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Game of Life Status page

Last updated: 28 Aug. 2013
Last reviewed: 28 Aug. 2013

This page documents what is known and what is not known in the Game of Life concerning certain classes of patterns. If you find an error on this page, please let me know.

For definitions of the terms used on this page, see Stephen Silver's Life Lexicon (listed here).

This page requires a browser that can display table cells and text with colored backgrounds.

Reference collection

Here's a collection of examples of most of the objects that this page claims are known:

It does not include:

Contents

Key:  
greenAn example is known (or at least an explicit method of construction)
redNo example is known
yellowOnly trivial or partial examples are known
grayProven to be impossible

Some sections include historical notes that list one or more discoverers with the more recent discoveries. Primary discoverers are listed first, and others who made substantial contributions leading to the discovery are listed after the word "with". The list of names is not meant to imply that no one else contributed to the discovery; it is simply impractical to list everyone, and I have to draw the line somewhere. Please call any obvious errors or bad judgments to my attention.

Key to initials: DE   David Eppstein
DIB  David Bell
DJB  David Buckingham
DL   Dietrich Leithner
DRH  Dean Hickerson
HH   Hartmut Holzwart
JS   Jason Summers
NB   Nicolay Beluchenko
NDE  Noam Elkies
PT   Paul Tooke
SAS  Stephen Silver
TC   Tim Coe


Oscillator periods

For green status, an oscillator must have a cell that oscillates at the full period, rather than some smaller factor of that period. One such cell is sufficient.

Yellow means that the only known examples contain no cells that oscillate at the full period.

1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72
All higher periods are known
Most recent discoveries:
Apr 2013: p43 and p53 oscillators [Mike Playle]
Nov 2010: p31 oscillator [Matthias Merzenich]
Apr 2009: p37 oscillator [NB]
Feb 2009: p51 oscillator [NB]
Nov 2002: p27 oscillator [NDE]
Jul 2000: p39 oscillator [NDE with DJB]
Aug 1999: p49 oscillator [NDE]
Dec 1997: p57 oscillator [DL with DJB]
Jun 1997: p33 oscillator [NDE, Achim Flammenkamp]
27 Apr 1997: p17 oscillator [DRH]
17 Apr 1997: p22 oscillator [NDE]. ([DRH] found a second, unrelated, p22 oscillator a day or two later.)
11 Apr 1997: p59 oscillator [DJB]
Oct 1996: Herschel track method of constructing any period 61 or higher [DJB]


Glider reflectors

This table indicates whether a period-N glider stream can be reflected 90 degrees by an object whose period is N, or some factor of N.

This may seem to be a rather odd thing to keep track of, but 90-degree glider reflectors are very useful, and happen to be quite difficult to find in Life. Note that this table fits neatly between oscillators and guns -- if you have a gun, you can build a reflector, and if you have a reflector, you can build an oscillator.

Yellow means that the reflector requires the glider stream to have no gaps.

1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72
All higher periods are known.
Most recent discoveries:
28 Aug 2013: p29 independent reflector [Matthias Merzenich]
25 Aug 2013: p29 dependent reflector [Matthias Merzenich]
May 2013: p20 [follows from p20 gun]
Apr 2013: Independent reflector for all periods 43 and over [Mike Playle]. Specifically: p43 and p53 (had nothing); p47 and p51 (had oscillators); p57 and p61 (had dependent reflectors).
Sep 2012: p58 independent reflector [Matthias Merzenich]
Sep 2012: p52 reflector [Matthias Merzenich]
Feb 2012: p26 dependent reflector [Matthias Merzenich with Mike Playle]
Nov 2010: p31 [Matthias Merzenich]
Mar 2010: p37 [NB]
Dec 2009: p59 [follows from p59 gun]


Glider gun true-periods

1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72
All higher periods are known
Most recent discoveries:
May 2013: p20 gun [Matthias Merzenich with Noam Elkies]
Mar 2013: p40 gun [Matthias Merzenich with Jason Summers, Adam P. Goucher]
Apr 2010: p45 gun [Matthias Merzenich]
Dec 2009: p59 gun [Adam P. Goucher with JS]
Jul 2004: p36 gun [JS]
Aug 2000: p22 gun [DE,JS]
Oct 1998: p55 gun [SAS,NDE with DJB]
29 Jan 1998: p56 gun [DL,NDE with DJB]
26 Jan 1998: p54 gun [DL with DJB,NDE]
Jun 1997: p24 gun, and related p48 gun [NDE]
13 Oct 1996: p50 gun [DRH with NDE,DJB]
12 Oct 1996: Herschel track method of constructing any period 62 or higher [DJB]


Gun pseudo-periods

GliderLWSSMWSSHWSS
All lower periods are impossible.
13 13 13 13
14 14 14 14
15 15 15 15
16 16 16 16
17 17 17 17
18 18 18 18
19 19 19 19
20 20 20 20
21 21 21 21
22 22 22 22
23 23 23 23
All higher periods are known.

