Introduction
Orthogonal spaceships:
c/2 |
3c/7 (almost) |
2c/5 |
17c/45 |
c/3 |
2c/7 |
c/4 |
c/5 |
c/6 |
c/7
Diagonal spaceships:
c/4 |
c/5 |
c/6 |
c/7 |
c/12
Oblique spaceships:
(2,1)c/6 Knight-ship (almost) |
Half-baked Knight-ships |
Gemini
Since the vast majority of spaceships, flotillae and puffer trains with known syntheses move orthogonally at a velocity of c/2, and use the same period 4 base mechanism, those are shown on separate pages. Most spaceships (and a small number of flotillae) on this page move at different velocities.
Syntheses of spaceships, spaceship flotillae and puffer trains are more difficult than those of oscillators, because not only are the parts changing as they are being formed, they are moving as well. The process is reminiscent of assembling racing cars on an assembly line, with the engines running as they are installed, or performing surgery on a patient who is in a moving convertible, while the surgeon is stationary. As a result, very few have known syntheses. Fortunately, the ones based on the standard spaceships are sufficient to create a large variety of mechanisms needed to create computational circuitry.
The only spaceships, flotillae, and puffers for which syntheses are currently known are the following:
Most c/2 orthogonal spaceships are use the same basic mechanism (i.e. the front advances 1 spaces and flips from side to side every two generations), and they are too numerous to show here. This mechanism is exemplified by many methuselahs, most notably the B heptomino, and most of the simple spaceships. This is also used by most of the flotillae.
This is one unusual spaceship that moves orthogonally at a velocity of c/2, and does not use the common mechanism.
| 47-bit c/2 orthogonal spaceship #1 [x] |
These two almost-working spaceships, although they do not actually work, are so close to working that they strongly suggest that spaceships of this velocity are likely to exist in Life.
The images show the spaceships at generations 0 and 7, with pink cells in the respective images indicating living cells that do not properly reform, or unwanted births.
| Mike Playle's 3c/7 almost- spaceship [x] | Paul Tooke's 3c/7 almost- spaceship [x] |
This is a small sampling of spaceships that move orthogonally at a velocity of 2c/5.
Caterpillar is a huge spaceship, engineered in 2013, assembled by Gabriel Nivasch from components designed by Jason Summers, based on some ideas by David Bell.
The actual assembly was done by a computer program. With a width of 4105, a height of over 330721, and a population of 11880063, it is much too large to work with by hand. It is currently the largest (in terms of population) and most complex Life pattern ever assembled. (Since the full RLE file for Caterpillar is huge - 29MB (7MB zipped), it is not included here.)
It moves 102 spaces every 270 generations, and is based on a mechanism where a pi heptomino eats through a line of blinkers. This mechanism has long been known; unfortunately, there was no known way to lay down a line of blinkers at the same rate they were being consumed, without another similar spaceship.
Caterpillar works by pulling itself up by its own bootstraps. Several of the pi-crawler mechanisms rub their exhaust plumes together to create gliders, which are then cycled around to the front of the ship to create blinker tracks for those same pi-crawlers.
The same basic technology that Caterpillar uses can also be used to create similar huge spaceships based on other natural Life mechanisms.
Dave Greene, A.P. Goucher and Hartmut Holzwart are currently working on engineering a 31c/240 spaceship that should be slightly smaller than Caterpillar.
This is a small sampling of spaceships that move orthogonally at a velocity of c/3. The first three are from an infinitely-extensible series of spaceships found by Dean Hickerson. The first two are the smallest in this series.
| 25-bit c/3 orthogonal spaceship #1 [x] | 25-bit c/3 orthogonal spaceship #2 [x] | 60-bit c/3 orthogonal spaceship [x] | Turtle [x] | Dart[x] | P9 dart w/ tag-along [x] |
This is a remarkable spaceship, found by David Eppstein on 2000-01-12, that moves orthogonally at a velocity of 2c/7.
| Weekender [x] | Tag-along behind 2 weekenders [x] |
This is a small sampling of spaceships that move orthogonally at a velocity of c/4. The top 3, bottom left 2, and bottom right 3 show samples of 3 different families of spaceships.
This is a small sampling of spaceships that move orthogonally at a velocity of c/5. The Snail was found by Tim Coe. The Spider was found by David Bell. The 3 pre-pulsar-pushers are period 30.
| Snail [x] | Spider [x] | Symmetrical pulsar-pushing spaceship (SPPS) [x+4] |
| Asymmetrical pulsar-pushing spaceship (APPS) [x+4] | ||
| Glide-symmetrical pulsar-pushing spaceship (GPPS) [x+6] |
This is a small sampling of spaceships that move orthogonally at a velocity of c/6.
| Dragon [x] | Dragon on dragon [x] | Two dragons sucking a toad [x] |
| 56-bit c/6 orthogonal spaceship [x] | 158-bit c/6 orthogonal spaceship [x] |
| Loafer [8] |
In February 2013, Josh Ball discovered the Loafer, the only known spaceship that moves orthogonally at a velocity of c/7. It moves up one cell every 7 generations. It is remarkable due to its small size, the fact that it is easily synthesized from gliders, and that despite its small population and size, nobody had ever found it before.
