Loaf
| Loaf | |||||||||
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| Pattern type | Strict still life | ||||||||
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| Number of cells | 7 | ||||||||
| Bounding box | 4 × 4 | ||||||||
| Frequency class | 2.7 | ||||||||
| Discovered by | John Conway | ||||||||
| Year of discovery | 1969 | ||||||||
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Loaf is a 7-cell still life discovered by John Conway in 1969 as a result of tracking the evolution of the twelve pentominoes. It can be seen as a weld of two beehives or as containing a photonegative pre-block.
Applications
In still lifes
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 three 14-cell still lifes, namely half-bakery, bi-loaf 2 and loaf back tie loaf, and siamesing gives the 11-cell loaf siamese loaf.
In catalysis
A loaf has a partial eater property: certain collisions, particularly that of gliders, 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, popover, p68 lumps of muck hassler (the basis of a record-breaking period-68 glider gun) and the stable form of twirling T-tetsons 2.
Some extensions of carnival shuttle hassles a loaf that is involved similarly to a beehive.
Loaves are common enough that they can reappear in the same position by chance after being hit. In signal circuitry, examples are RF48H, HRx65R, one form of RF28B, speed tunnel, Bandersnatch and the family of bumpers.
Others
There are at least three ways in which a glider can collide with a loaf which eventually results in a single loaf reappearing. The first reaction is the aforementioned loaf flipping reaction utilised by eater 3. A second collision produces a phi spark, with the loaf being shifted and rotated 90 degrees; four glider guns of an appropiate period can be positioned around a loaf to continue this reaction indefinitely.[1] The third reaction is another sparky reaction which causes the loaf to be moved roughly towards the point of collision without rotation.
| Three ways in which a glider can hit a loaf to result in another loaf (click above to open LifeViewer) RLE: here Plaintext: here |
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.[2]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.[3]
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:
| 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
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See also
References
- ↑ https://conwaylife.com/forums/viewtopic.php?f=2&t=1437&p=43558#p43558
- ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
- ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
External links
- Loaf at the Life Lexicon
- Loaf at Adam P. Goucher's Catagolue
- The 4 seven-bit still-lifes at Mark D. Niemiec's Life Page (download pattern file: 0/7lf.rle)
- Loaf at Heinrich Koenig's Game of Life Object Catalogs
- Patterns
- Patterns with Catagolue frequency class 2
- Natural periodic objects
- Periodic objects with minimum population 7
- Patterns with 7 cells
- Patterns found by John Conway
- Patterns found in 1969
- Patterns that can be constructed with 2 gliders
- Still lifes
- Strict still lifes
- Strict still lifes with 7 cells
- Patterns with bilateral diagonal symmetry
- Diagonal line stabilisations