c/2 orthogonal

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c/2 orthogonal
Spaceship Yes
Puffer Yes
Rake Yes
Wickstretcher Yes
Gun Yes

c/2 orthogonal is an orthogonal speed that is equivalent to one half of the speed of light: one cell every two generations.


Several of the small Game of Life methuselahs will grow forward at c/2 during some part of their propagation. E.g.:

  • The R-pentomino, from generation 7 to 42 (from generation 28 on this is the same as the B-heptomino)
  • The Herschel, from generation 20 to 33
  • The pi heptomino, forward from generation 7 to 15; sideways from generation 6 to 19; and backward from generation 123 to 138.
  • The teardrop, in two directions from generation 0 to generation 7


c/2 orthogonal was the second spaceship speed to be discovered, after that of the c/4 diagonal glider. The first c/2 spaceship to be found was the lightweight spaceship, which was discovered by John Conway in 1970. Conway found the middleweight spaceship and heavyweight spaceship soon afterwards. For almost twenty years all new spaceships consisted of these basic spaceships and some tagalongs such as the Schick engine. On July 28, 1989 Dean Hickerson began searching for period 2 with an automated search program. This turned up several results, one of the first being 64P2H1V0. These were the first c/2 spaceships to be found that were not based on the basic spaceships. Hickerson then found a grammar for creating arbitrarily large period 2 spaceships. Since then many other c/2 spaceships of various periods have been discovered.

Puffer engines

The engines that are most commonly used in puffers are the p12 Schick engine, the p16 Coe ship, the p20 B-heptomino-based engine found in the space rake, and a related period-12 puffer engine. This period-12 B-heptomino-based engine is found in Gosper's total aperiodic pattern.


The first known puffer, puffer 1, traveled orthogonally at c/2, and was found in early 1971. Cleaning up puffer output with the sparks of the standard spaceships allowed the creation versatile puffers of most periods which are multiples of 4. One method of creating very high period puffers is by having a long line of live cells supported on one side by a c/2 component. These are known as line puffers. Original stabilisations of line puffers yielded unstable results, which burn out after millions of generations. Since then, a much more resilient modification has been found. It is an open problem as to whether this line puffer is stable for all lengths.

In November 2014, Richard Schank discovered pufferfish, the first known c/2 object, that is wholly neither p2 or p4, in a symmetric soup, making it the third (at least, semi-) natural infinite growth pattern, after block-laying and glider-producing switch engines.

x = 156, y = 32, rule = B3/S23 34b3o27b3o13b3o27b3o$33bo3bo25bo3bo11bo3bo25bo3bo$32b2o4bo11bo11bo4b2o 9b2o4bo11bo11bo4b2o$31bobob2ob2o3b4ob2ob2ob4o3b2ob2obobo7bobob2ob2o3b 4ob2ob2ob4o3b2ob2obobo$30b2obo4bob2ob4o7b4ob2obo4bob2o5b2obo4bob2ob4o 7b4ob2obo4bob2o$29bo4bo3bo4bo2b2obobob2o2bo4bo3bo4bo3bo4bo3bo4bo2b2obo bob2o2bo4bo3bo4bo$6bo17bo16bo4bo7bo4bo27bo4bo7bo4bo25bo17bo$5b3o15b3o 3b2o7b2o6bo7bo6b2o7b2o3b2o7b2o6bo7bo6b2o7b2o12b3o15b3o$3b2ob3o13b3ob2o 100b2ob3o13b3ob2o$4bo2bob2o4bo4b2obo2bo18b2o7b2o35b2o7b2o27bo2bob2o4bo 4b2obo2bo$b2obo4bobob2ob2obobo4bob2o17bo5bo39bo5bo26b2obo4bobob2ob2obo bo4bob2o$b2obobo2bobo7bobo2bobob2o15bo2bo3bo2bo35bo2bo3bo2bo24b2obobo 2bobo7bobo2bobob2o$bo8b3obobob3o8bo16bo2bobo2bo37bo2bobo2bo25bo8b3obob ob3o8bo$2o7b2o9b2o7b3obo15bobo43bobo24bob3o7b2o9b2o7b2o$33b2o12bobobob o39bobobobo21b2o$31b2obo11b2obobob2o37b2obobob2o20bob2o$34b2o9bo3bobo 3bo35bo3bobo3bo18b2o$33bo88bo$35b3o7b2ob2ob2ob2o35b2ob2ob2ob2o16b3o$7b 3o15b3o9b2o78b2o9b3o15b3o$6bo3bo13bo3bo9bo7bo3bo3bo37bo3bo3bo16bo9bo3b o13bo3bo$5b2o4bo11bo4b2o8b2o6bo3bo3bo7b3o9b3o9b3o3bo3bo3bo4b3o8b2o8b2o 4bo11bo4b2o$4bobob2ob2o3b3o3b2ob2obobo8bo21bo3bo7bo3bo7bo3bo14bo3bo7bo 8bobob2ob2o3b3o3b2ob2obobo$3b2obo4bob2ob3ob2obo4bob2o6bobo5b2o5b2o5b2o 3b2o5b2o3b2o5b2o3b2o5b2o5b2o3b2o5bobo6b2obo4bob2ob3ob2obo4bob2o$2bo4bo 3bo4bobo4bo3bo4bo6b3o3b4o3b4o3b2obobob2o3b2obobob2o3b2obobob2o3b4o3b2o bobob2o3b3o6bo4bo3bo4bobo4bo3bo4bo$14bo5bo20b2ob2o2b2ob2o2b2ob2ob2ob2o b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2b2ob2ob2ob2ob2ob2o20bo5bo$2b2o7b2o9b2o 7b2ob3o5bobo4bobo4bobo3bobo3bobo3bobo3bobo3bobo3bobo4bobo3bobo3bobo5b 3ob2o7b2o9b2o7b2o$36bo82bo$34bo6b2ob2o2b2ob2o2b2ob2ob2ob2ob2ob2ob2ob2o b2ob2ob2ob2ob2ob2o2b2ob2ob2ob2ob2ob2o6bo$34bob2o80b2obo$39b78o$38bo78b o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 800 HEIGHT 500 ]]
A line puffer
(click above to open LifeViewer)
RLE: here Plaintext: here


