Life Period-4 Oscillators

Size in bits: 12 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | Larger
Cost in gliders: 5 | 1 glider/bit | >1 glider/bit | unknown
Frequency of occurrence | Methuselahs with P2 censuses



Because Mold is the smallest period-4 oscillator, and its rotor can grow on any object with a loaf-like bonding site, most period-4 oscillators are mold-based. In fact, these alone comprise around 94% of all such oscillators up to 25 bits. The next two easily-expandible period-4 oscillators occur at 20 bits: Confused eaters and Eater block frob. Variants of these each comprise around 2.5% of period-4 oscillators up to 25 bits, with less than 1% remaining that do not belong to one of these three categories.



The 2 twelve-bit period 4 oscillators

12-bit P4

Mold [5] Mazing [5]

Mold is the smallest oscillator that produces a period 4 diagonal bit spark. Also, mold forms on most still-lifes that have a bonding surface like the long diagonal side of a loaf (from which its name was inspired), so it forms the basis for many larger period 4 oscillators (and many with periods that are multiples of 4, such as period 12).


The 3 eighteen-bit period 4 oscillators

18-bit period 4

Mono- gram; Initials; JHC [15] Up mold on table [10] Down mold on table [10]

Monogram (whose name is derived from the fact that it resembles the letters JHC, the initials of John Horton Conway, the inventor of Life), while it has no sparks, can be used as a sparker oscillator in some circumstances, because it can delete blinkers.


The 7 nineteen-bit period 4 oscillators

19-bit period 4 oscillators

Mold tie up bun [17] Mold tie up bookend [18] Mold tie loaf [12] Mold tie down bun [12] Mold tie down bookend [14] Mold siamese cis hook w/ tail [21] Mold siamese hat [20]


The 23 twenty-bit period 4 oscillators

20-bit period 4 oscillators

Up mold on cap [10] Up mold on up long bookend [12] Down mold on down long bookend [10] Up mold on down long bookend [10] Up mold tie wing [16] Down mold on cap [10] Mold siamese up long hat [22] Mold tie hook w/ tail [25]
Mold siamese short cis hook w/ tail [71] Mold siamese down long hat [22] Mold tie up bookend w/ tub [21] Down mold on up long bookend [12] 20-bit P4 #1 [24] Mold siamese cis fuse w/ two tails [30] Snake siamese mold siamese snake [27] Carrier siamese mold siamese snake [33]
Carrier siamese mold siamese carrier [39] Mold tie pond [14] Mold bit tie loaf [26] Down mold tie wing [15] Down mold tie bookend w/ tub [20] Eater block frob; Eater and block eating loaf w/ tail [12] Con- fused eaters [20]  


The 34 21-bit period 4 oscillators

21-bit period 4 oscillators

Down boat on mold sharing tail [52] Up mold on up long bookend w/ hook [15] Down mold on down long bookend w/ hook[13] Up mold tie Z w/ pre-block [23] Up mold on up long bookend w/ tub [15] Up mold on down long bookend w/ hook [13] Up mold on down long bookend w/ tub [13] Down mold on down long bookend w/ tub [13] 21-bit P4 oscillator #1 [x]
Mold tie hook w/ long tail [34] Up mold tie dove [18] Up boat on mold sharing tail [41] Mold tie down boat w/ tail [27] Up mold siamese very long hat [22] Down mold siamese very long hat [22] Up mold tie bookend w/ boat [23] Down mold on up long bookend w/ hook [15] Mold siamese boat on table [23]
Eater siamese mold siamese snake [22] Mold w/bit tie long side [44] Mold siamese long hat siamese boat [24] Snake siamese mold siamese eater [29] Mold siamese boat below carrier [27] Carrier siamese mold siamese eater [35] Eater siamese mold siamese carrier [28] Down mold tie Z w/ pre-block [20] Mold w/ bit tie canoe [30]
Snake siamese mold siamese snake [27] Carrier siamese mold siamese snake [33] Mold w/ bit tie mango [40] Down mold on up long bookend w/ tub [15] Up mold tie dove [17] Down mold tie bookend w/ boat [22] Con- fused eaters w/ tub [20]  


The 120 22-bit period 4 oscillators

Unfortunately, due to time limitations, these cannot yet be shown. These consist of:

The ones based on mold on a still-life are too numerous to show, but all are are easy to synthesize using standard techniques. The others are shown.

22-bit period-4 oscillators

22-bit P4 oscillator #1 [16] 22-bit P4 oscillator #3 [27] 22-bit P4 oscillator #2 [34] 22-bit P4 oscillator #4 [x] 22-bit P4 oscillator #5 [x]
Eater and block eating integral w/ loaf [12] Confused eaters w/ boat [21] Integral and block eating loaf w/ tail [15] Confused eaters w/ integral [23]  


The 239 23-bit period 4 oscillators

Unfortunately, due to time limitations, these cannot yet be shown. These consist of:

The ones based on mold on a still-life are too numerous to show, but all are are easy to synthesize using standard techniques. The others are shown.

