# Life Oscillators by Period

Introduction | Known periods
Period: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 20 | 21 | 22 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 39 | 40 | 42 | 44 | 45 | 46 | 47 | 50 | 51 | 52 | 54 | 55 | 56 | 60 | 63 | 64 | 70 | 72 | 75 | 88 | 90 | 100 | 120 | 138 | 144 | 156 | 177 | 256 | 276 | 300 | 312

## Introduction

In Life, naturally-occurring oscillators exist of many periods, and almost all additional periods are obtainable using highly artificial mechanisms. The oscillators shown are ones that have known glider syntheses. (Also, some of these oscillators, and their corresponding syntheses, are infinitely extensible.)

The oscillators here could be classified into three broad categories:

• Most of the oscillators have rotors of the given period.
• Some of the oscillators consist of sparkers with two rotors of periods x and y, whose sparks interact to create an additional trivial spark whose period is GCD(x,y).
• Some of the oscillators have two rotors of periods x and y that do not interact with each other. These are called trivial oscillators, and are said to have a pseudo-period of GCD(x,y), as no rotor cells actually have that period. Many pseudo-oscillators with composite periods also work this way. The only known period 34 oscillators are also of this form.

The last two methods are useful for creating oscillators with periods that are otherwise unavailable. Unfortunately, it is impossible to use these to obtain prime periods (like 17), prime powers (like 16, 27, 49, 64 and 81), and products of prime powers (e.g. there are no synthesized oscillators of periods 48 and 80, as these both require a period 16 component, and the only synthesized period-16 oscillator can neither spark, be sparked by, nor form objects or pseudo-objects with oscillators of other periods.)

In 1996, Buckingham revealed a suite of track components that use eaters and other still-lifes or sparking oscillators to move a Herschel heptomino (the 20th generation of B heptomino, after it has left behind a block). By combining several of these, in much the same way as one assembles toy train tracks, one can produce looping conduits that take arbitrarily long to cycle a single Herschel. By placing multiple Herschels in such a conduit, one can obtain oscillators of arbitrarily small fractions of such large periods. (These were improvements over his earlier track components that used spark-producing oscillators as still-lifes as stabilizers; unfortunately, those could only produce oscillators whose periods are multiples of those of the spark-producers.)

Oscillators of all periods 58 and above can be obtained in this way. Since Herschels naturally release gliders, this also yields glider guns of all periods 62 and above. (The Herschels collide with each other if closer than 58 generations apart, and they collide with the escaping gliders if closer than 62 generations apart.) Dietrich Leithner has constructed specific Herschel-based oscillators of periods 56 and 57 by adding in one of Buckingham's earlier spark-stabilized sections (as those periods are divisible by 4 and 3 respectively, allowing use of sparkers of those periods).

This is basically a variation of the method described by Conway in the 1970s to construct oscillators of arbitrary period using stable glider-reflectors. (Until recently, most known stable glider-reflectors were derived from the above, turning a glider into a Herschel, shuttling the Herschel, and then turning the Herschel back into a glider.)

In April 2013, Mike Playle found a small 90-degree stable reflector that allows construction of glider-loop oscillators of all periods 43 and above.

At present, Life contains known oscillators of all periods except 19 and 38. (There are also no known non-trivial period 34 oscillators; all known ones consist of independent period 2 and period 17 components).

Furthermore, since the Herschels, eaters, and other small still-lifes can easily be synthesized, syntheses exist for almost all oscillator periods.

Unlike synthesis of still-lifes, synthesis of oscillators is usually much more difficult. It more closely resembles sculpting liquids, chemical synthesis of unstable compounds, or performing open heart surgery on a patient whose heart is still beating. Most of the oscillators with known syntheses are either small, composed of many small and simple interacting pieces, or create seemingly random messes that eventually spontaneously erupt into the object or component desired. Many large pulsators and hassled oscillators were discovered out of searches of random broths, and their syntheses frequently consist of building a few pieces that are similar to pieces seen in the broths that created the desired components (i.e. "art imitating life").

