Game of Life Status page

This page documents what is known and what is not known in the Game of Life concerning certain classes of patterns.

I have reason to believe that the information here is accurate (excluding perhaps the historical notes), so if you think you spot an error (or if you find something new!), 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.

Contents:

• Oscillator periods
• Glider reflectors
• Glider gun true-periods
• Gun pseudo-periods
• Spaceship velocities (and puffer, wickstretcher, gun velocities)
• Spaceship periods
• c/2 orthogonal spaceships and puffers
• c/2 orthogonal rake true-periods
• c/2 orthogonal rake pseudo-periods
• c/3 orthogonal spaceships and puffers
• c/4 orthogonal spaceships and puffers
• 2c/5 orthogonal spaceships and puffers

Key:	green An example is known (or at least an explicit method of construction) red No example is known yellow Only trivial or partial examples are known gray Proven 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: AF   Achim Flammenkamp AH   Alan Hensel DE   David Eppstein DG   Dave Greene DIB  David Bell DJB  David Buckingham DL   Dietrich Leithner DRH  Dean Hickerson GN   Gabriel Nivasch HH   Hartmut Holzwart JS   Jason Summers NB   Nicolay Beluchenko NDE  Noam Elkies PT   Paul Tooke SAS  Stephen Silver TC   Tim Coe

Oscillator periods

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:
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,AF]
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]

For examples, refer to:

• My all-osc collection
• Dean Hickerson's "stamp collection"
• Pretty much any Life pattern collection

Glider reflectors

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.

For examples, refer to:

• Patterns called "reflectors" and "reflectors2" in my jslife collection
• "gun" patterns in my all-osc collection

Glider gun true-periods

For examples, refer to:

• "gun" patterns in my all-osc collection
• Dieter and Peter's gun collection (but many guns there are pseudoperiod)

Gun pseudo-periods

For examples, refer to:

• Dieter and Peter's gun collection
• Stephen Silver's non-glider gun collection

Velocities of spaceships and related objects

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.

Velocity	Spaceship?	Puffer?	Versatile puffer?	Wick- stretcher?	Gun?
(1,0)c/2	Yes	Yes	Yes	Yes	Yes
(1,0)c/3	Yes	Yes	Yes	No	No
(1,0)c/4	Yes	Yes	Yes	Yes	No
(1,1)c/4	Yes	Yes	Yes	Yes	Yes
(1,0)c/5	Yes	Yes	Yes	No	No
(2,0)c/5	Yes	Yes	Yes	No	Yes
(1,1)c/5	Yes	No	--	No	No
(1,0)c/6	Yes	No	--	No	No
(2,1)c/6	No	No	--	No	--
(1,1)c/6	Yes	No	--	No	No
(1,0)c/7	No	No	--	No	--
(2,0)c/7	Yes	No	--	No	No
(3,0)c/7	No	No	--	No	--
(2,1)c/7	No	No	--	No	--
(1,1)c/7	No	No	--	No	--
(1,1)c/12	Yes	Yes	Yes	Yes	Yes
(17,0)c/45	Yes	Yes	Yes	No	No
Although spaceships of all sufficiently slow rational velocities have been proven to exist, no explicit method of constructing a spaceship (or other object in this table) of any other velocity is known.

Most recent discoveries (new velocities):
Sep 2005: c/6 diagonal spaceship [NB]
Dec 2004: 17c/45 orthogonal spaceship [GN,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):
Oct 2005: versatile c/4 diagonal puffer [DIB with JS,NB]
Mar 2004: c/4 diag puffer [HH]
Mar 2003: 2c/5 gun [NDE,DG]
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]

There's no efficient single reference collection for examples of all the items in this section, but try:

• My jslife collection
• 17c/45 spaceship
• Alan Hensel's collection
• David Bell's collection
• Stephen Silver's small spaceships collection

Spaceship periods

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		...
c/5 diag				5					10			15			20				25				30				35		None
c/6 orth					6					12				18				24					30					36	None
c/6 diag					6					12				18				24					30					36	None
2c/7 orth						7					14					21						28					35		None
c/12 diag										12								24										36	96, 192, ...
17c/45 orth																													270, ...

Most recent discoveries, excluding new velocities:
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 AH]
Dec 1993: c/3 orth p15 [DIB]
Jul 1993: c/2 orth p6 [DIB]
May 1992: c/3 orth p9 [DIB]

For examples, refer to:

• Stephen Silver's small spaceships collection
• c/2 rakes collection
• "velocity-*/*-hp.lif" files in my jslife collection

c/2 orthogonal spaceships, puffers, rakes

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

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.

For examples, refer to:

• c/2 rakes collection

c/2 orthogonal rake true-periods

For examples, refer to:

• c/2 rakes collection

c/2 orthogonal rake pseudo-periods

For examples, refer to:

• c/2 rakes collection

c/3 spaceships and puffers

c/3 orthogonal spaceship periods

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

c/4 orthogonal spaceships, puffers, rakes

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

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

2c/5 spaceships and puffers

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=Spacechip, P=Puffer, R=Rake.

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