23-bit period-4 oscillators

Up mold on griddle [21] Down mold on griddle [21] Eater and block eating integral w/ loaf and hook [15] Confused eaters w/ barge [21] Eater and block eating integral w/ loaf and tub [15]
Integral w/ hook and block eating loaf w/ tail [18] Integral w/ tub and block eating loaf w/ tail [18] Confused eaters w/ tub and integral [23] Confused eaters w/ integral w/ hook [26] Confused eaters w/ integral w/ tub [26]


The 571 24-bit period 4 oscillators

Unfortunately, due to time limitations, these cannot yet be shown. These consist of:

The ones based on mold on a still-life are too numerous to show, but most are are easy to synthesize using standard techniques, except some that are based on 19-bit still-lifes that do not yet have syntheses. The others are shown.

24-bit period-4 oscillators

24-bit P4 oscillator #1 [x] 24-bit P4 oscillator #2 [x] 24-bit P4 oscillator #3 [x] 24-bit P4 oscillator #4 [19] Quarter jack w/ carrier [61] Quarter jack w/ curl [32] Trans molds sharing sparks [10]
Cis molds sharing sparks [x] Eater and block eating loaf w/ tail w/ cape [20] Eater w/ cape and block eating loaf w/ tail [20] Carrier siamese eater and block eating loaf w/tail [17] Snake siamese eater and block eating loaf w/tail [18] Eater and block eating loaf w/ tail siamese carrier [16] Eater and block eating loaf w/ tail siamese snake [15]
Eater and block eating integral w/ loaf and tail [16] Down mold tie mold [20] Up mold tie mold [20] Confused eaters w/ long boat [21] Eater and block eating integral w/ loaf and long hook [16] Integral w/ tail and block eating loaf w/ tail [19] Eater and block eating integral w/ loaf and down boat [14]
Integral and block eating integral w/ loaf [15] Eater and block eating gull w/ loaf [14] Eater and block eating integral w/ loaf and up boat [15] Integral w/ down boat and block eating loaf w/ tail [19] Confused eaters w/ eater w/ cape [28] Confused eaters w/ snake siamese eater [26] Confused eaters w/ carrier siamese eater [25]
Integral w/ down boat and block eating loaf w/ tail [17] Confused eaters w/ boat and integral [24] Gull and block eating loaf w/ tail [14] Integral w/ up boat and block eating loaf w/ tail [18] Confused eaters w/ integral w/ tail [27] Confused eaters w/ tub and integral w/ hook [26] Confused eaters w/ integral w/ long hook [27]
Confused eaters w/ integral w/ down boat [25] Confused eaters w/ tub and integral w/ tub [26] Confused eaters w/ two integrals [26] Confused eaters w/ gull [22] Confused eaters w/ integral w/ up boat [26]  


The 1343 25-bit period 4 oscillators

Unfortunately, due to time limitations, these cannot yet be shown. These consist of:

The ones based on mold on a still-life are too numerous to show, but most are are easy to synthesize using standard techniques, except some that are based on 20-bit still-lifes that do not yet have syntheses. The others 75 are shown.

25-bit period-4 oscillators


22 period 4 oscillators 26 bits and larger

larger period 4 oscillators

1-2-3-4 w/ tub [29] 1-2-3-4 w/ tub and tail [27-29] 30-bit P4 #1 [44] Light- weight emulator [111] Middle- weight emulator [20] Heavy- weight emulator [28] Two buns w/ tail hassled by eaters [22]
Half jack [46] Skewed half jack [50] Cloverleaf; Dual 1-2-3-4; Flammen- kamp's P4 [7] 40-bit period 4 oscillator #1 [20] Snake pit w/ beehives [32] Snake pit w/ claws [24] 4 Blocks on Octagon IV [34]
Gray counter [30-32] Jack [34] Skewed Jack [54] Hustler II [155] Dual Gray counter [24] Pinwheel [24] Snake pit w/ curls [22]

The three spaceship emulators produce edge-sparks like the correspondingly-named spaceships. Because it is so large, the larger, original synthesis of the light-weight emulator is included in a separate file.

There are five basic versions of Jack: two shown here, offset by 0 generations and 0 or 2 spaces vertically, two offset by 2 generations and 0 or 2 spaces vertically, and one offset by 1 generation and one space vertically. Only the first two currently have syntheses.



2 period 4 oscillators buildable from 5 gliders

5g P4

Mold [5] Mazing [5]

Mold is the smallest oscillator that produces a period 4 diagonal bit spark. Also, mold forms on most still-lifes that have a bonding surface like the long diagonal side of a loaf (from which its name was inspired), so it forms the basis for many larger period 4 oscillators (and many with periods that are multiples of 4, such as period 12).


