The period of an oscillator, spaceship, or puffer is the number of generations it takes to reappear in its original form. For a puffer, the trail of debris is ignored. For general information about periods in cellular automata see Period on LifeWiki.

Live Free or Die is home to objects of a variety of periods and objects with arbitrarily high periods. It is unknown whether Live Free or Die is omniperiodic.

A table of the smallest objects for each known period is at the end of this article. The rest is a summary of the known objects for each period and how common they are.

P1

There are only two p1 objects in Live Free or Die: the dot, a stable pattern (a p1 oscillator, or still life) consisting of a single, isolated live cell, and the moon, a p1 c spaceship with only four cells, which is the smallest spaceship. Both are extremely common naturally, and the dot is the most common puffer output. There is no such thing as a p1 puffer.

P2

The only small, natural p2 object in Live Free or Die is the checker, a p2 oscillator and a very common puffer output. Larger oscillators include the Cecil B. DeMille and the ball pit, both of which are extensible in size. There are two known p2 spaceships: the flicker ship and the flutter ship. The only known p2 puffer is the flicker rake.

P3

There are no natural p3 objects in Live Free or Die, but p3 oscillators, spaceships, and puffers have all been discovered. Oscillators include the sandbar, rotunda and trilogy. Spaceships include the tricycle ship and wide tricycle ship. Puffers include the bent tricycle puffer, tricycle puffer, wide tricycle puffer, ellipsis puffer, and a puffer formed from the tricycle ship. There is also a p3 clean backward moon rake, the tricycle rake, making p3 the shortest period with known puffers and rakes.

P4

By the total number of objects discovered, p4 is by far the most common period in Live Free or Die. P4 objects include small oscillators such as the lever, radar, and the anchor, the last of which is useful in anchor track technology. Larger p4 oscillators include the control tower, buoy, shortwave, longwave, beacon, and flotsam. There are a huge number of p4 c spaceships and puffers, along with a number of trailers and tagalongs. Small, natural p4 spaceships include the key ship, plus ship, robot ship, and sun ship, and small, natural p4 puffers include the dot puffer, double dot puffer, robot puffer, and sun puffer. Many p4 c spaceships and puffers appear with various wing lengths (see Iteration guides) and can be anchored. Others, like the metronome puffer, can be extended infinitely in other ways. There are also two p4 c clean backward moon rakes, the pocket rake and the flip-flop rake, and a p4 c sideways moon rake, the zipper rake. Rakes can also be formed using the p4 c plow trailer. Arbitrarily large p4 c spaceships can be built by combining spaceships, puffers, trailers, and tagalongs.

P4 is also the shortest period with known spaceships that travel slower than light and the only known period with spaceships that travel diagonally. P4 c/2 spaceships, all of which are large and artificial, include the crab ship, rhino ship, wide rhino ship, elephant ship, Eppstein's slow ship, and the fox ship, along with many unicorn ships, buffalo ships, hippo ships, and horned ships. There are also p4 c/2 backward moon rakes, the buffalo rake, hippo rake, and horned rake. P4 c/4 diagonal spaceships include the giraffe ship, ram ship, and slanted ship.

The only known gun in Live Free or Die is the p4 moon laser.

P5

There are no natural p5 objects in Live Free or Die, but p5 oscillators, spaceships, puffers, and rakes have all been discovered. The only known p5 oscillators are the starfish and crossroads. There are known p5 spaceships that travel at c (the nickel ship), 2c/5 (the zirconium ship), and c/5 (the quintessential ships and the hammerhead ship). There is also a p5 c/5 backward moon rake, the quintessential rake. There is also a p5 c puffer, the nickel puffer, and a p5 c backward moon rake, the nickel rake.

P6

Objects at p6 are fairly common. P6 oscillators include the ant, anthill, mantis, six shooter, big six shooter, and big six shooter stacks. Three known p6 spaceships travel at c and occur naturally: the extremely common free ship, the hex ship, and the short free ship. P6 puffers include the revolver puffer and the trombone puffer, which is infinitely extensible. There is also a p6 sideways moon rake, the hex rake. The only known c/3 object is the p6 wasp ship.

P7

There are no known p7 oscillators or spaceships. The only known p7 puffer is the rake and bake puffer, which has been known to occur naturally.

