128 129 130
5 101 129 129 78
5 102 130 78 130
6 103 131 132 133
6 104 132 132 107
6 105 133 107 133
7 106 134 135 136
6 107 107 107 107
7 108 135 135 138
7 109 136 138 136
8 110 137 139 140
2 5 0 5 0
3 111 32 142 32
4 112 52 143 52
4 113 52 52 52
5 114 129 144 145
5 115 78 145 145
6 116 132 146 147
6 117 107 147 147
7 118 135 148 149
7 119 138 149 149
8 120 139 150 151
2 4 0 0 23
3 121 32 32 153
4 122 52 52 154
5 123 130 145 155
6 124 133 147 156
7 125 136 149 157
8 126 140 151 158
9 127 141 152 159

@TABLE
n_states:4
neighborhood:Moore
symmetries:permute
var a={0,1,3}
var b={0,1,2,3}
var ba={b}
var bb={b}
var bc={b}
var bd={b}
var be={b}
var c={1,3}
var d={1,2,3}
var da={d}
var db={d}
var dc={d}
var dd={d}
0,1,1,1,0,0,0,0,0,1
0,2,2,2,0,0,0,0,0,2
0,2,2,2,2,2,2,0,0,2
0,3,3,3,0,0,0,0,0,3
0,3,3,3,3,3,3,0,0,3
0,3,3,3,3,3,3,3,3,3
c,a,0,0,0,0,0,0,0,0
1,1,d,da,db,b,ba,bb,bc,0
2,0,0,0,0,0,0,0,0,0
2,2,d,da,b,0,0,0,0,0
2,2,d,da,db,dc,dd,b,ba,0
3,3,d,da,0,0,0,0,0,0
3,3,d,da,db,dc,dd,b,ba,0
0,1,1,2,0,0,0,0,0,3
0,1,2,2,0,0,0,0,0,3
0,1,1,3,0,0,0,0,0,2
0,1,3,3,0,0,0,0,0,2
0,2,2,3,0,0,0,0,0,1
0,2,3,3,0,0,0,0,0,1
1,2,3,b,ba,bb,bc,bd,be,0
2,1,3,b,ba,bb,bc,bd,be,0
3,2,1,b,ba,bb,bc,bd,be,0

