Switch engine

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Switch engine
x = 6, y = 4, rule = B3/S23 bobo$o$bo2bo$3b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
Pattern type Methuselah
Number of cells 8
Bounding box 6×4
MCPS 10
Lifespan 3911 generations
Final population 842
L/I 488.9
F/I 105.3
F/L 0.215
L/MCPS 391.1
Discovered by Charles Corderman
Year of discovery 1971

A switch engine (or Corder engine[1]) is a methuselah that was found by Charles Corderman in 1971.[2] It produces a copy of itself after 48 generations, glide-reflected 4 cells northwest (starting in the form to the right), along with some active junk. If left unattended, the accumulating exhaust overtakes and destroys the engine after 24 cycles, but it can be stabilized to make c/12 diagonal puffers and spaceships.

History

In 1971, Charles Corderman investigated the fate of all the small polyominoes exhaustively. Records indicate that he found the switch engine while investigating the decominoes (polyominoes having 10 cells). However, there do not appear to be[citation needed] decominoes which result in a clean switch engine. There is, on the other hand, a unique nonomino switch engine predecessor whose 2-tick descendant matches that of a switch engine:[3]

x = 6, y = 3, rule = B3/S23 3o$2bobo$2b4o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 Z 20 HEIGHT 480 GPS 1 AUTOSTART PAUSE 2 T 2 PAUSE 2 LOOP 3 ]]
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RLE: here Plaintext: here

It is the smallest known polyomino to do so. If Corderman was examining polyominoes in order of size, then this smaller predecessor should have been found first in any case.

Stabilization

The movement of a switch engine can be sustained in different types of patterns.

Infinite growth

There are two basic types of stabilized switch engine orbits, both of which were also found by Charles Corderman: the period 288 block-laying switch engine (the more common of the two) and period 384 glider-producing switch engine. These two puffers are the most natural infinite growth patterns in Conway's Game of Life, being by far the most common ones to occur from non-symmetric random starting patterns.[4] Switch engine-based puffers, and combinations thereof, are also the only infinite growth patterns observed to have emerged from asymmetric soups on Catagolue.

Because the switch engine lends itself so naturally to infinitely-growing patterns, it appears in many of the smallest known superlinear growth patterns, including the mosquitoes, catacryst, metacatacryst, Gotts dots, and 26-cell quadratic growth.

In addition to the puffers based on a single switch engine, puffers such as Noah's ark can be created by combining two switch engines. Such puffers are generally quite dirty.

Spaceship

Main article: Cordership

it is also possible to create spaceships made of switch engines that interact to remove their combined exhaust. They are named "Cordership" in honor of Charles Corderman. These spaceships move at c/12 diagonally and are thus the slowest known non-adjustable spaceships in Life. Such spaceships can be constructed by combining as few as two switch engines.

'Swimmer' tracks

Main article: Switch engine channel

Like Herschels, switch engines can be supported by conduits made out of well-separated still lifes. These 'swimmer tracks' were first constructed by David Bell in 2005. Stable converters have since been constructed that convert Herschels or gliders to switch engines and back.

Stable pattern

The stable pattern that results from a lone switch engine has 842 cells. It consists of 60 blocks, 33 beehives (including one honey farm), 50 blinkers (including eight traffic lights), 12 gliders, 11 boats, 11 loaves, four ships, two long boats, two ponds, and two tubs.

Generation 3911

Synthesis

In 1973, Douglas G. Petrie employed a 4-glider recipe of a switch engine in his synthesis for a block-laying switch engine.[5] Decades later, Luka Okanishi discovered a surprisingly small 3-glider synthesis for a clean switch engine on March 12, 2017.[6]

References

  1. "Corder engine". The Life Lexicon. Stephen Silver. Retrieved on June 10, 2009.
  2. Robert Wainwright (December 1971). "Lifeline Volume 4". Lifeline page 2.
  3. Dave Greene (July 18, 2015). Re: CMD shape switch engine (discussion thread) at the ConwayLife.com forums
  4. "Census - Catagolue". Retrieved on September 28, 2015.
  5. Robert Wainwright (June 1973). "Lifeline Volume 10". Lifeline page 5.
  6. Luka Okanishi (March 12, 2017). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums

External links