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 | Unspecified | ||||||||
| Discovered by | Robert Wainwright | ||||||||
| Year of discovery | 1975 | ||||||||
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Integral sign (or simply integral) is a 9-bit still life. 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.
Commonness
Integral sign is the nineteenth most common still life in Achim Flammenkamp's census, being less common than shillelagh but more common than boat-tie.[1] It is also the twenty-fifth most common object on Adam P. Goucher's Catagolue.[2]
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. The integral has the unusual property of being rarer in symmetries with an axis of reflection; while most objects have approximately the same frequency in symmetries that aren't applicable, the integral is about four times rarer in 8-fold symmetry than in asymmetric soups.
Integrals replace fishhooks in natural oscillators at a ratio of about 5 fishhooks for 1 integral.
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
- ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
- ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
External links
- Integral sign at the Life Lexicon
- The 10 nine-bit still-lifes at Mark D. Niemiec's Life Page
- Patterns
- Patterns with Catagolue frequency class 13
- Natural periodic objects
- Periodic objects with minimum population 9
- Patterns with 9 cells
- Patterns found by Robert Wainwright
- Patterns found in 1975
- Patterns that can be constructed with 4 gliders
- Still lifes
- Strict still lifes
- Strict still lifes with 9 cells
- Patterns with 180-degree rotation symmetry