Life Object Counts

Still-lifes and pseudo-still-lifes | Objects | Pseudo-objects | c/2 Spaceships | Other spaceships

Numbers in bold face have been confirmed by computer search.

Still-lifes and pseudo-still-lifes up to 24 bits:

Bits	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
Still-lifes	2	1	5	4	9	10	25	46	121	240	619	1353	3286	7773	19044	45759	112243	273188	672172	1646147	4051711
Pseudo-still-lifes	0	0	0	0	1	1	7	16	55	110	279	620	1645	4067	10843	27250	70637	179011	462086	1184882	3068984

Objects up to 20 bits:

Bits	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Still-lifes	0	2	1	5	4	9	10	25	46	121	240	619	1353	3286	7773	19044	45759	112243
P2 oscillators	1	0	0	3	0	1	1	1	1	6	3	20	29	98	199	484	1083	?
P3 oscillators	0	0	0	0	0	0	0	0	0	1	1	1	0	7	8	39	64	199
P4 oscillators	0	0	0	0	0	0	0	0	0	2	0	0	0	0	0	3	7	23
P5 oscillators	0	0	0	0	0	0	0	0	0	0	0	0	1	1	0	1	1	5
P6 oscillators	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	4	0	10
P8 oscillators	0	0	0	0	0	0	0	0	0	1	0	0	1	0	2	1	0	0
P14 oscillators	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
P15 oscillators	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	1	0
P30 oscillators	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2
Spaceships	0	0	1	0	0	0	1	0	1	0	1	0	0	0	0	0	0	5

Pseudo-objects up to 20 bits:

Bits	8	9	10	11	12	13	14	15	16	17	18	19	20
Pseudo-still-lifes	1	1	7	16	55	110	279	620	1645	4067	10843	27250	70637
P2 pseudo-oscillators	0	0	1	2	14	17	46	78	225	484	1519	3350	?
P3 pseudo-oscillators	0	0	0	0	0	0	0	0	0	2	5	20	45
P4 pseudo-oscillators	0	0	0	0	0	0	0	0	1	2	11	14	33
P5 pseudo-oscillators	0	0	0	0	0	0	0	0	0	0	0	2	4
P6 pseudo-oscillators	0	0	0	0	0	0	0	0	0	0	0	4	3
P8 pseudo-oscillators	0	0	0	0	0	0	0	0	0	0	2	1	2
P15 pseudo-oscillators	0	0	0	0	0	0	0	0	1	1	5	7	15
P30 pseudo-oscillators	0	0	0	0	0	0	0	0	0	0	1	0	1
Pseudo-spaceships	0	0	0	0	0	0	0	0	0	0	1	0	0

c/2 Spaceships:

Most of the known Life spaceships (at least the small ones) move at a velocity of c/2. These have a base period of 4, but some of the larger variants have periods which are multiples of this.

H. Koenig's computer searches have not revealed any spaceships which were not previously known, but they have confirmed that the previously-known lists of small spaceships have been complete up to 24 bits.

Bits	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
Orthogonal c/2 P4	0	0	0	0	0	1	0	1	0	1	0	0	0	0	1(pseudo)	0	5	0	9	2	7

Other spaceships:

Except for the glider, Life has no small spaceships which move at velocities other than c/2. H. Koenig's computer searches have not revealed any spaceships which were not previously known, but they have confirmed that the previously-known lists of small spaceships have been complete up to the following sizes:

Direction	Velocity	Period	Synopsis
Orthogonal	>c/2		None possible
	c/2	P2	None up to 35 bits; many larger*
		P4	Many (See previous section)
		P6	None up to 13 bits
	3c/7	P7	None up to 13 bits
	2c/5	P5	None up to 17 bits; some larger*
	c/3	P3	None up to 24 bits; two 25-bit; many larger*
		P6	None up to 17 bits
	2c/7	P7	None up to 11 bits
	c/4	P4	None up to 15 bits; many larger*
	c/5	P5	None up to 12 bits; many larger*
	c/6	P6	None up to 11 bits
	c/7	P7	None up to 10 bits
Diagonal	>c/4		None possible
	c/4	P4	one 5-bit; no others up to 15 bits; many larger*
	c/12	P96	Several large ones
	c/5	P5	None up to 12 bits
	c/6	P6	None up to 12 bits
	c/7	P7	None up to 10 bits
Knight-move	>c/3		None possible
	c/3	P6	None up to 14 bits
	2c/7	P7	None up to 11 bits
Oblique (x,y) x>y	>xc/(x+y)		None possible
	<=xc/(x+y)		None up to 10 bits

Groups marked * are also known to include spaceships whose periods are larger multiples of the base period.

See also: Life objects sorted by: counts, gliders, name, size, or type.

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