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Orthogonoid image
Pattern type Spaceship
Number of cells 467746
Bounding box 868856×707
Direction Orthogonal
Period 3476016
Mod 1738008
Speed 16c/217251
Speed (unsimplified) 256c/3476016
Heat Unknown
Discovered by Dave Greene
Year of discovery 2017

The Orthogonoid is a self-constructing spaceship analogous to the Demonoids, with a slow orthogonal direction of travel. The first example was completed by Dave Greene on 29 June 2017, with a top speed of 16c/217251 (this is just 256c/3476016 in lowest terms).[1]

The construction recipe is a stream of MWSSes, with the recovery time limited to 90 ticks by the Lx200 dependent conduit that follows the initial syringe converter. The design is hashlife-friendly, meaning that the spaceship can be trivially adjusted so that spatial and temporal offsets are exact powers of two; period 4194304 and period 8388608 versions have been constructed, with speeds of c/16384 and c/32768 respectively. A script is available that can build any other sufficiently large Orthogonoid period.[2]

The MWSSes are converted to Herschels, which produce a standard single-channel glider stream that runs the Orthogonoid's single construction arm. After the child circuitry is complete, a previously constructed Snark in the parent is removed from the construction arm lane, converting it to a "destruction arm" that efficiently shoots down the previous constructor/reflector in the series as soon as it is no longer needed.

Fast Orthogonoids

In October 2018, Dave Greene and Adam P. Goucher built sparse, fast, HashLife-friendly Orthogonoids with speeds of c/128, c/64 and c/16. Greene noticed that the last of these could be accelerated to 65536c/951573, which is only marginally slower than the theoretical upper bound of c/12 (limited by the 2-engine Cordership and 3-engine Cordership).[3]

The construction of this, together with a Demonoid and loopship, made extensive use of slmake.[4]


  1. Dave Greene (June 29, 2017). Re: Orthogonoid working notes (discussion thread) at the ConwayLife.com forums
  2. Dave Greene (February 3, 2018). "Re: Orthogonoid spaceship -- completed!". Retrieved on February 3, 2018.
  3. Dave Greene (October 28, 2018). "Re: Orthogonoid spaceship -- completed!". Retrieved on November 25, 2018.
  4. Dave Greene (November 10, 2018). "New Tools for Self-Construction". Retrieved on November 25, 2018.

External links