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.


A line puffer of width 76
RLE: here

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.


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.


A simple c/2 orthogonal wickstretcher
RLE: here

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.


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