The first rake to be constructed was the space rake, which fired forward gliders at a period of 20. Since then many rake periods have been found, the smallest being that of backrake 1. Some adjustable period rakes have been created, but there is no known method of creating period x + 2n rakes.

Adjustable-period rakes

Adjustable-period rakes are generally composed of a period-8 blinker puffer and a fleet of standard spaceships. The trail of blinkers produced by the puffer form a fuse, which can be ignited by a pair of gliders to burn at a speed greater than c/2. This allows the spark to catch up with the puffer. This repeats periodically, the period of which can be increased by moving the spaceships outward.


There are several known c/2 orthogonal wickstretchers. The most simple wickstretcher of this speed stretches a period 6 wick from a stationary stabilizer. This wickstretcher can be widened with the zebra stripes agar bounded by the period 6 wick. This was the basis of halfmax, a spacefiller that fills half of the Life plane with zebra stripes. There is also a known incomplete wickstretcher which stretches a period 16 wick.

#N c/2 wickstretcher #C A c/2 orthogonal wickstretcher that stretches a period 6 wick x = 43, y = 61, rule = b3/s23 3bo39b$bo41b$o6bo35b$o6bo35b$6obo35b2$5b2o36b$4bo38b$7bo35b$2b2o39b$bo 41b$bo2bo38b$b2o40b$3b2o38b2$5b3o35b$3bob3o35b$bo4bo36b$o5bobo34b$o4b 2obo34b$5o12bo25b$15b3o8bobo7b2o5b$14bo7b2obob2o2bo3bo2bo2b2o$4b2o5b2o 2b5o2bob2o5b3o2b2obo2bo$3b3o5bob2o5bobo4b4o3b2o3bobob$3ob2o10b2obobob 5o3bobo2b4ob2o$o2bo6bo2b3o3bobo6b3obobobo2bobob$o4bo4bob2obobobo2b2ob 3o2b2ob2o3b2obob$b6obobo4bobob3o3b3o5bo2bo3bo2b$3bob2o8b5o15b5o3b2$3bo b2o8b5o15b5o3b$b6obobo4bobob3o3b3o5bo2bo3bo2b$o4bo4bob2obobobo2b2ob3o 2b2ob2o3b2obob$o2bo6bo2b3o3bobo6b3obobobo2bobob$3ob2o10b2obobob5o3bobo 2b4ob2o$3b3o5bob2o5bobo4b4o3b2o3bobob$4b2o5b2o2b5o2bob2o5b3o2b2obo2bo$ 14bo7b2obob2o2bo3bo2bo2b2o$15b3o8bobo7b2o5b$5o12bo25b$o4b2obo34b$o5bob o34b$bo4bo36b$3bob3o35b$5b3o35b2$3b2o38b$b2o40b$bo2bo38b$bo41b$2b2o39b $7bo35b$4bo38b$5b2o36b2$6obo35b$o6bo35b$o6bo35b$bo41b$3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 8 HEIGHT 600 ]]
A simple c/2 orthogonal wickstretcher
(click above to open LifeViewer)
RLE: here Plaintext: here


The only known spacefillers stretch the zebra stripes agar at a speed of c/2 orthogonally in either three or all four cardinal directions on the Life plane. Examples of this include max and halfmax.


The three standard spaceships all have relatively simple glider syntheses, which makes the creation of c/2 orthogonal spaceship guns rather simple. Known glider synthesis techniques for these spaceships, however, only allow the creation of period 23 or higher spaceship streams. Many other c/2 spaceships also have known glider syntheses, which allows the creation of a variety of c/2 spaceship guns.

See also


External links