Velocities of spaceships and related objects

Velocity is the combination of speed and slope (direction).

In this section, velocity is in the form (X,Y)c/P, where X>=Y, and no factor is common to all of X, Y, and P. (c is the "speed of light": 1 cell/generation.) P is therefore the minimum possible period for that velocity; X and Y are the (average) number of cells moved horizontally and vertically in P generations. The slope (direction) is Y/X, and the speed is Xc/P.

For example, (2,0)c/5 indicates movement of 2 cells horizontally and no cells vertically every 5 generations.

"Versatile puffer," means that for some period, we can build a clean glider rake with the gliders traveling in any of the possible directions.

Whether an object is a "wickstretcher" is to some extent a judgment call. For this table, the wick is required to be reasonably closely connected in all phases, and must in some sense be extended at a single location, rather than being built up slowly from pieces.

The "Gun?" column indicates whether a gun has been built which fires spaceships of that velocity.

VelocitySpaceship? Puffer?Versatile
puffer?
Wick-
stretcher?
Gun?
(1,0)c/2YesYesYesYesYes
(1,0)c/3YesYesYesNoNo
(1,0)c/4YesYesYesYesNo
(1,1)c/4YesYesYesYesYes
(1,0)c/5YesYesYesYesNo
(2,0)c/5YesYesYesNoYes
(1,1)c/5YesYesYesYesNo
(1,0)c/6YesNo--NoNo
(2,1)c/6NoNo--No--
(1,1)c/6YesNo--NoNo
(1,0)c/7YesNoNoNoyes
(2,0)c/7YesNo--NoNo
(3,0)c/7NoNo--No--
(2,1)c/7NoNo--No--
(1,1)c/7YesNo--NoNo
(1,1)c/12YesYesYesYesYes
(17,0)c/45YesYesYesNoNo
Other Universal constructor-based spaceships (and other objects) that move very slowly have been made. The first such object has a velocity of (5120,1024)c/33699586. See "Gemini", listed at the top of this page.
Most recent discoveries (new velocities):
Feb 2013: c/7 orthogonal spaceship [Josh Ball]
Aug 2011: c/7 diagonal spaceship [Matthias Merzenich]
May 2010: Universal constructor-based "Gemini" spaceship [Andrew Wade]
Sep 2005: c/6 diagonal spaceship [NB]
Dec 2004: 17c/45 orthogonal spaceship [Gabriel Nivasch, JS with DIB]
Nov 2000: c/5 diagonal spaceship [JS; search software by DIB]
Apr 2000: c/6 orthogonal spaceship [PT; search software by DE]
Jan 2000: 2c/7 orthogonal spaceship [DE]
Jan 1996: c/5 orthogonal spaceship [TC]

Most recent discoveries (other):
Mar 2013: c/5 orthogonal wickstretcher [Matthias Merzenich]
Jan 2011: c/5 diagonal wickstretcher [Matthias Merzenich]
Sep 2010: (versatile) c/5 diagonal puffer [Matthias Merzenich]
Jul 2010: Gun for Gemini spaceship [Dave Greene]
Oct 2005: versatile c/4 diagonal puffer [DIB with JS,NB]
Mar 2004: c/4 diag puffer [HH]
Mar 2003: 2c/5 gun [NDE, Dave Greene]
Oct 2002: c/2 wickstretcher [DRH,JS]
Oct 2000: versatile c/4 puffer [DIB,JS]
Jun 2000: versatile 2c/5 puffer [DIB,JS with PT]
Jul 1999: c/12 gun [SAS,JS]
Mar 1999: c/12 wickstretcher [JS with DRH,DJB]
Feb 1999: 2c/5 puffer [JS]
Jan 1999: c/4 puffer [JS]
Jun 1998: versatile c/12 puffers [SAS,DRH]
Sep 1997: versatile c/5 puffers [DIB]
May 1997: c/5 puffer [TC,DIB]
Jun 1996: versatile c/3 puffers [DIB]
Apr 1996: c/3 puffer [DIB]


Spaceship periods

This table lists the known spaceship periods up to 36 for each velocity. Periods not possible at any of the known velocities are omitted to save space.

