Pi-heptomino

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Pi-heptomino
x = 3, y = 3, rule = B3/S23 3o$obo$obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
Pattern type Methuselah
Number of cells 7
Bounding box 3×3
MCPS 7
Lifespan 173 generations
Final population 55
L/I 24.7
F/I 7.9
F/L 0.318
L/MCPS 24.7
Discovered by John Conway
Year of discovery 1970

Pi-heptomino (or pi; sometimes called blasting cap at MIT after its shape at generation 1[1]) is a common heptomino that stabilizes at generation 173, leaving behind six blocks, five blinkers and two ponds. The name "pi" is also applied to some slight variations of this object that follow that same evolutionary sequence – in a pi ship, for example, the pi-heptomino itself never actually arises. Forms that are synonymous with the pi-heptomino are displayed below.

In April 1992, Bill Gosper discovered that two blocks can be used to eat a pi, as shown below. The eating reaction takes 65 generations to complete. Gosper also discovered in the same month that a pi, along with two blocks and two blinkers, can be used to create a queen bee shuttle.

It is the most common methuselah to occur naturally in a specific orientation; while less common than the R-pentomino, the R-pentomino has eight orientations, while the pi-heptomino only has four, and more common sequences like the traffic light and honey farm are not methuselahs.

Image gallery

Generation 1 of pi-heptomino
A grandparent (a pentaplet) and parent (a hexomino) of pi
An alternative parent of generation 1
This pattern, which resembles the word "Pi", evolves exactly like the Pi-heptomino after two generations, stabilizing at generation 174.
2o5b2o$2o5b2o8$3b3o3b$3bobo3b$3bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]
A pi eater
(click above to open LifeViewer)
RLE: here Plaintext: here
2o19b2o$bo8b3o8bob$bobo6bobo6bobob$2b2o6bobo6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ]]
Another pi eater
(click above to open LifeViewer)
RLE: here Plaintext: here
71b3o$70bo3bo$70b2ob2o8$62bo9bo$60b2ob2o6b3o$60b2ob2o5b2ob2o8$62bo9bo 19bo$b3o57bobo7bobo17bobo7b3o7b3o$2ob2o55b2ob2o5bo3bo15bo3bo6bo2bo6bo 2bo$71bobo16bo3bo6bo3bo4bo4bo7$12bo9bo$b2obo6bobo7bobo37b3o7b3o$bobo7b obo7bo2bo36bobo7b3o$bobo7bobo7bo2bo36bobo7bobo7$o3bo$4bo6b3o18bo19bo9b o9bo9bo$b3o7b2o18b3o17b3o7b3o7b3o7b3o$b2o30bo17bo2bo6bobo$12b2o18bo39b o8bobo7$11bo2bo$11b2obo26b3o7b3o7b3o7b3o$12bo27bo3bo6bo2bo6bo2bo7bo$12b 2o29bo10bo16bobo141$10b3o$9bo2bo$13bo$12b2o$12bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ Y -72 ZOOM 5.5 GPS 1 HEIGHT 600 WIDTH 800 ]]
Common formations equivalent to the pi-heptomino. Patterns in the same row are in the same generation.
To follow an evolutionary sequence, start from the bottom and move up; if there is nothing above a pattern,
its evolutionary sequence converges with the closest column inward that has a pattern until they all reach the top.
(click above to open LifeViewer)
RLE: here Plaintext: here

See also

References

  1. "Blasting cap". The Life Lexicon. Stephen Silver. Retrieved on May 14, 2016.

External links