Boat

From LifeWiki
Revision as of 19:45, 24 December 2021 by Muzik (talk | contribs)
Jump to navigation Jump to search
Boat
x = 3, y = 3, rule = B3/S23 bo$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]]
View static image
Pattern type Strict still life
Number of cells 5
Bounding box 3 × 3
Frequency class 2.8
Static symmetry Unspecified
Discovered by JHC group
Year of discovery 1970

The boat is the only still life with 5 cells and was discovered by the JHC group in 1970.[1]

It can be thought of as a tub with an extra cell in one of the corners, or a ship with one of the corner cells removed. It can also be seen as a very deep siamization of two hooks.

Use in higher still lifes

As a small starting pattern, there are very, very many ways in which a boat can be used to construct higher-order still lifes.

Perhaps the most notable property is that the boat begins an infinite series of still lifes which consist of two parallel diagonal lines being stabilised. The next still lifes in this line, the long boat, very long boat and so on, show that this allows for the construction of a still life with any odd number of cells equal to or greater than 5. It is possible to have spaceships and other such patterns arbitrarily extend the boat in this manner as a wickstretcher, referred to as a boatstretcher.

The boat also begins a second infinite series in a less obvious way as a cis- extension of a single diagonal line of length 2, stabilised by two tails. In the case of the boat, the two tails are welded together into a pre-block due to a lack of space. The loaf can be considered its length 3 counterpart, in which the tails are also welded. For length 4 and onwards, the two tails stabilising this string are clearly defined, beginning with cis-fuse with two tails for length 4 and continuing onward from there. The trans version of a boat seen this way would be the melusine, which already uses two defined tails for length 2.

Boats can be connected diagonally to each other, or to other objects, to form yet more larger still lifes. Cases in which the pre-block segment is connected are referred to as "ties", which are listed below:

Oscillator ties are also possible:

It is also possible to "tie" boats in the opposite direction such that the exposed duoplet sections connect, which results in either longer boats (if tied to a tub or barge), or long variants of ships (if tied to another boat).

Boats can also be augmented with several different smaller unstable components to form larger still lifes, generally in multiple different ways due to its incomplete symmetry. A sample of such still lifes are as follows:

Boats can be used as induction coils. Due to having lower symmetry than the block, arrangements which would be invariant for the block have two distinct versions for a boat.

Boats also can serve as induction coils for oscillators:

Uses in catalysis

The boat sees uses in, and can arise as a result of, certain interactions.

In the orientation shown in the infobox, moving the leftmost cell up one cell turns it back into a boat in one generation. This property allows it to be used as a catalyst in certain situations, such as the p21 B-heptomino hassler, p22 lumps of muck hassler, p35 honey farm hassler, the still life form of diuresis, the loaf spin reaction found in the p130 shuttle, and more. See Tutorials/Catalyses for more examples.

The boat can be hit by a glider to cleanly produce another glider, travelling perpendicular to the direction of the input glider. It is thus a one-time reflector.

A glider hitting certain still lifes in the correct way, such as a snake or eater 1, as well as oscillators such as the beacon if correctly timed, will produce a boat; another glider in the same lane will cleanly destroy the boat. This is called a boat-bit. This reaction can be used in a similar way to an eater which works on pairs of gliders.

Commonness

The boat is the fourth most common still life in Achim Flammenkamp's census, being slightly less common than loaf and over four times as common as tub.[2] It is also the sixth most common object on Adam P. Goucher's Catagolue.[3]

Glider synthesis

All strict still lifes with a population of 22 or fewer cells, all oscillators with 16 or fewer cells, and all spaceships with 31 or fewer cells are known to be glider-constructible. A glider synthesis of this object can be found in the infobox to the right.

See also

References

  1. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on June 18, 2009.
  2. ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  3. ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.

External links

Vessels
No corners (barges) (^-2) • (^-1) • ^0 • ^1 • ^2 • ^3
One corner (boats) (^-2) • (^-1) • ^0 • ^1 • ^2 • ^3
Two corners (ships) (^-1) • ^0 • ^1 • ^2 • ^3
Retrieved from "https://conwaylife.com/w/index.php?title=Boat&oldid=87288"