Yellow means that only "trivial" examples exist, with no single section that repeats at the full period.

Velocity Period
2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 22 24 25 26 27 28 30 32 33 34 35 36 other
c/2 orth 2  4  6  8  10 12 14  16 18 20  22 24  26  28 30 32  34  36 ...
c/3 orth   3  6  9  12  15  18  21  24  27  30  33  36 ...
c/4 orth   4  8  12  16  20  24  28  32  36 ...
c/4 diag   4  8  12  16  20  24  28  32  36 ~4508, ...
2c/5 orth   5  10  15  20  25  30  35  ...
c/5 orth   5  10  15  20  25  30  35  60, ...
c/5 diag   5  10  15  20  25  30  35  85, ...
c/6 orth   6  12  18  24  30  36 None
c/6 diag   6  12  18  24  30  36 None
c/7 orth   7  14  21  28  35  None
2c/7 orth   7  14  21  28  35  None
c/7 diag   7  14  21  28  35  None
c/12 diag   12  24  36 96, 192, ...
17c/45 orth   270, ...
Most recent discoveries, excluding new velocities:
Oct 2010: c/4 orth p24 [Matthias Merzenich]
Sep 2005: c/4 diag p12 [HH]
Nov 2004: c/5 orth p10 [PT]
Nov 2003: c/4 orth p32 [PT with JS]
Feb 2003: c/2 orth p18 [PT]
Dec 2002: nontrivial c/3 orth p18 [DIB,JS]
Oct 2002: c/3 orth p27 [PT]
May 2002: 2c/5 orth p35 [PT]
8 Feb 2002: 2c/5 orth p15 and p25 [PT]
4 Feb 2002: 2c/5 orth p20 and p30 [PT]
14 Jan 2002: c/3 orth p21 [PT]
8 Jan 2002: c/2 orth p30 [PT]
Dec 2001: c/2 orth p10 and p14 [PT]
May 2001: c/2 orth p22 [DIB,PT with JS]
Apr 2001: c/2 orth p26 [DIB,PT]
Dec 2000: c/4 diag p8 [JS]
Nov 2000: c/3 orth p12 [DIB,JS]
Oct 2000: c/4 orth p8 and p12 [JS], and resulting trivial p24
Sep 2000: c/4 orth p20 [DIB with JS]
May 2000: 2c/5 orth p10 [DIB,PT]
Feb 1999: c/3 orth p6 [SAS], and resulting trivial p18 and p30
May 1998: c/5 orth p30 [DIB with NDE]
Mar 1998: c/3 orth p36 [DIB]
Dec 1997: c/5 orth p15 [NDE with TC]
Apr 1996: c/3 orth p24 [DIB]
?May 1994: c/2 orth p28 [HH with Alan Hensel]
Dec 1993: c/3 orth p15 [DIB]
Jul 1993: c/2 orth p6 [DIB]
May 1992: c/3 orth p9 [DIB]


c/2 orthogonal spaceships, puffers, rakes

S=Spaceship, P=Puffer, R=Rake.

  2:SPR   4:SPR   6:SPR   8:SPR  10:SPr  12:SPR  14:SPr  16:SPR  18:SPR  20:SPR  22:SPR  24:SPR
 26:SPR  28:SPR  30:SPR  32:SPR  34:sPr  36:SPR  38:SPR  40:SPR  42:SPR  44:SPR  46:SPR  48:SPR
 50:SPR  52:SPR  54:SPR  56:SPR  58:SPR  60:SPR  62:SPR  64:SPR  66:SPR  68:SPR  70:SPR  72:SPR
 74:spr  76:SPR  78:SPR  80:SPR  82:spr  84:SPR  86:spr  88:SPR  90:SPR  92:SPR  94:SPR  96:SPR
 98:SPR 100:SPR 102:SPR 104:SPR 106:spr 108:SPR 110:SPR 112:SPR 114:SPR 116:SPR 118:spr 120:SPR
122:spr 124:SPR 126:SPR 128:SPR 130:SPR 132:SPR 134:SPR 136:SPR 138:SPR 140:SPR 142:spr 144:SPR
146:spr 148:spr 150:SPR 152:SPR 154:SPR 156:SPR 158:spr 160:SPR 162:SPR 164:SPR 166:spr 168:SPR
170:spr 172:spr 174:SPR 176:SPR 178:spr 180:SPR 182:SPR 184:SPR 186:SPR 188:SPR 190:SPR 192:SPR
194:spr 196:SPR 198:SPR 200:SPR

For periods over 200, this section only includes periods that are a multiple of 4 but not 8. All multiples of 8 are known. Periods over 200 that are not a multiple of 4 are not documented here.