Of course, for any period where guns exist, oscillators must also necessarily exist, since any gun can be turned into an oscillator by adding eaters to eat any escaping gliders.

## Known oscillator periods

This is a table of known oscillator periods up to 100. Status is shown in color:

• Periods for which oscillators exist, and syntheses exist, are shown shown in white.
• Periods for which oscillators exist, and syntheses presumably exist, but which have not been specifically instantiated, are shown in teal.
• Periods for which oscillators exist, but syntheses exist only for trivial examples (i.e. ones with composite periods where no cells actually oscillate with the full period), are shown in green.
• Periods for which oscillators exist, but no syntheses are yet known, are shown in yellow.
• Periods for which only trivial oscillators exist, and syntheses exist, are shown in blue. (Period 34 the only period of this kind).
• Periods for which there are no known oscillators are shown in red. (Only periods 19 and 38 are unknown).

As Herschel conduits exist for all periods 56 and higher, and all their components can be synthesized from gliders, syntheses presumably exist for all oscillator periods 56 and higher. Due to their large sizes, however, no such oscillators are shown.

The Snark reflector allows glider loops of all periods 43 and higher. The Snark can be synthesized, and if such loops can be synthesized, this would mean syntheses would also exist for all oscillator periods 43 through 55. However, no attempt has yet been made to synthesize full glider loops containing multiple Snarks, so this has not yet been demonstrated.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 28 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 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 and higher

## Period-1 oscillators

Period-1 oscillators are called still-lifes, and are generally considered separate from oscillators of higher periods. Due to the the large number of still-lifes, these are shown on a separate page.

## Period-2 oscillators

Due to the the large number of oscillators, these are shown on a separate page.

## Period-3 oscillators

Due to the the large number of oscillators, these are shown on a separate page.

## Period-4 oscillators

Due to the the large number of oscillators, these are shown on a separate page.

## Period-5 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

 Octagon II [6] Silver's P5 on snake [19] Silver's P5 on snake [14] Fumarole [7] Silver's P5 on python [23] Silver's P5 on eater [24] Silver's P5 above eater [12] Fumarole w/ tub [12] Silver's P5 on very long snake [16] Silver's P5 on canoe [16] Silver's P5 above shil- lelagh [23] Silver's P5 behind shil- lelagh [17] Silver's P5 on hook w/ tail [31] Silver's P5 above hook w/ tail [15] Silver's P5 above tub w/ tail [14] Fumarole w/ up boat [10] Fumar- ole w/ two tubs [16] Silver's P5 on integral [27] Silver's P5 above long shil- lelagh [27] Silver's P5 on long canoe [20] Silver's P5 on long hook w/ tail [23] Silver's P5 above extra long snake [20] Elkies's P5 [24] Silver's P5 above tub w/ long tail [26] Silver's P5 on hat [18] Silver's P5 behind tub w/ long tail [22] Silver's P5 above down boat w/ tail [14] Silver's P5 above up boat w/ tail [15] Silver's P5 above long hook w/ tail [16] Pentoad between two eaters [12] Fumarole w/ tub and up boat [14] Silver's P5 before cis shillelagh [22] Silver's P5 on cis hook w/ tail [30] Silver's P5 above integral w/ hook [30] Silver's P5 above integral w/ tub [30] Silver's P5 on snake siamese snake [27] Silver's P5 on snake siamese carrier [24] Silver's P5 above tub w/ very long tail [30] Silver's P5 on carrier siamese snake [22] Silver's P5 on carrier siamese carrier [19] Silver's P5 on very long hook w/ tail [27] Silver's P5 above very long shillelagh [20] Silver's P5 on extra extra long snake [20] Fumarole w/ up barge [14] Fumarole w/ fuse w/ tail [16] Silver's P5 above boat w/ long tail [28] Silver's P5 on very long canoe [20] Elkies's P5 w/ tub [28] Silver's P5 on up long hat [21] Silver's P5 on block on table [22] Silver's P5 on down long hat [40] Silver's P5 behind boat w/ long tail [24] Silver's P5 above block on table [31] Silver's P5 on integral w/ hook [37] Hooks on snake [17] Hooks on carrier [14] Silver's P5 above cis hook w/ tail [43] Silver's P5 on beehive w/ tail [14] Silver's P5 on down barge w/ tail [17] Silver's P5 above claw w/ tail [14] Silver's P5 on fuse w/ two tails [18] Silver's P5 on up barge w/ tail [16] Silver's P5 above very long hook w/ tail [18] Elkies's P5 w/ claw and pre-block [x] Silver's P5 before cis shil- lelagh w/ tub [x] Elkies's P5 w/ boat [30] Hooks on eater [22] Hooks on python [17] Silver's P5 above long cis hook w/ tail [53] Hooks above eater [15] Elkies's P5 w/ claw w/ tub and pre-block [x] Pentoad 1h2; Pentoad between eater and bookend and block [19] Block on Elkies's P5 w/ loaf [28] Elkies's P5 w/ claw w/ boat and pre-block [x] Elkies's P5 w/ long bookend and claw and pre-block [x] Elkies's P5 siamese snake [x] Pseudo- barber- pole; Flammen- kamp's P5 [28] Pseudo- barber- pole tie boat [36] Up table on pseudo barber pole [31] Up table below pseudo barber pole [31] Down table below pseudo barber pole [33] Down table on pseudo barber pole [33] Pseudo barber pole tie up snake [41] Pseudo barber pole tie down snake [41] Pseudo barber pole tie ship [38] Pseudo barber pole tie up carrier [40] Pseudo barber pole tie down carrier [40] Two pentoads between two eaters [17] Two pentoads between two eaters and a pond [19] Hooks on two snakes [22] Heart [15] 40-bit P5 oscillator [27] Harbor [34]

