Integral sign
| Integral sign | |||||||||
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| Pattern type | Strict still life | ||||||||
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| Number of cells | 9 | ||||||||
| Bounding box | 5 × 5 | ||||||||
| Frequency class | 13.4 | ||||||||
| Static symmetry | .c | ||||||||
| Discovered by | Unknown | ||||||||
| Year of discovery | 1971 | ||||||||
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Integral sign (or simply integral) is a 9-bit still life found in 1971.[1] It can eat gliders the same way that an Eater 1 eats, from either end. If the middle cell of the vertical line is removed, it becomes a bipole.
It can also be seen as a trans version of the house or two pre-blocks connected by a three-cell-long line.
Occurrence
Integral sign is the eighteenth most common still life on Adam P. Goucher's Catagolue, being less common than long ship but more common than shillelagh. Among all still lifes with 9 cells, it is the absolute most common, followed by trans-boat with tail.[2] It is also the twenty-fifth most common object overall on Catagolue.
Integral sign was the nineteenth most common still life in Achim Flammenkamp's census, being less common than shillelagh but more common than boat-tie.[3]
The most common way for an integral to form is for a pi-heptomino to hit an object at a specific location. A block is shown below; in general, any object that has exactly two cells in its leftmost column works, although in some cases, the integral is destroyed after being created.
| A pi-heptomino hitting a block, creating an integral in its ash (click above to open LifeViewer) RLE: here Plaintext: here |
Despite having rotational symmetry, the integral is no more common in rotationally symmetric soups than asymmetric ones. This is because the integral typically forms as described above. In soups with empty space, integrals typically form at the edge of a soup; this makes integrals less common in toruses and larger soups.
Integrals replace fishhooks in natural oscillators at a ratio of about 5 fishhooks for 1 integral.
Glider synthesis
- Main article: 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
- ↑ Robert Wainwright (September 1971). Lifeline, vol 3, page 2.
- ↑ 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
- Integral sign at the Life Lexicon
- Integral sign at Adam P. Goucher's Catagolue
- The 10 nine-bit still-lifes at Mark D. Niemiec's Life Page (download pattern file: 0/9-4.rle)
- Integral at Heinrich Koenig's Game of Life Object Catalogs
- Patterns
- Patterns with Catagolue frequency class 13
- Natural periodic objects
- Periodic objects with minimum population 9
- Patterns with 9 cells
- Patterns found in 1971
- Patterns that can be constructed with 4 gliders
- Still lifes
- Strict still lifes
- Strict still lifes with 9 cells
- Strict still lifes with .c symmetry