P8

P8 objects are fairly common. P8 oscillators include the sparkler and the different variations of the black widow. P8 spaceships include the octopus ship, squid ship, and pinwheel ship, which travel at c, and many c/2 spaceships, including the dust mite ship and many unicorn ships, buffalo ships, hippo ships, and horned ships. There are a large number of p8 c puffers, including the eclipse puffer, forge puffer, occidental puffer, scale puffer, scorpion puffer, and tick puffer, many of which have variations with different wing lengths (see Iteration guides). Arbitrarily large p8 c spaceships can be built by combining spaceships, puffers, trailers, and tagalongs.

P9

There are no known p9 oscillators or spaceships. The only known p9 puffers are the arrow puffer and the nearly identical long arrow puffer.

P10

There are no natural p10 objects in Live Free or Die. The only known p10 object is the c/5 decade ship, making it the only period with a known spaceship that travels slower than c but no known c spaceship.

P12

No p12 objects occur naturally, but p12 oscillators, spaceships, and puffers have all been discovered or constructed. Oscillators include the two-slot anchor track and new wave. There are no known indivisible spaceships, but p4 and p6 c spaceships and puffers can be used to build p12 flotillas, including anchor track flotillas, that are spaceships, puffers, or rakes. For example, a free ship can partially consume the trail of a dot puffer to form a p12 puffer, and two free ships can consume the trail completely to form a p12 spaceship. The only known indivisible p12 puffer is the zodiac puffer, which has the highest period of any known indivisible spaceship or puffer.

P19

There are no known p19 spaceships or puffers. The only known p19 oscillators are the monster and monster stacks built from monsters whose sparks interact.

Other periods

Many spaceships and puffers of higher periods can be formed by flotillas with interacting spaceships and puffers of different periods. Flotillas of period 16 and 6 × 2n can be built using freedom fighters. Some objects based on anchor tracks have infinitely extensible period. Anchor tracks of different sizes can have any period 4 × 2n - 4, and spaceships and puffers created using anchor nibblers and anchor eaters can have any period 8 × 2n.

Smallest known objects for each period
Period
Smallest known oscillator
Minimum population
1
dot
1
2
checker
2
3
sandbar
32
4
lever
4
5
starfish
64
6
ant
6
8
sparkler
12
12
two-slot anchor track
6
19
monster
6
28
three-slot anchor track
8
60
seven-slot anchor track
16
124
five-slot anchor track
12
252
six-slot anchor track
14
4 × 2n - 4
(2n - 1)-slot anchor track
2n+1

Period
Smallest known spaceship
Minimum population
1
moon
4
2
flicker ship
54
3
wide tricycle ship
108
4
key ship
8
5
nickel ship
98
6
free ship
12
8
squid ship
20
10
decade ship
114
12
(free ships and dot puffer)
42
16
six-slot anchor eater ship
70
24
(free ships and octopus ship)
60
32
ten-slot anchor eater ship
70
48
(freedom fighter flotilla)
411
64
18-slot anchor eater ship
86
96
(freedom fighter flotilla)
1476
128
34-slot anchor eater ship
118
256
66-slot anchor eater ship
180
8 × 2n
(2 × 2n + 2)-slot anchor eater ship
4 × 2n + 60
6 × 2n
(freedom fighter flotilla)
?

Period
Smallest known puffer
Initial population
2
flicker rake
82
3
tricycle puffer
34
4
double dot puffer
6
5
nickel rake
98
6
(two free ships)
24
7
rake and bake puffer
12
8
eclipse puffer
13
9
arrow puffer
18
12
(free ship and dot puffer)
19
16
(eclipse puffers and freedom fighter)
36
18
(free ship and arrow puffer)
30
20
(2-3 robot puffer and nickel puffer)
157
24
(free ship and eclipse puffer)
25
30
(hex ship and nickel rake)
114
32
ten-slot anchor nibbler puffer
49
48
(hex ship and six-slot half anchor biter puffer)
59
64
18-slot anchor nibbler puffer
65
96
(hex ship and ten-slot half anchor biter buffer)
67
128
34-slot anchor nibbler puffer
97
256
66-slot anchor nibbler puffer
161
8 × 2n
(2 × 2n + 2)-slot anchor nibbler puffer
4 × 2n + 35
24 × 2n
(hex ship and (2 × 2n + 2)-slot half anchor biter puffer)
4 × 2n + 51

Period
Smallest known rake
Initial population
3
tricycle rake
130
4
pocket rake
32
5
nickel rake
98
12 × 2n
(anchor track / freedom figher flotilla)
?