  204:SPR 212:SPR 220:SPR 228:SPR 236:SPR 244:spr 252:SPR 260:SPR 268:SPR 276:SPR 284:SPR
292:SPR 300:SPR 308:SPR 316:spr 324:SPR 332:SPR 340:SPR 348:SPR 356:spr 364:SPR 372:SPR 380:SPR
388:spr 396:SPR 404:SPR 412:spr 420:SPR 428:SPR 436:SPR 444:SPR 452:spr 460:SPR 468:SPR 476:SPR
484:SPR 492:SPR 500:SPR 508:spr 516:SPR 524:SPR 532:SPR 540:SPR 548:SPR 556:spr 564:SPR 572:SPR
All higher multiples of 4 are known.


c/2 orthogonal rake true-periods

Forw
glider
Back
glider
Side
LWSS
Back
LWSS
Side
MWSS
Back
MWSS
Side
HWSS
Back
HWSS
All lower periods are impossible.
8 8 8 8 8 8 8 8
10 10 10 10 10 10 10 10
12 12 12 12 12 12 12 12
14 14 14 14 14 14 14 14
16 16 16 16 16 16 16 16
18 18 18 18 18 18 18 18
For higher true period rakes, consult the c/2 puffer section above.


c/2 orthogonal rake pseudo-periods

Forw
glider
Back
glider
Side
LWSS
Back
LWSS
Side
MWSS
Back
MWSS
Side
HWSS
Back
HWSS
All lower periods are impossible.
8 8 8 8 8 8 8 8
10 10 10 10 10 10 10 10
12 12 12 12 12 12 12 12
14 14 14 14 14 14 14 14
16 16 16 16 16 16 16 16
18 18 18 18 18 18 18 18
All higher pseudo-periods are known.


c/3 spaceships, puffers, rakes

S=Spaceship, P=Puffer, R=Rake. A yellow S means that only "trivial" spaceships are known, with no single section that repeats at the full period.

  3:SPR   6:SPR   9:SPr  12:Spr  15:SPr  18:SPr  21:Spr  24:SPr  27:SPR  30:spr  33:spr  36:SPR
 39:spr  42:spr  45:SPR  48:SPR  51:spr  54:SPR  57:spr  60:spr  63:spr  66:spr  69:spr  72:SPR
 75:spr  78:SPR  81:SPR  84:SPR  87:spr  90:SPR  93:spr  96:SPR  99:spr 102:spr 105:spr 108:SPR
111:spr 114:SPR 117:spr 120:spr 123:spr 126:spr 129:SPR 132:spr 135:SPR 138:spr 141:spr 144:SPR
All periods over 144 are known. *
* Here is a pattern that demonstrates that all periods 144 and higher can, in principle, be constructed. (Actually, this can probably be reduced to around 90-100). The method of construction is not easy, and it could be argued that these periods are not really "known".

c/4 orthogonal spaceships, puffers, rakes

S=Spaceship, P=Puffer, R=Rake. A yellow S means that only "trivial" spaceships are known, with no single section that repeats at the full period.

  4:SPR   8:SPR  12:Spr  16:spr  20:SPr  24:SPR  28:spr  32:SPR  36:spr  40:spr  44:SPr  48:SPR
 52:SPR  56:spr  60:spr  64:SPR  68:spr  72:SPR  76:SPR  80:Spr  84:SPR  88:sPr  92:spr  96:SPR
100:SPR 104:SPR 108:spr 112:spr 116:spr 120:SPR 124:spr 128:SPR 132:spr 136:spr 140:spr 144:SPR
148:sPr 152:SPR 156:SPR 160:SPR 164:spr 168:SPR 172:spr 176:spr 180:spr 184:spr 188:spr 192:SPR
196:spr 200:SPR

All periods over about 800 are known. (Could probably be reduced to about 400.) The intervening periods are not documented here.


2c/5 spaceships, puffers, rakes

Almost all the 2c/5 technology referred to below was found in whole or in part by [PT]. The original method of building p205+10N and p410+5N rakes was developed mostly by [DIB,JS]; [PT] improved it to p200+5N and later p185+5N.

S=Spaceship, P=Puffer, R=Rake.

  5:SPR  10:SPr  15:SPr  20:SPR  25:SPR  30:SPR  35:SPR  40:SPR  45:SPR  50:SPR  55:SPR  60:SPR
All periods over 60 are known.

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