@COLORS
1 255 0 0
2 0 255 0
3 0 0 255

Rule:2.5life

2023-06-20T00:30:55Z

Atavoidirc: adding color

@RULE 2.5life

https://conwaylife.com/forums/viewtopic.php?p=13929#p13929

@TREE

num_states=6
num_neighbors=8
num_nodes=133
1 0 0 0 4 5 0
2 0 0 0 0 0 0
1 0 1 2 4 5 0
1 3 1 2 4 5 0
2 0 2 3 2 0 0
2 0 3 2 2 0 0
2 0 2 2 3 0 0
3 1 4 5 6 1 1
1 1 1 2 4 5 0
2 2 8 2 8 2 2
2 3 2 2 2 3 3
2 2 8 2 2 2 2
3 4 9 10 11 4 4
1 2 1 2 4 5 0
2 2 2 13 13 2 2
2 2 2 13 2 2 2
3 5 10 14 15 5 5
3 6 11 15 10 6 6
4 7 12 16 17 7 7
1 0 0 2 4 5 0
2 8 19 0 2 8 8
2 2 0 0 2 2 2
2 8 2 2 2 8 8
3 9 20 21 22 9 9
2 2 2 2 2 2 2
3 10 21 21 24 10 10
3 11 22 24 24 11 11
4 12 23 25 26 12 12
1 0 1 0 4 5 0
2 13 0 28 2 13 13
2 13 2 2 2 13 13
3 14 21 29 30 14 14
3 15 24 30 24 15 15
4 16 25 31 32 16 16
3 10 24 24 24 10 10
4 17 26 32 34 17 17
5 18 27 33 35 18 18
2 19 19 0 2 2 2
2 0 0 0 2 2 2
3 20 37 38 24 22 22
3 21 38 38 24 24 24
3 22 24 24 24 22 22
3 9 22 24 22 9 9
4 23 39 40 41 42 42
3 24 24 24 24 24 24
4 25 40 40 44 34 34
4 26 41 44 44 26 26
4 12 42 34 26 12 12
5 27 43 45 46 47 47
2 28 0 28 2 2 2
3 29 38 49 24 30 30
3 30 24 24 24 30 30
3 14 24 30 30 14 14
4 31 40 50 51 52 52
4 32 44 51 44 32 32
4 16 34 52 32 16 16
5 33 45 53 54 55 55
4 34 44 44 44 34 34
5 35 46 54 57 35 35
5 18 47 55 35 18 18
6 36 48 56 58 59 59
3 37 37 38 24 24 24
3 38 38 38 24 24 24
4 39 61 62 44 41 41
4 40 62 62 44 44 44
4 41 44 44 44 41 41
4 42 41 44 41 42 42
5 43 63 64 65 66 66
4 44 44 44 44 44 44
5 45 64 64 68 57 57
5 46 65 68 68 46 46
5 47 66 57 46 47 47
6 48 67 69 70 71 71
3 49 38 49 24 24 24
4 50 62 73 44 51 51
4 51 44 44 44 51 51
4 52 44 51 51 52 52
5 53 64 74 75 76 76
5 54 68 75 68 54 54
5 55 57 76 54 55 55
6 56 69 77 78 79 79
5 57 68 68 68 57 57
6 58 70 78 81 58 58
6 59 71 79 58 59 59
7 60 72 80 82 83 83
4 61 61 62 44 44 44
4 62 62 62 44 44 44
5 63 85 86 68 65 65
5 64 86 86 68 68 68
5 65 68 68 68 65 65
5 66 65 68 65 66 66
6 67 87 88 89 90 90
5 68 68 68 68 68 68
6 69 88 88 92 81 81
6 70 89 92 92 70 70
6 71 90 81 70 71 71
7 72 91 93 94 95 95
4 73 62 73 44 44 44
5 74 86 97 68 75 75
5 75 68 68 68 75 75
5 76 68 75 75 76 76
6 77 88 98 99 100 100
6 78 92 99 92 78 78
6 79 81 100 78 79 79
7 80 93 101 102 103 103
6 81 92 92 92 81 81
7 82 94 102 105 82 82
7 83 95 103 82 83 83
8 84 96 104 106 107 107
5 85 85 86 68 68 68
5 86 86 86 68 68 68
6 87 109 110 92 89 89
6 88 110 110 92 92 92
6 89 92 92 92 89 89
6 90 89 92 89 90 90
7 91 111 112 113 114 114
6 92 92 92 92 92 92
7 93 112 112 116 105 105
7 94 113 116 116 94 94
7 95 114 105 94 95 95
8 96 115 117 118 119 119
5 97 86 97 68 68 68
6 98 110 121 92 99 99
6 99 92 92 92 99 99
6 100 92 99 99 100 100
7 101 112 122 123 124 124
7 102 116 123 116 102 102
7 103 105 124 102 103 103
8 104 117 125 126 127 127
7 105 116 116 116 105 105
8 106 118 126 129 106 106
8 107 119 127 106 107 107
9 108 120 128 130 131 131

@TABLE
n_states:6
neighborhood:Moore
symmetries:permute
var a={0,1,2}
var aa={a}
var ab={a}
var ac={a}
var b={0,1,2,3,4,5}
var ba={b}
var bb={b}
var bc={b}
var bd={b}
var be={b}
var bf={b}
var bg={b}
var c={1,2}
var ca={c}
var cb={c}
var d={0,4,5}
var da={d}
var db={d}
var dc={d}
var dd={d}
var de={d}
var df={d}
var dg={d}
0,1,1,1,d,da,db,dc,dd,1
0,2,2,2,d,da,db,dc,dd,2
1,1,c,ca,cb,a,aa,ab,ac,0
1,b,d,da,db,dc,dd,de,df,0
2,2,c,ca,cb,a,aa,ab,ac,0
2,b,d,da,db,dc,dd,de,df,0
0,3,3,d,da,db,dc,dd,de,3
3,b,ba,bb,bc,bd,be,bf,bg,4
4,b,ba,bb,bc,bd,be,bf,bg,5
5,b,ba,bb,bc,bd,be,bf,bg,0
0,1,2,d,da,db,dc,dd,de,3
0,c,c,3,d,da,db,dc,dd,c