The pseudo-barber-pole superficially resembles the whole series of period 2 barber-pole oscillators, but strangely enough, has a period of 5 instead. It forms the basis for a large number of larger period 5 oscillators (and many with periods that are multiples of 5, such as period 10).

Octagon II has eight fingers that can sometimes be used to hassle other oscillators like the period 50 Traffic Jam.

The Fumarole is the smallest oscillator that produces a period 5 domino spark.

## Period-6 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

 Unix [6] Up beacon on up candel- frobra [13] Up beacon on down candel- frobra [13] Down beacon on down candel- frobra [13] Down beacon on up candel- frobra [13] Up bipole on up candel- frobra [16] Up bipole on down candel- frobra [16] Down bipole on down candel- frobra [16] Down beacon on cuphook w/ pre- block [17] Up beacon on cuphook w/ pre- block [18] Up beacon on down cuphook w/ tail [9] Up beacon on up cuphook w/ tail [14] Down beacon on up cuphook w/ tail [12] Blonker [25] Down bipole on up candel- frobra [17] Down beacon on down cuphook w/ tail [13] Up tripole on up candel- frobra [19] Up tripole on down candel- frobra [19] Down tripole on down candel- frobra [19] Up beacon on cuphook w/ pre- block w/ tub [21] Down beacon on cuphook w/ pre- block w/ tub [20] Up beacon on down cuphook w/ tub and tail [12] Up beacon on up cuphook w/ tub and tail [17] Down beacon on up cuphook w/ tub and tail [15] Down beacon on down cuphook w/ tub and tail [16] Up beacon on up long bookend eating eater [12] Eater eating test tube baby [12] Down beacon on down long bookend eating eater [12] Up beacon on down long bookend eating eater [12] Down tripole on up candel- frobra [17] Down beacon on up long bookend eating eater [12] P6 w/ block and head [x] Nicolay Belu- chenko's P6 between two eaters [24] Four blinkers around four blocks [12] P6 w/ block and tub [x+5] P6 w/ block and boat [x+7] Short key and skewed pole tie bipole [55] Bent key and skewed pole tie bipole [49] A for All [14] Jason Summers's P6 [40] Sesqui- unix [12] Merzenich's unix on eater [13] Extremely impressive [30-35] Two cis unices [11] \$rats [101-124] 32-bit P6 #1 [72] Two trans unices [11] Two touching trans- unices [14] Two touching cis- unices [14] 33-bit eater- hassled P6 [50-72] Lonely bee hassled by four toads [19] Ship hassled by two unices [17] Three cis cis unices [23] Three cis trans unices [16] Three trans trans unices [17] Beluchenko's two unices and block on corner table [24] Merzenich's unix on dual eater-2 [49] Merzenich's 4 clocks hassling 2 siamese unices [42] Unicycle; Four cis unices [28]

