Life Object Counts

Computer searches | Objects | Pseudo-objects | Spaceships



Computer searches

Computer searches have counted still-lifes and pseudo-still-lifes up to 24 bits (by Raynham, Buckingham, and Niemiec and Koenig), period 2 oscillators and pseudo-oscillators up to 21 bits (by Niemiec and Koenig), period 3 oscillators and pseudo-oscillators up to 20 bits (by Beluchenko), and all objects of all types up to 10 bits (by Thompson).

Such lists of objects can also yield robust hand-assembled lists of pseudo-objects, since their assembly typically involves fairly trivial combinatorical procedures.

Numbers in bold face have been confirmed by computer search (or trivial hand-assembly). Other given numbers are believed to be complete, but have not yet been verified. Lists with large numbers of objects that have not yet been counted are shown with "many".

Status of object lists on sub-pages is shown by background color:


Objects up to 25 bits

Bits 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Still-lifes 0 2 1 5 4 9 10 25 46 121 240 619 1353 3286 7773 19044 45759 112243 273188 672172 1646147 4051726 many
P2 oscillators 1 00 3 0 1 1 1 1 6 3 20 29 98 199 484 1083 2722 6596 many many many many
P3 oscillators 00 00 00 0 00 1 1 1 0 7 8 39 66 216 420 many many many many
P4 oscillators 00 000 00 00 2 00 000 3 7 23 34 120 239 571 1343
P5 oscillators 00 000 00 000 00 1 1 2 4 8 16 42 76 210 419 many
P6 oscillators 00 000 00 00000 0 1 0 4 0 11 15 43 71 186 many
P8 oscillators 00 000 00 00 1 00 1 0 2 1 00 2 0 8 12 18
P10 oscillators 00 00 00 0 000 00 000 00 000 5 2 1
P12 oscillators 00 000 00 00000 00000 0000 4 1
P14 oscillators 00 000 00 00000 0 1 000 00000 0
P15 oscillators 00 000 00 00 1 00 0000 1 0 1 2 8 24 40
P24 oscillators 00 000 00 00000 00000 0000 4 4
P30 oscillators 00 00 00 0 000 00 000 00 2 0 2 2 2 8
P36 oscillators 00 000 00 00000 00000 00 1 0 1 2
P60 oscillators 00 000 00 00000 00000 0000 1 0
Other periods 00 000 00 00000 00000 00000 0
All oscillators 1 0 0 3 0 1 1 1 1 11 4 21 31 108 211 535 1165 2990 7119 244* 539* 1225* 1417**
Orthogonal c/2 P4 00 000 0 1 0 1 0 1 0 000 00 5 0 9 2 7 2
Orthogonal c/3 P3 00 000 00 00000 00000 00000 3
Orthogonal c/7 P7 00 000 00 00000 00000 1 00000
Diagonal c/4 P4 00 1 00 00 00000 00000 00000 1
Other velocities 00 000 00 00000 00000 00000 0
All spaceships 00 1 00 0 1 0 1 0 1 00 00 00 6 0 9 2 7 5

(NOTE: * also include an as-yet-uncounted number of P2 and P3 oscillators; ** also include an as-yet-uncounted number of P2, P3, P5, and P6 oscillators.)


Pseudo-objects up to 25 bits

Bits 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Pseudo-still-lifes 1 1 7 16 55 110 279 620 1645 4067 10843 27250 70637 179011 462086 1184882 3069134 many
P2 pseudo-oscillators 00 1 2 14 17 46 78 225 484 1519 3350 9460 22134 many many many many
P3 pseudo-oscillators 00 000 00 00 2 5 20 44 90 265 many many many
P4 pseudo-oscillators 00 000 00 0 1 2 11 14 33 50 154 manymanymany
P5 pseudo-oscillators 00 00 00 0 000 0 2 4 28 55 220 490 1370
P6 pseudo-oscillators 00 000 00 0000 4 3 6 41 74 394 734
P8 pseudo-oscillators 00 000 00 000 2 1 2 12 18 44 78 176
P10 pseudo-oscillators 00 000 00 00000 0 4 0 24 37 89
P12 pseudo-oscillators 00 000 00 00000 00000 4
P15 pseudo-oscillators 00 00 00 0 0 1 1 5 7 15 22 68 151 460 many
P30 pseudo-oscillators 00 000 00 000 1 0 1 1 5 7 61 82
P60 pseudo-oscillators 00 000 00 00000 0000 1 0
Other periods 00 000 00 00000 00000 0
All pseudo-oscillators 00 1 2 14 17 46 78 227 489 1543 3398 9562 22347 604* 520** 1521** 2455***
Orthogonal c/2 P4 00 000 00 000 1 0 000 00 1
Other velocities 00 000 00 000 00 00 000 0
All pseudo-spaceships 00 00 00 00 00 1 00 00 00 1

(NOTE: * also include an as-yet-uncounted number of P2 pseudo-oscillators; ** also include an as-yet-uncounted number of P2, P3, and P4 pseudo-oscillators.; *** also include an as-yet-uncounted number of P2, P3, and P4 and P15 pseudo-oscillators.)


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 that are multiples of this.

H. Koenig's computer searches have not revealed any spaceships that were not previously known, but they have confirmed that the previously-known lists of c/2 spaceships have been complete up to 24 bits, as well as smaller limits for other velocities. In 2013, Josh Ball added the loafer to this list.

DirectionVelocity PeriodSynopsis
Orthogonal
(x,0)c/d
>c/2 anyNone possible
c/2 2None up to 35 bits; many larger*
4 Many (See previous section)
6None up to 13 bits
3c/7 7None up to 13 bits; two larger (almost)
2c/5 5None up to 17 bits; several larger*
17c/45 270None up to 10 bits; one very large
c/3 3None up to 24 bits; two 25-bit; many larger*
6None up to 17 bits
2c/7 7None up to 11 bits; several larger
c/4 4None up to 15 bits; many larger*
c/5 5None up to 12 bits; many larger*
c/6 6None up to 11 bits; several larger
c/77 None up to 10 bits; one 20-bit
OtheranyNone up to 10 bits
Diagonal
(x,x)c/d
>c/4 anyNone possible
c/44 One 5-bit; no others up to 15 bits; many larger*
c/5 5None up to 12 bits; several larger*
c/6 6None up to 12 bits; several larger
c/7 7None up to 10 bits; several larger
c/12 96None up to 10 bits; several larger
OtheranyNone up to 10 bits
Knight-move
(2x,x)c/d
>(2,1)c/6 anyNone possible
(2,1)c/6 6None up to 14 bits; one larger (almost)
(2,1)c/77None up to 11 bits
(2,1)c/k, k≥2400000  None up to 10 bits; infinitely many larger
(8192,4096)c/35567490 35567490None up to 10 bits; one very large
OtheranyNone up to 10 bits
Oblique
(x,y)c/d, x>y
>(x,y)c/2(x+y) anyNone possible
(5120,1024)c/33699586 33699586None up to 10 bits; one very large
OtheranyNone up to 10 bits

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



See also: Life objects sorted by: counts, frequency of occurrence, cost in gliders, name, size in bits, or type.

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Copyright © 1997, 1998, 1999, 2013, 2014 by Mark. D. Niemiec. All rights reserved.
This page was last updated on 2015-02-19.