The 2 period 4 oscillators up to 21 bits costing 1 glider/bit

1 glider/bit P4

Down mold tie bookend w/ tub [20] Confused eaters [20]


The 34 period 4 oscillators up to 21 bits costing >1 glider/bit

gt. 1 glider/bit p4 oscillators

Mold siamese cis hook w/ tail [21] Mold siamese hat [20] Mold siamese up long hat [22] Mold tie hook w/ tail [25] Mold siamese short cis hook w/ tail [71] Mold siamese down long hat [22] Mold tie up bookend w/ tub [21] 20-bit P4 #1 [24] Mold siamese cis fuse w/ two tails [30]
Snake siamese mold siamese snake [27] Carrier siamese mold siamese snake [32] Carrier siamese mold siamese carrier [39] Mold bit tie loaf [26] Down boat on mold sharing tail [52] Up mold tie Z w/ pre-block [23] Mold tie hook w/ long tail [34] Up boat on mold sharing tail [41] Mold tie down boat w/ tail [27]
Up mold siamese very long hat [22] Down mold siamese very long hat [22] Up mold tie bookend w/ boat [23] Mold siamese boat on table [23] Eater siamese mold siamese snake [22] Mold w/ bit tie long side [44] Mold siamese long hat siamese boat [24] Snake siamese mold siamese eater [29] Mold siamese boat below carrier [27]
Carrier siamese mold siamese eater [35] Eater siamese mold siamese carrier [28] Mold w/ bit tie canoe [30] Snake siamese mold siamese snake [27] Carrier siamese mold siamese snake [33] Mold w/ bit tie mango [40] Down mold tie bookend w/ boat [22]  


10 period 4 oscillators up to 25 bits without any known syntheses

(NOTE: this excludes many mold-based oscillators from 24-25 bits that are based on still-lifes from 19-20 bits that do not yet have syntheses.)

unknown P4 oscillators

21-bit P4 oscillator #1 [x] 24-bit P4 oscillator #1 [x] 24-bit P4 oscillator #2 [x] 24-bit P4 oscillator #3 [x] Cis molds sharing sparks [x]
22-bit P4 oscillator #4 [x] 22-bit P4 oscillator #5 [x] 25-bit P4 oscillator #2 [x] 25-bit P4 oscillator #1 [x] Eater and block eating integral w/loaf and cis hook [x]



The top 3 naturally-occurring period 4 oscillators

natural P4

Mold [5] (4.6e7) Mazing [5] (2.2e8) Cloverleaf; Dual 1-2-3-4; Flammen- kamp's P4 [7] (1.0e9)

Mold is the smallest oscillator that produces a period 4 diagonal bit spark. Also, mold forms on most still-lifes that have a bonding surface like the long diagonal side of a loaf (from which its name was inspired), so it forms the basis for many larger period 4 oscillators (and many with periods that are multiples of 4, such as period 12).



11 methuselahs whose censuses are period 4

P4 methuselahs

R pent- omino (@2) [3] B Hept- omino (@1) [2] Block and glider; Wing (@2); R-loaf (@2) [3] Herschel parent; Herschel (@1) [3] Acorn [4] Multum in parvo [4]
Loaf, ship, 4 beehives, boat, 8 blocks, 4 blinkers, 6 gliders (@1105) Ship, 3 blocks, 2 gliders (@149) Block and glider (@106) Ship, 2 blocks, glider (@128) Oak: Mango, 2 ponds, 5 loaves, 2 barges, 2 ships, 30 beehives, 3 ships, 8 boats, 34 blocks, 41 blinkers, 13 gliders (@5206) Block on beehive, pond, 6 loaves, toad, 28 beehives, 6 ships, 8 boats, 2 tubs, 40 blocks, 36 blinkers, 13 gliders (@3933)
  Gliders by the dozen, Gliders- omino (@-1) [3] J (@6) [3] Un- stabil- ized switch engine [4] Jaydot (@-1) [4] Bunnies; Rabbits (@1) [5]
4 Beehives, 4 blocks, 4 blinkers, 12 gliders (@184) Fleet, loaf, ship, 2 beehives, 2 boats, 8 blocks, blinker, 2 gliders (@556) 2 Ponds, 2 long boats, 11 loaves, 33 beehives, 4 ships, 11 boats, 2 tubs, 60 blocks, 50 blinkers, 12 gliders (@3911) 1 Fleet, 1 pond, 13 loaves, 1 toad, 5 ships, 9 boats, 5 tubs, 68 blocks, 66 blinkers, 26 gliders (@6929) 3 Ponds, 18 loaves, 2 toads, 65 beehives, 7 ships, 18 boats, 4 tubs, 109 blocks, 136 blinkers, 40 gliders (@17332)

These all have a period of 4 because of gliders.

Note that the minimum sizes of Acorn and Multum in parvo are the same size (7 bits), their censuses are the same size (633 bits), and both release 13 gliders, but they are totally unrelated in any other way.



Related: period-4 pseudo-oscillators.

Other oscillators by period: 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 24, 30, 36, 60, other.

Other types: still-lifes, pseudo-still-lifes, oscillators, pseudo-oscillators, oscillators by period, pseudo-oscillators by period, guns, multi-colored Life, basic spaceships and pseudo-spaceships, exotic spaceships, spaceships flotillae, puffers, constellations, methuselahs, not quite stable objects.

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

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This page was last updated on 2015-02-19.