Loaf

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Loaf
x = 4, y = 4, rule = B3/S23 b2o$o2bo$bobo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C Still life
Pattern type Strict still life
Number of cells 7
Bounding box 4 × 4
Frequency class 2.7
Discovered by JHC group
Year of discovery 1970

Loaf is a 7-cell still life discovered by the JHC group in 1970.[1] It can be seen as a weld of two beehives.

Uses

A loaf has a partial eater property: certain collisions can destroy the upper rightmost two cells (in the orientation shown in the picture), after which the remainder of the pattern will evolve into a new loaf, flipped 180°. Eater 3 is an actual eater making use of this reaction.

A similar reaction to this involves a block "eating" a loaf, similarly to how the beehives in the queen bee shuttle are removed; stabilising this can be used to construct the Baker's dozen and is also used in the current smallest p68 glider gun[2].

Loaves are common enough that they can reappear in the same position by chance after being hit. Two examples are one form of RF28B and the family of bumpers.

Loaf is the stator in both mold and jam, and it can be augmented with tails to give the cis- and trans-loaf with tail, or equivalently with nines to yield the cis- and trans-loaf with nine.

Loaf can be attached to itself to give four still lifes, namely half-bakery, bi-loaf 2, loaf back tie loaf and loaf siamese loaf.

Commonness

Main article: List of common still lifes

Loaf is the third most common still life on Adam P. Goucher's Catagolue, being less common than beehive but more common than boat. Among all still lifes with 7 cells, it is the absolute most common, followed by long boat.[3] It is also the fifth most common object overall on Catagolue.

Loaf is also the third most common still life in Achim Flammenkamp's census, again being about a third as common as beehive but only slightly more common than boat.[4]

Occurrence

The V-pentomino turns into the W-pentomino after one generation, which then turns into a loaf after two more.

The earliest 5-cell predecessor of the loaf is five generations away; one example is a horizontal line of five with the rightmost cell moved up one position.

There are also two somewhat common constellations of two loaves, the predecessors of which can be seen here:

x = 18, y = 6, rule = B3/S23 b2o$o2bo$o14b3o$bo2bo10bo$2b2o13bo$16b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 4 THUMBSIZE 2 ]]
Two semi-common sequences that evolve into two loaves. The first is called "sandwich", and the second is called "toast" (click above to open LifeViewer)
RLE: here Plaintext: here

Glider synthesis

There is a head-on 2-glider collision that produces a loaf facing towards a direction perpendicular to both approaching lanes. Two other perpendicular collisions produce a blinker in addition to a loaf. A glider hitting a blinker can also make a loaf.

Gallery

x = 23, y = 8, rule = B3/S23 21b2o$21bo$19bobo$19b2o$b2o7b2o$o2bo5bo2bo$b3o6bobo$11bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 8 THUMBSIZE 2 ]]
A honey farm hitting a loaf a certain way restores the loaf (click above to open LifeViewer)
RLE: here Plaintext: here
x = 14, y = 13, rule = B3/S23 5b2o$5b2o4$2o4b2o4b2o$2o3bo2bob2o$5bobo2bo$6bo2$3bo$2bobo$2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 8 THUMBSIZE 2 ]]
Sidesnagger loaf-spin reaction, used in the p130 shuttle (click above to open LifeViewer)
RLE: here Plaintext: here
x = 13, y = 19, rule = B3/S23 4bo$3bobo$3bobo$b3ob2o$o9b2o$b3ob2o3b2o$3bob2o2$9b2o$8bo2bo$5bo3bobo$ 4bobo3bo$5bo3$11bo$9b2obo$12bo$10b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 8 THUMBSIZE 2 ]]
A different loaf-spin reaction, turning a phi spark into a century (click above to open LifeViewer)

See also

References

  1. Dean Hickerson's oscillator stamp collection. Retrieved on June 18, 2009.
  2. gun_68
  3. Adam P. Goucher. "Statistics". Catagolue. Retrieved on September 9, 2022.
  4. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.

External links