All of these with a beacon, bipole, tripole or test tube baby have a pseudo-period of 6, a composite of 2 and 3.

The Unix is the smallest oscillator that produces a period 6 diagonal bit spark.

Extremely impressive is an unusual oscillator. It appears at first glance to be a billiard table, but isn't really, as one of the sides temporarily falls apart, but then re-forms later.

## 5 Period-7 oscillators

 28-bit P7 #1 [57] Burloaf- erimiter [27] Jason Summers's P7 [22] Cheaper (but larger) Burloaf- erimiter [24] 29-bit P7 #1 [59]

The 29-bit P7s (and its related 28-bit minimal form) can have their period increased by 1 with a diagonal bit spark, allowing them to be used in oscillators with periods 7n+1. There are period-8 and period-15 examples.

## Period-8 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

 Figure-8; Big beacon [4] Blocker [6] Coe's P8; Tim Coe's P8 [8] Smiley [28] Flammen- kamp's P8 [13] Down table on blocker [9] Up table on blocker [11] Down blocker on cap [9] Down blocker on down long bookend [11] Up blocker on down long bookend [11] Up blocker on cap [11] Down blocker on up long bookend [11] Up Coe's P8 on table [13] Up blocker on up long bookend [13] Down Coe's P8 on table [13] Down blocker on up long bookend w/ hook [14] Up blocker on up long bookend w/ hook [14] Up blocker on up long bookend w/ tub [14] Down blocker on up long bookend w/ tub [14] Down blocker on up long bookend w/ hook [14] Up figure-8 and trans mold sharing sparks [13] Down blocker on up long bookend w/ tub [14] Up blocker on up long bookend w/ hook [16] Up figure-8 and cis mold sharing sparks [13] Up blocker on up long bookend w/ tub [16] Down figure-8 and trans mold sharing sparks [9] Down figure-8 and cis mold sharing sparks [9] Down blocker on down long bookend w/ long hook [15] Down blocker on dock [12] Up blocker on down long bookend w/ down boat [13] Down blocker on down long bookend w/ down boat [13] Down blocker on down table w/ gull [11] Down blocker on down long bookend w/ up boat [14] Up blocker on down table w/ gull [13] Up blocker on down long bookend w/ up boat [14] Down blocker on up long bookend w/ long hook [15] Up blocker on down long bookend w/ long hook [15] Up blocker on dock [12] Down blocker on up long bookend w/ down boat [13] Down blocker on up table w/ gull [11] Down blocker on up long bookend w/ up boat [14] Up blocker on up long bookend w/ long hook [17] Up blocker on up long bookend w/ down boat [15] Up blocker on up table w/ gull [13] Up blocker on up long bookend w/ up boat [16] 28-bit P8 #1 [25] Kok's Galaxy [12] Figure-8 and up mazing sharing sparks [9] Figure-8 and down mazing sharing sparks [12] Two trans blockers [16] Two cis blockers [16] Cauldron, Crucible [26-63] Toad sucked by two figure-8s #2 [17] Toad flipped by two figure-8s #2 [14] Toad flipped by two figure-8s #3 [17] Toad sucked by two figure-8s #4 [14] Toad sucked by two figure-8s #3 [17] Toad sucked by two figure-8s #1 [12] Toad flipped by two figure-8s #1 [11] 36-bit P8 oscillator [27] Hertz oscillator [11-14] Tumbling T-tetson; Traffic light hassled by two figure-8s [10] Honeyfarm hassled by four eaters [14] Blocker rephasing P7 [69] Dual Hertz oscillator [20-24]

Figure-8 is the smallest oscillator that produces a period 8 (delayed) domino spark.

