Spaceship

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The lightweight spaceship in Conway's Game of Life
A spaceship (much less commonly referred to as a glider[1] or a fish[2]) is a finite pattern that returns to its initial state after a number of generations (known as its period) but in a different location.


Spaceship Speed

Main article: Speed

The speed of a spaceship is the number of cells that the pattern moves during its period divided by the period length. This is expressed in terms of c (the metaphorical "speed of light") which is one cell per generation; thus, a spaceship with a period of five that moves two cells to the left during its period travels at the speed of 2c/5. Until the construction of Gemini in May 2010, all known spaceships in Life traveled either orthogonally (only horizontal or vertical displacement) or diagonally (equal horizontal and vertical displacement). Other recently constructed large spaceships such as the waterbear and the Parallel HBK. It is known that Life has spaceships that travel in all rational directions at arbitrarily slow speeds (see universal constructor). Spaceships traveling in other directions and at different speeds have also been constructed in other two dimensional cellular automata.[3]

Spaceship types

An "almost knightship"
Main article: Spaceship types

Although Spaceships are most commonly categorized by their speed and direction, other categorizations have been applied to spaceships based on their appearances, components, or other properties. One such categorization is the symmetry of spaceships: spaceships can be bilaterally symmetric, Such as Tim Coe's snail, may exhibit glide symmetry, such as the glider, or may be asymmetric, such as the caterpillar. Other, somewhat subjective categorizations have also been made, such as greyships, spaceships filled with large amounts of static, live cells, or smoking ships, which produce large sparks, a notable example being the Schick engine. A spaceship may also support other components which would not function as spaceships on their own. Given a freestanding spaceship, such additional components are often referred to as tagalongs; perhaps even pushalongs. Unstable spaceships immersed in a sustaining cloud are known as flotillae. A well known example is that of the overweight spaceships, which are unstable alone but may be 'escorted' by two or more smaller spaceships.

A greyship found by Hartmut Holzwart
Speed Direction Smallest known Minimum # of cells Notes
c/2 orthogonal lightweight spaceship 9
2c/5 orthogonal 30P5H2V0 30
17c/45 orthogonal caterpillar 11,880,063
c/3 orthogonal 25P3H1V0.2 25
2c/7 orthogonal weekender 36
c/4 orthogonal 37P4H1V0 37
c/5 orthogonal spider 58 There is a known method to build spaceships of all orthogonal speeds slower than c/4, see Caterloopillar.
c/6 orthogonal 56P6H1V0 56
c/7 orthogonal loafer 20
31c/240 orthogonal centipede caterloopillar 361,070
c/10 orthogonal copperhead 28
(5120,1024)c/16849793 slope 5 Gemini 846,278
(23,5)c/79 slope 23/5 waterbear 197,896
(3072,1024)c/36000001 slope 3 Gemini 3 <=850932
(4096,2048)c/17783745 slope 2 Gemini 2 <=872252
(6,3)c/245912 slope 2 Parallel HBK 132,945
(6,3)c/2621440 slope 2 Half-baked knightship 1,049,395
c/4 diagonal glider 5
c/5 diagonal 58P5H1V1 58
c/6 diagonal 77P6H1V1 77
c/7 diagonal lobster 83
c/12 diagonal 4-engine Cordership 134
65c/438856 diagonal 0hd Demonoid 27,250
65c/818356 diagonal 10hd Demonoid 47,701

History

The four smallest spaceships in life, the glider, lightweight spaceship, middleweight spaceship and heavyweight spaceship, were all found by hand in 1970. For almost twenty years spaceship development was limited to adding tagalongs to the known c/2 spaceships. Significant advances in spaceship technology came in 1989, when Dean Hickerson began using automated searches based on a depth-first backtracking algorithm. These searches found orthogonal spaceships with speeds of c/3, c/4, and 2c/5, as well as the first spaceship other than the glider to travel at the speed of c/4 diagonally, dubbed the big glider. Hickerson also found several ways to combine switch engines to create the first diagonal c/12 spaceships, named Corderships in honour of Charles Corderman. The next spaceship speed to be discovered was that of the orthogonal c/5 snail, found by Tim Coe in 1996, with a program he had designed using breadth-first searching, and which could split tasks between multiple CPUs.[4] In the following year David Bell found the much smaller c/5 spider using lifesrc, a program based on Hickerson's search algorithm.[5]

In March of 1998 David Eppstein created gfind, a breadth-first program that uses a depth-first search to limit the size of the search queue.[6] In 2000 he used this program to find the first spaceship that travels at the speed of 2c/7 orthogonally, the weekender. A search by Paul Tooke using the same program found the first c/6 orthogonal spaceship, the dragon, later that year. Also in 2000, Jason Summers found the first c/5 diagonal spaceship using David Bell's lifesrc program.

