Life Spaceship Flotillae

Two-spaceship flotillae: 2-spaceship | Schick ships | 2-spaceship draggers | 2-spaceship A-draggers
Three-spaceship flotillae: Basic | Complex | Schick-ship | Pre-block-draggers
Overweight spaceship flotillae: 7WSS | 8WSS | 9WSS | 10WSS | 11WSS | 12WSS | 13WSS | 14WSS Four-spaceship flotillae: Comma-pushers | Hive-nudgers



All spaceship flotillae here are composed of spaceships that move at a velocity of c/2 orthogonally. A few flotillae of other velocities are included with spaceships of those velocities.

For counting purposes here, the number of spaceships in a flotilla includes self-sustaining spaceships (e.g. LWSS, MWSS, HWSS), and unstable components that nevertheless are capable of forward motion on their own (e.g. OWSS, B heptomino, Coe ship, Wainwright ship, sidecar, push-along, half of X66). It does not include components that normally do not move by themselves (e.g. still-lifes, pre-block, comma, A, Schick ship).



The 47 two-spaceship flotillae

These are all the two-spaceship flotillae composed of the three basic c/2 orthogonal spaceships (LWSS, MWSS, and HWSS), plus four other related simple spaceship-like attachments that cannot exist on their own (i.e. sidecar, Coe ship, push-along, and half of X66).

2-spaceship flotillae

LWSS on LWSS [7]@ LWSS on MWSS #1 [7] LWSS on MWSS #2 [6] LWSS on MWSS #3 [7] LWSS on HWSS #1 [7] LWSS on HWSS #2 [7] LWSS on HWSS #3 [6]
LWSS on HWSS #4 [6] LWSS on HWSS #5 [7] LWSS on HWSS #6 [7] LWSS on HWSS #7 [7] LWSS on HWSS #8 [7]@ MWSS on MWSS #1 [7] MWSS on MWSS #2 [7]
MWSS on MWSS #3 [7] MWSS on MWSS #4 [7] MWSS on MWSS #5 [7] MWSS on HWSS #1 [7] MWSS on HWSS #2 [7] MWSS on HWSS #3 [7] MWSS on HWSS #4 [7]
MWSS on HWSS #5 [7] MWSS on HWSS #6 [7] MWSS on HWSS #7 [7] MWSS on HWSS #8 [7] MWSS on HWSS #9 [7] MWSS on HWSS #10 [7] MWSS on HWSS #11 [7]
MWSS on HWSS #12 [7] MWSS on HWSS #13 [7] MWSS on HWSS #14 [7] MWSS on HWSS #15 [7] HWSS on HWSS #1 [7] HWSS on HWSS #2 [7] HWSS on HWSS #3 [7]@
HWSS on HWSS #4 [6] HWSS on HWSS #5 [7] HWSS on HWSS #6 [7] HWSS on HWSS #7 [7] HWSS on HWSS #8 [7] HWSS on HWSS #9 [7] HWSS on HWSS #10 [7]
Sidecar on HWSS [8]* MWSS pushing push- along [x] Half of X66 on HWSS [x] X66 [x] LWSS on Coe ship [8]*  

NOTE: The three marked @ are pseudo-spaceships. Three on the bottom row do not yet have syntheses. All the others except the two marked * can be built from either side, facilitating construction of most arbitrarily large flotillae.

The Coe ship is an unstable spaceship that can be stabilized by an escort LWSS, producing a period 16 spaceship. When so stabilized, it produces plumes of dying debris, so it is considered a clean puffer train engine. Many puffer trains can be built from it by perturbing these plumes with other spaceships. In fact, when combined with a Schick ship, another clean puffer engine, the two produce a large dirty exhaust plume. It can also be placed between two escort HWSS, creating a period 20 (mod 10) spaceship; in this case, it can also be lengthened by two and operates the same way.


The 4 two-spaceship Schick ship flotillae

The Schick ship is a period 12 tag-along that can be dragged by two c/2 orthogonal spaceships. When so stabilized, it produces plumes of dying debris, so is considered a clean puffer train engine. Many puffer trains can be built from it by perturbing these plumes with other spaceships. In fact, when combined with a Coe ship, another clean puffer engine, the two produce a large dirty exhaust plume.

These are all the ways a Schick ship engine can be dragged by a two-spaceship flotillae. Unfortunately, the escort spaceships must be synthesized in place, with the engine being simultaneously inserted behind them. It is extremely difficult to insert anything behind moving spaceships, because they moves at a speed of c/2, so the insertion would need to approach faster than that - and Life patterns can only maintain average sustained speeds that do not exceed c/2, this is a major problem. The only thing that can approach faster is a very wide ever-shrinking straight line. While it might be technically possible for such synthesis methods to be developed, they would likely be extremely expensive, unwieldy, and usually impractical.