The blocker is the smallest oscillator that produces a period 8 diagonal bit spark.

Kok's Galaxy is produces a period 8 diagonal bit spark.

## 8 Period-9 oscillators

 Lonely bee; Worker bee [19] Double lonely bee [24] Triple lonely bee [29] (n lonely bees [19+5n]) Cis triple snacker [25] 38-bit P9 [85] Snacker [17] Double snacker [20] Trans triple snacker [23] (n snackers [14+3n])

The Snacker is just a pentadecathlon whose period has been hassled from 15 down to 9. It produces a period 9 domino spark. Multiple snackers (for example, the cis triple snacker) make the spark slightly more accessible.

## Period-10 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

The ones involving pseudo-barber-poles or Silver's P5 have a pseudo-period of 10, a composite of 2 and 5.

## Period-12 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

All of these have a pseudo-period of 12, a composite of 3 and 4.

Note that caterers and/or molds could be used as hasslers in both the first and last oscillators on the bottom row, and either oscillator could also be flipped vertically, yielding 10 distinct versions of the Baker's dozen, and 16 of the Crown.

## Period-14 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

The second one has a pseudo-period of 14, a composite of 2 and 7.

## Period-15 oscillators

Due to the the large number of oscillators, these are shown on a separate page.

## 1 Period-21 oscillator

This has a pseudo-period of 21, a composite of 3 and 7.

## Period-24 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

All of these involving figure-8s have a pseudo-period of 24, a composite of 3 and 8.

## 1 Period-26 oscillator

This has a pseudo-period of 26, a composite of 2 and 13.

## Period-30 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

The Queen bee is extremely versatile. It is a shuttle that flips over every 15 generations, leaving a beehive egg, which must be removed; in both cases above, by a block. The Queen bee forms the basis for the first glider gun ever discovered, as well as many oscillators with periods of 30n.

It can also eat gliders many different ways:

• Row 1 #1+2: left sides cook glider into block, then into toxic boat; right sides cook glider into toxic block
• Row 1 #3: cooks glider into boat, then into toxic blinker
• Row 1 #4: both sides cook glider into toxic loaf
• Row 1 #5: cooks glider into toxic beehive
• Row 2 #1+2: cook glider into block, then eat the block
• Row 2 #3+4: cook glider into something the block then eats
• Rows 3-6: eat glider directly

In addition to being able to being able to eat gliders in all the same ways a queen bee can, plus several others, the Buckaroo can also naturally reflect gliders 90 degrees, making it useful in constructing glider loops of period 30n.

The "bad gun" is a an arrangement of two queen bee shuttles that forms a glider gun that doesn't quite work, because the escaping glider hits the right shuttle at the last moment; if it were advanced only 2 more generations, it would have escaped. This is rescued and turned into a period 30 oscillator by eating the glider before the right shuttle returns.

## 2 Period-31 oscillators

Merzenich's 48-bit period 31 oscillator generates a diagonal domino spark, allowing it to reflect gliders 90 degrees

The period 31 glider loop uses a special reflector, where a glider hits a mangled honeyfarm, producing a honeyfarm predecessor and a rotated glider. Unfortunately, this only works if a glider is present each cycle, so it cannot be used to produce oscillators whose periods are multiples of 31.

## 1 Period-34 oscillator

This has a pseudo-period of 34, a composite of 2 and 17.

## Period-36 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

## 1 Period-39 oscillator

This has a pseudo-period of 39, a composite of 3 and 13.