@COLORS

1 0 0 255
2 255 0 255
3 255 0 0
4 255 128 0
5 255 255 0

Long tail

2023-05-29T18:59:56Z

Atavoidirc: adding to category

{{StillLifeComponent
|name = Long tail
|pname = longtail
|c = 5
|bx = 2
|by = 4
|plaintext = true
|rle = true
}}
'''Long tail''' (sometimes referred to as '''L''' or '''J''') is a [[Polyplet#Pentaplets|pentaplet]] and great-grandparent of the [[V spark]]. It can often be attached to [[still life]]s to create a larger still life. The simplest such example is [[shillelagh]], in which a long tail and a [[pre-block]] mutually stabilize one another.

The long tail is not very strongly related to the usual [[tail]], and does not attach to as wide an array of objects, and those which it does generally have fewer isomers.

== As a still life component ==
A green background indicates that the object the tail is added to is stable without it; a red background indicates this is not the case.

{| class="wikitable"
! colspan="2" | Object
! Population
! colspan="2" | Other part
|-
! [[File:Shillelagh.png|64px]]
! [[Shillelagh]]
| 8
| style="background-color:#ffc7ce;" | [[File:Preblock.png|64px]]
| style="background-color:#ffc7ce;" | [[Pre-block]]
|-
! [[File:Tubwithlongtail.png|64px]]
! [[Tub with long tail]]
| 9
| style="background-color:#c6efce;" | [[File:Tub.png|64px]]
| style="background-color:#c6efce;" | [[Tub]]
|-
! [[File:Boatwithlongtail.png|64px]]
! [[Boat with long tail]]
| 10
| style="background-color:#c6efce;" | [[File:Boat.png|64px]]
| style="background-color:#c6efce;" | [[Boat]]
|-
! [[File:Bargewithlongtail.png|64px]]
! [[Barge with long tail]]
| rowspan="3" | 11
| style="background-color:#c6efce;" | [[File:Barge.png|64px]]
| style="background-color:#c6efce;" | [[Barge]]
|-
! [[File:Fusewithtailandlongtail.png|64px]]
! [[Fuse with tail and long tail]]
| colspan="2" style="background-color:#ffc7ce;text-align:center" | ''Unnamed''
|-
! [[File:Elevenloop.png|64px]]
! [[Eleven loop]]
| colspan="2" style="background-color:#ffc7ce;text-align:center" | ''Unnamed''
|}
[[Category:Sparks]]

Racetrack

2023-05-29T18:58:46Z

Atavoidirc: adding to category

{{StillLifeComponent
|name = Racetrack
|pname = racetrack
|type = Induction coil
|c = 12
|bx = 6
|by = 4
|plaintext = true
|rle = true
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 48 ]]
}}
'''Racetrack'''<ref>[[Catagolue]], ''infra''.</ref> is an [[induction coil]].

It can be [[weld]]ed onto itself to form racetrack-weld-racetrack (shown below), four of which form [[cloverleaf interchange]].

{{EmbedViewer
|pname = racetrackweldracetrack
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 24 ]]
|position = center
|caption = racetrack-weld-racetrack
|style = width:300px;
}}

== References ==
<references />

== External links ==
* {{LinkCatagolue|xp2_04aab96zc813|patternname=Racetrack and ortho-beacon}}
__NOTOC__
[[Category:Sparks]]

Griddle

2023-05-29T18:57:51Z

Atavoidirc: adding to category

{{OscillatorComponent
|name = Griddle
|pname = griddle
|type = Induction coil
|c = 11
|bx = 6
|by = 4
|p = 2
|rle = true
|plaintext = true
|viewerconfig = #C [[ GPS 2 THUMBSIZE 2 ]]
}}
'''Griddle''' is a period-2 [[induction coil]] which involves a [[flutter]] [[rotor]] and an 8-cell [[stator]] resembling a very long [[table]]. There are many possible stabilizations of the griddle, many small examples of which arise naturally.