2-spaceship schick ship flotillae

Schick ship behind two LWSS [10] Schick ship behind HWSS and LWSS [11] Schick ship behind two MWSS [11] Schick ship behind two HWSS [14]


2 Two-spaceship draggers

These are some ways that two spaceships can drag another object. Because there are many different escort possibilities for spaceships dragging an A, these are shown separately in the next section.

c/2 draggers

HWSS and MWSS dragging block [9] Two HWSS dragging boat [x]


The 10 two-spaceship A-draggers

c/2 A-draggers

LWSS + LWSS dragging A [19] MWSS + MWSS #1 dragging A [23] MWSS + MWSS #2 dragging A [23] MWSS + MWSS #3 dragging A [23] HWSS + LWSS dragging A [25]
MWSS + LWSS #1 dragging A [21] MWSS + LWSS #2 dragging A [21] HWSS + MWSS #1 dragging A [25] HWSS + MWSS #2 dragging A [25] HWSS + HWSS dragging A [31]



Three spaceship flotillae

There are numerous basic three-spaceship flotillae. There are too many to list individually, but they are summarized here. Some of these syntheses, or at least the mechanisms involved, may be added if time and space permit.

Three-spaceship basic flotillae

There are numerous three-spaceship flotillae based on the three basic spaceships. All of the basic two-spaceship syntheses can be built by adding the second spaceship to a first that already exists, combining the appropriate pieces unaltered from the two component two-spaceship flotilla recipes. This can be done from either side for all configurations.

By combining two of these, all basic three-spaceship flotillae can be built. Furthermore, these methods can be used repeatedly to construct flotillae containing any number of spaceships.

Three-spaceship complex flotillae

There are several three-component flotillae that include one or more non-self-sufficient components. The two previously one-sided components (Coe ship and sidecar) behave like HWSS and LWSS with respect to adding adjacent spaceships (although not every such adjacent spaceship geometry is viable). All can be synthesized by combining pairs of the above two-spaceship flotillae, except two that involve new geometries involving adding a HWSS to the outside of a sidecar. In both of these cases, while the specific synthesis is new, the actual method for adding the HWSS is the same as that used in the other conventional methods.

Three spaceship flotillae with Schick ships

There are several three-component flotillae that involve the Schick-ship engine tag-along. (The last two are dirty puffers, rather than spaceships.) All can be synthesized by combining pairs of the above two-spaceship flotilla mechanisms.

All of the above can be built in two stages using the mechanisms shown above in 2-spaceship flotillae, except for the following.

On the top row, the first is a much cheaper synthesis of a three-MWSS flotilla that would otherwise involve an extremely expensive insertion of one of the rear spaceships; the second and third involve new escort geometries involving a HWSS escorting a sidecar, but otherwise using mechanisms used elsewhere; the last three involve adding a trivial HWSS escort to the as-yet-unsynthesized MWSS w/push-along.

On the the bottom row, the first involves a P8 Wainwright puffer engine between two MWSS, resulting in a clean P8 spaceship; the second is an MWSS added to a standard Coe ship using standard techniques, but the resulting spaceship has a period of 12 rather than 16; the last two involve Coe engines between two HWSS, resulting in clean P20 (mod 10) spaceships.

complex 3-spaceship flotillae

MWSS #3 on MWSS on MWSS #3 [16] HWSS on sidecar on HWSS #9 [14] HWSS on sidecar on HWSS #10 [17] MWSS w/ push-along on HWSS #1 [x+4] MWSS w/ push-along on HWSS #2 [x+9] MWSS w/ push-along on HWSS #3 [x+9]
P8 Wainwright ship between two MWSS [10] P12 MWSS on Coe ship on LWSS #9 [16]   P20 Coe ship between two HWSS [24] P20 Very long Coe ship between two HWSS [20]  

These do not include the many spaceships and puffers that can be formed by adding an escort spaceship to spark the exhaust plume from a Coe ship or Schick ship (and that can be usually be synthesized using the above methods.)


The 36 three-spaceship pre-block-draggers

3-spaceship pre-block-draggers



Overweight spaceship flotillae

Spaceships with bodies greater than 6 bits long (HWSS) are naturally unstable because they produce sparks that survive long enough to damage the spaceship. However, such spaceships can exist in flotillae with escort spaceships that suppress such sparks. Such overweight spaceships (OWSS) with bodies from 7 bits (7WSS) to 14 bits long (14WSS) can exist in three-spaceship flotillae. OWSS longer than this themselves require smaller OWSS as escorts, requiring flotillae of 5 or more spaceships.

