Integral sign

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Integral sign
x = 5, y = 5, rule = B3/S23 3b2o$2bobo$2bo$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]] [[ ZOOM 48 ]]
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 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.


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 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.

x = 13, y = 3, rule = B3/S23 3o8b2o$obo8b2o$obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 16 THUMBSIZE 2 HEIGHT 500 ZOOM 10 THEME Book AUTOSTART T 0 PAUSE 3 T 34 PAUSE 2 T 42 PAUSE 2 T 62 PAUSE 3 LOOP 63 ]]
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

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 glider-constructible. A glider synthesis of this object can be found in the infobox to the right.

See also


  1. Robert Wainwright (September 1971). Lifeline, vol 3, page 2.
  2. Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
  3. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.

External links