In 2004 Gabriel Nivasch, with the help of Jason Summers and David Bell, finished construction on the caterpillar, the first known orthogonal 17c/45 spaceship, which made use of the 17c/45 reaction.

In May 2010 Andrew J. Wade created a universal constructor-based spaceship, Gemini, which travels at a speed of (5120,1024)c/33699586.[7] This was the first explicitly constructed spaceship in Life to travel in an oblique direction, and also yielded the first explicit method of constructing arbitrarily slow spaceships.

In Febuary 2013, the first c/7 orthogonal spaceship, loafer, was discovered by Josh Ball.

In July 2014 several half-bakery-based knightships were constructed using a new technique that did not require universal-constructor circuitry. These produced spaceships that were both much slower and much smaller than the Gemini variants.

In September 2014, Dave Greene and Chris Cain completed two 31c/240 orthogonal spaceships, along the same general lines as the original Caterpillar but using a number of new mechanisms.

In December 2014, an oblique caterpillar dubbed the Waterbear was completed by Brett Berger, traveling at (23,5)c/79.

In December 2015, Chris Cain completed a diagonal self-constructing spaceship -- a "0hd Demonoid" -- based on Geminoid technology, adapted from a larger 10hd version constructed in November in collaboration with Dave Greene.

David Eppstein's weekender

In March 2016, forum user zdr discovered an extremely small c/10 spaceship, named the Copperhead.

In April 2016 Michael Simkin finished adjustable caterloopillar project, making it possible to build spaceships of arbitrary orthogonal speeds slower than c/4.

Speed Direction First discovered Discoverer Year of discovery
c/4 diagonal glider Richard Guy 1970
c/2 orthogonal lightweight spaceship John Conway 1970
c/3 orthogonal 25P3H1V0.2 Dean Hickerson 1989
c/4 orthogonal 119P4H1V0 Dean Hickerson 1989
c/12 diagonal 13-engine Cordership Dean Hickerson 1991
2c/5 orthogonal 44P5H2V0 Dean Hickerson 1991
c/5 orthogonal snail Tim Coe 1996
2c/7 orthogonal weekender David Eppstein 2000
c/6 orthogonal dragon Paul Tooke 2000
c/5 diagonal 295P5H1V1 Jason Summers 2000
17c/45 orthogonal caterpillar Gabriel Nivasch, Jason Summers, and David Bell 2004
c/6 diagonal seal Nicolay Beluchenko 2005
(5120,1024)c/16849793 slope 5 Gemini Andrew J. Wade 2010
(4096,2048)c/17783745 slope 2 Gemini 2 Dave Greene 2010
(3072,1024)c/36000001 slope 3 Gemini 3 Dave Greene 2010
c/7 diagonal Lobster Matthias Merzenich 2011
c/7 orthogonal loafer Josh Ball 2013
(6,3)c/2621440 slope 2 Half-baked knightship Adam P. Goucher 2014
(6,3)c/245912 slope 2 Parallel HBK Chris Cain 2014
31c/240 orthogonal shield bug Dave Greene 2014
(23,5)c/79 slope 23/5 waterbear Brett Berger 2014
130c/(1636712+16N) diagonal 10hd Demonoid Chris Cain and Dave Greene 2015
65c/(438852+16N) diagonal 0hd Demonoid Chris Cain 2015
c/10 orthogonal Copperhead‎‎ zdr 2016
All speeds slower than c/4 orthogonal caterloopillar Michael Simkin 2016

See also

Notes

  1. "Glider". The Life Lexicon. Stephen Silver. Retrieved on April 18, 2009.
  2. "Fish". The Life Lexicon. Stephen Silver. Retrieved on April 18, 2009.
  3. "Gliders in Life-Like Cellular Automata". David Eppstein. Retrieved on April 18, 2009.
  4. Tim Coe. "c/5 Orthogonal spaceship". Paul's Page of Conway's Life Miscellany. Retrieved on April 18, 2009.
  5. David Bell. "New c/5 spaceship". Paul's Page of Conway's Life Miscellany. Retrieved on April 18, 2009.
  6. David Eppstein. "Searching for Spaceships (PDF)". Retrieved on April 18, 2009.
  7. Adam P. Goucher (May 19, 2010). "Oblique Life spaceship created". Game of Life News. Retrieved on May 21, 2010.

External links