There are four fairly general mechanisms that can synthesize many of the overweight spaceships.

The first mechanism involves variations of the two-glider-into-boat synthesis of the MWSS, yielding simple syntheses of 7WSS, 8WSS, and 9WSS. Most, if not all, LWSS/MWSS/HWSS escorts can be added on the right side (assuming that the frontmost glider that turns into the spaceship comes from the left); however, escorts on the left side (the one from which two gliders come) must generally be ahead of or beside the OWSS.

The second mechanism involves colliding four gliders into a long-ship, yielding a double-headed spaceship, that expands in two directions. 2-3 additional gliders are then used to remove one of the heads once the body has reached the desired length. This can produce all OWSS engines 7WSS through 14WSS. Most, if not all, escorts can be added on the left side; however, escorts on the right side must generally be behind or beside the OWSS.

The third mechanism involves colliding two gliders into a shillelagh, yielding a double-headed spaceship, that expands in two directions. 2-3 additional gliders are then used to remove one of the heads once the body has reached the desired length. This is much less useful than the previous method, and is not actually used in any complete syntheses.

The fourth mechanism involves colliding two gliders into a forming teardrop to form an HWSS, and one additional glider hits the rear end of the HWSS to lengthen it by 2 into an 8WSS. A similar mechanism can produce a 10WSS.

For the smaller engines (7WSS-9WSS), the first two methods tend to complement each other well, and can produce most configurations.

Unfortunately, due to time limitations, these cannot yet be shown; however, they should be added as time permits.

Seven-bit-long overweight spaceship (7WSS) flotillae

There are 238 three-spaceship flotillae including seven-bit-long overweight spaceships (7WSS). Also, one or both of the escort ships can replaced by a Coe ship (that can be escorted by 7WSS instead of LWSS). Finally, a Coe ship (and its escort LWSS or 7WSS) can be lengthened by one, making it behave like a 7WSS. All of these can be synthesized. (Also, half of an X66 can be used as an escort, but no synthesis exists for that yet; there are an additional 22 of these.)

Eight-bit-long overweight spaceship (8WSS) flotillae

There are 190 three-spaceship flotillae including eight-bit-long overweight spaceships (8WSS). All can be synthesized.

Nine-bit-long overweight spaceship (9WSS) flotillae

There are 153 three-spaceship flotillae including nine-bit-long overweight spaceships (9WSS). All but one of these can be synthesized.

Ten-bit-long overweight spaceship (10WSS) flotillae

There are 105 three-spaceship flotillae including ten-bit-long overweight spaceships (10WSS). At present, around half of these can be synthesized.

Eleven-bit-long overweight spaceship (11WSS) flotillae

There are 45 three-spaceship flotillae including eleven-bit-long overweight spaceships (11WSS). At present, around a quarter of these can be synthesized. (Also, half of an X66 can be used as an escort, but no synthesis exists for that yet; there are an additional 10 of these.)

Twelve-bit-long overweight spaceship (12WSS) flotillae

There are 15 three-spaceship flotillae including twelve-bit-long overweight spaceships (12WSS). At present, none of these can be synthesized.

Thirteen-bit-long overweight spaceship (13WSS) flotillae

There are three three-spaceship flotillae including thirteen-bit-long overweight spaceships (13WSS). At present, none of these can be synthesized. (Also, half of an X66 can be used as an escort, but no synthesis exists for that yet either; there are an additional 3 of these.)

Fourteen-bit-long overweight spaceship (14WSS) flotillae

There is one three-spaceship flotilla including a fourteen-bit-long overweight spaceship (14WSS). At present, this cannot be synthesized.



Four-spaceship flotillae

This is one example of a four-spaceship flotilla. Because they both have multiple escort configurations, comma-pushers and hive-nudgers are described in the following sections.

4s flotilla

Ecologist [12]

The Ecologist is a stabilization of Gosper's P20 B heptomino puffer that adds one escort MWSS that turns it into a clean smokeless spaceship.


The 6 four-spaceship comma-pushers

None of these can currently be synthesized.

4-spaceship comma-pushers

Two LWSS and two MWSS dragging comma [x] MWSS and LWSS and two MWSS dragging comma [x] Two MWSS and two MWSS dragging comma [x] HWSS and LWSS and two MWSS dragging comma [x] HWSS and MWSS and two MWSS dragging comma [x] Two HWSS and two MWSS dragging comma [x]


The 45 four-spaceship hive-nudgers

4-spaceship hive-nudgers



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.