== Stabilisations ==
{| class="wikitable" style="text-align:center"
! Image
! Name
! Population
! Stabilization
|-
! [[File:Blockongriddle.png|64px]]
! [[Block on griddle]]
| [[:Category:Oscillators with 15 cells|15]]
| - [[Block]], ×1
|-
! [[File:Boatongriddle.png|64px]]
! Boat on griddle
| [[:Category:Oscillators with 16 cells|16]]
| - [[Boat]], ×1
|-
! [[File:Beehiveongriddle.png|64px]]
! [[Beehive on griddle]]
| [[:Category:Oscillators with 17 cells|17]]
| - [[Beehive]], ×1
|-
! [[File:Shipongriddle.png|64px]]
! Ship on griddle
| [[:Category:Oscillators with 17 cells|17]]
| - [[Ship]], ×1
|-
! [[File:Griddleandtable.png|64px]]
! Griddle and table
| [[:Category:Oscillators with 17 cells|17]]
| - [[Table]], ×1
|-
! [[File:Loafongriddle.png|64px]]
! Loaf on griddle
| [[:Category:Oscillators with 18 cells|18]]
| - [[Loaf]], ×1
|-
! [[File:Pondongriddle.png|64px]]
! Pond on griddle
| [[:Category:Oscillators with 19 cells|19]]
| - [[Pond]], ×1
|-
! [[File:Blocksongriddle.png|64px]]
! Blocks on griddle
| [[:Category:Oscillators with 19 cells|19]]
| - [[Block]], ×2
|-
! [[File:Griddleanddock.png|64px]]
! Griddle and dock
| [[:Category:Oscillators with 21 cells|21]]
| - [[Dock]], ×1
|}
[[Category:sparks]]

Dock

2023-05-29T18:57:04Z

Atavoidirc: adding to category

{{StillLifeComponent
|name = Dock
|pname = dock
|type = Induction coil
|c = 10
|bx = 6
|by = 3
|plaintext = true
|rle = true
}}
'''Dock''' (or '''long house''') is an [[induction coil]].

Unlike [[house]], dock can function as an [[eater]] for individual [[glider]]s, using the [[pre-block]] tipped ends similarly to that of the original [[fishhook]] eater.

The dock is the most common 4-cell induction coil to attach to a block as part of an oscillator, such as dock on [[unix]] and dock on [[blocker]]. With a bare block, the table is marginally more common than the dock.

== Gallery ==
Dock is a component of many other patterns, some examples of which are the following:

'''Oscillators'''

{|class="wikitable"
| <center>[[Image:cisbeaconondock.png|96px]]</center>
| <center>[[Image:transbeaconondock.png|96px]]</center>
| <center>[[Image:griddleanddock.png|96px]]</center>
|-
| <center>[[Cis-beacon on dock]]</center>
| <center>[[Trans-beacon on dock]]</center>
| <center>[[Griddle and dock]]</center>
|}

'''Still lifes'''

{|class="wikitable"
| <center>[[Image:beehiveondock.png|96px]]</center>
| <center>[[Image:capanddock.png|96px]]</center>
| <center>[[Image:mirroreddock.png|96px]]</center>
| <center>[[Image:pondondock.png|96px]]</center>
| <center>[[Image:tableanddock.png|96px]]</center>
|-
| <center>[[Beehive on dock]]</center>
| <center>[[Cap and dock]]</center>
| <center>[[Mirrored dock]]</center>
| <center>[[Pond on dock]]</center>
| <center>[[Table and dock]]</center>
|}

== External links ==
{{LinkLexicon|filename=lex_d.htm#dock}}

{{Symmetry|orthogonal2}}
[[Category:Sparks]]

Table

2023-05-29T18:51:10Z

Atavoidirc: adding to category

{{StillLifeComponent
|name = Table
|pname = table
|type = Induction coil
|c = 6
|bx = 4
|by = 2
|discoveryear = 1970
|plaintext = true
|rle = true
|viewerconfig = [[ ZOOM 63 ]]
}}
'''Table''' is a simple [[induction coil]] and [[hexomino]]. If left to evolve by itself, it becomes a [[line-of-six spark]] in three generations.

It can be used as a catalyst, such as in [[dueling banjos]]; the table itself is unstable, but any stabilization (most commonly a block in one of two positions or a second table) works.

== See also ==
* [[Block on table]]
* [[Mirrored table]]

== External links ==
{{LinkLexicon|lex_t.htm#table}}

{{Symmetry|orthogonal2}}
[[Category:Polyominoes]]
[[Category:Sparks]]