Integral sign
Integral sign  
View static image  
Pattern type  Strict still life  

Number of cells  9  
Bounding box  5 × 5  
Frequency class  13.4  
Discovered by  Unknown  
Year of discovery  1971  
 
 
 

Integral sign (or simply integral) is a 9bit 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 preblocks connected by a threecelllong line.
Commonness
 Main article: List of common still lifes
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 transboat with tail.^{[2]}It is also the twentyfifth 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 boattie.^{[3]}
Occurrence
The most common way for an integral to form is for a piheptomino 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 piheptomino 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
All strict still lifes with a population of 21 or fewer cells, as well as all oscillators and spaceships with 16 or fewer cells, are known to be gliderconstructible. 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 ninebit stilllifes at Mark D. Niemiec's Life Page (download pattern file: 0/94.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
 Patterns with 180degree rotation symmetry