This is a small sampling of spaceships that move diagonally at a velocity of c/4. A few of them can also be turned into wick-stretchers.
These are a few spaceships that move diagonally at a velocity of c/5.
These are two spaceships that move diagonally at a velocity of c/6.
| 77-bit c/6 diagonal spaceship [x] | Beluchenko's Seal [x] |
These are two spaceships that move diagonally at a velocity of c/7.
| Merzenich's 83-bit c/7 diagonal spaceship [x] | Merzenich's c/7 diagonal spaceship pushing multiple copies of its head [x] |
Charles Corderman's switch-engine forms the basis for several puffer-trains. Dean Hickerson has found several ways to combine multiple switch-engines to produce clean spaceships that move diagonally at a velocity of c/12. The 6-engine one is the first one found. The 3-engine one is the smallest one known. Since switch-engines are made of common components, they can easily be synthesized from gliders, making it easy to construct large spaceships and flotillae of them, and guns and puffers that make them.
All these syntheses here involve gliders coming from the sides and behind, but never in front of the spaceships, avoiding complications that would arise if constructed spaceship streams headed directly into arriving gliders necessary for subsequent spaceships. Furthermore, the synthesis of the 7-engine one involves only gliders coming from two directions below; if a third direction is allowed, the cost could be slightly reduced by removing some of the kick-back reactions.
| Glide-symmetric 3-engine Cordership [15] | Glide-symmetric 7-in-a-row-engine Cordership [48] |
| Glide-symmetric 6-engine Cordership [37] |
Oblique spaceships are any spaceships that move neither orthogonally nor diagonally. Since such spaceships in Life must be asymmetric and have periods of 6 or larger, they have been difficult to search for with standard search programs.
In March 23, 2004, Eugene Langvagen created this almost-working period 6 "knight-ship" (i.e. a spaceship that moves like a knight in chess - one square in one direction, and two in another, every cycle). In 6 generations, it moves up two cells and left one, totally re-forming except for two bits at the rear - one bit is missing, and another spurious one is formed. While this does not actually work, it is so close to working that it suggests that other similar ships may not be too far away.
The images show the spaceship at generations 0 and 6, with pink cells in the respective images indicating living cells that do not properly reform, or unwanted births.
| Eugene Langvagen's P6 almost-knight-ship [x] |
In July 2014, Adam P. Goucher" completed work on the Half-baked knight-ship, a series of spaceships of any velocity (2,1)c/k for any sufficiently large k (e.g. around 2400000 or larger). This is based on a remarkable interaction where a glider hits a half-bakery, shifting the half-bakery (3,6) cells, and shifting the glider one row. He has created a Python script that will create such a spaceship, given any sufficiently large k.
In May 2010, Andrew J. Wade constructed Gemini, Life's first spaceship based on constructor technology. It consists of two constructor arms. Each arm interprets instructions on data encoded in streams of gliders, and generates customized glider flotillae that slowly construct a totally new copy of the the spaceship. Once this is done, the original copy is cleanly deconstructed, leaving only the new copy, offset in space. It moves obliquely, with a velocity of (5120,1024)c/33699586, or approximately (5,1)c/32910.
The actual assembly was done by a computer program. With a bounding box of 4217807 by 4220191, and a population of 846278, it is much too large to work with by hand. It is currently the largest (in terms of bounding box) Life pattern ever assembled. (Since the full RLE file for Gemini is huge, it is not included here.)
Its mechanism theoretically allows creation of spaceships of all rational directions, and all rational velocities less than (1,1)c/580.
In June 2010, Dave Greene constructed a knight-ship based on Gemini, with a velocity of (8192,4096)c/35567490, or approximately (2,1)c/8683.
In November 2013, Dave Greene completed construction of several "Geminoid" constructors that work on the same basic principle, but with many technical improvements. Because these do not destroy the original after making a copy, they are technically puffers whose output consists of copies of themselves, rather than true spaceships, and they are discussed further in that section. However, it would probably not be too difficult to modify these to delete the original after making a copy, converting them into true spaceships.
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.
Copyright © 1997, 1998, 1999, 2013, 2014 by Mark. D. Niemiec.
All rights reserved.
This page was last updated on
2015-02-19.