## 1 Period-42 oscillator

This has a pseudo-period of 42, a composite of 6 and 7.

## 1 Period-46 oscillator

Twin Bees is one of the simplest natural shuttles found in Life, and one of the first to be found. It produces useful plumes of clean debris, which is is why it was used in some of the earliest glider guns found. The toxic unstable eggs at the ends can be eaten in many different ways, by blocks, eaters, even hats. Interestingly, it is possible to eat the engine prematurely, altering its period to 54. By controlling the eating mechanism, the same shuttle can alternate between the two periods, resulting in the period 100 Centinal.

## 1 Period-50 oscillator

This is the simplest of many similar traffic-jam oscillators. The Traffic light push reaction has a period of 25, but one traffic light will patiently wait for another to move into position, so it is easy to construct traffic jams of periods that are not multiples of 25, by using appropriate sparkers of other periods. For example, a period 40 traffic jam sparked by period 8 sparkers, and the period 110 Traffic circle, where period 5 sparkers hassle traffic-light predecessors arranged in a large square.

## 2 Period-52 oscillators

The second oscillator has 30 trivial variations. First, there are six different versions of the outside. Any of the mold hasslers can be reversed to hassle the opposite side of the moving signal: none (as shown), one, two (cis), two (trans), three, or four molds can be reversed. Second, there are five different versions of the inside. The block pairs are quiescent except when passing an unstable signal. Multiple signals can be in the same interior as long as they are at least 16 generations apart, so there can be one signal (as shown), two signals (separated by 16+36, 20+32, or 24+28 generations), or three signals (separated by 16+16+20 generations). The additional signals can be injected into the interior from any side by repeating the last step of the synthesis.

## 1 Period-55 oscillator

This has a pseudo-period of 55, a composite of 5 and 11.

## Period-60 oscillators

Due to the the large number of oscillators, these are detailed on a separate page.

## 1 Period-63 oscillator

This has a pseudo-period of 63, a composite of 7 and 9.

## 1 Period-100 oscillator

The Centinal alternates between the natural period 46 and hassled period 54 versions of Twin Bees, by creating a pair of blocks in the middle and then destroying them.

## 1 Period-156 oscillator

This is actually a period 156 glider gun that shoots two pairs of gliders along one set of diagonals, then 78 generations later, two pairs along the other diagonals. Pairs of eaters eat the gliders, turning this into an oscillator. (There are other mechanisms for eating the gliders that double the period to 312.)

## 1 Period-177 oscillator

This oscillator can reflect gliders 90 or 180 degrees in several different ways.

Because it is so large, a larger, earlier synthesis is included in a separate file.

## 1 Period-256 oscillator

This is actually a period 256 glider gun that shoots one glider every 64 generations and rotates 90 degrees, resulting in a one glider in all four diagonal directions every 256 generations. Four eaters eat the gliders, turning this into an oscillator.

## 3 Period-312 oscillators

This is actually a period 156 glider gun that shoots two pairs of gliders along one set of diagonals, then 78 generations later, two pairs along the other diagonals. Here are three different ways of stabilizing this, each of which doubles the period to 312:

• A remarkable reaction where a pair of gliders hit a beehive in the path of one of the gliders, creating a beehive in the path of the other glider. The next pass flips the beehive back.
• Two gliders hit a loaf using the "boat-bit" mechanism, creating two boats. During the next pass, the gliders remove the boats.
• As above, except with a pond instead of a loaf.

These mechanisms (as well as the true period 156 one.) can be used together in any combinations, and the syntheses are simple combinations of the ones above. It is also possible to create other variations that have different symmetry classes (e.g. rotational symmetry by flipping two of the beehives, orthogonal symmetry with orthogonal glide symmetry by alternating the phase of adjacent pairs of boat-bits, diagonal symmetry with diagonal glide symmetry by alternating the phase of opposite pairs of boat-bits, etc.)

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