Figure eight

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Figure eight
2o$2obo$4bo$bo$2bob2o$4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ GPS 4 THUMBSIZE 2 ]]
Pattern type Oscillator
Number of cells 12
Bounding box 10×10
Frequency class 23.4
Period 8
Mod 8
Heat 16.5
Volatility 1.00
Strict volatility 1.00
Discovered by Simon Norton
Year of discovery 1970

Figure eight (or less frequently, big beacon[1] or lemniscate) is a period-8 oscillator found by Simon Norton in 1970.[2] With 12 cells in its initial phase, it is the smallest known period 8 oscillator, behind blocker at 15 cells. It is known that no period 8 oscillators exist with 10 or fewer cells.[3]

Producing a domino spark, it is useful for constructing larger oscillators with period that is a multiple of eight. For example, it appears in tumbling T-tetson (period 8), sailboat (period 16), caterer on figure eight (the smallest period 24 oscillator), and figure eight on Jason's p22 (period 88). It is also the key component in the p8 bouncer.


Figure eight is the tenth most common naturally-occurring oscillator in Achim Flammenkamp's census, being less common than the great on-off but more common than the spark coil.[4] On Catagolue, it is the most common period 8 oscillator, being more common than blocker.[5]

Glider synthesis

A diagonally symmetric collision between two gliders and a teardrop, which costs two gliders, produces a figure eight cleanly, leading to its 4-glider synthesis.

x = 11, y = 11, rule = B3/S23 b2o$o2bo$o2bo$b3o$9b2o$8b2o$10bo2$5bo$4b2o$4bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The reaction of the glider synthesis of figure eight
(click above to open LifeViewer)


One of the phases of the oscillator, which led to both of its names.
x = 18, y = 6, rule = B3/S23 4b2o6bo$2bob2o4bo3b4o$bo8bo3bo$4bo5bo$2obo9bo$2o9b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 12 THUMBSIZE 2 ]]
Caterer on figure eight, the smallest
known p24 oscillator by population
(click above to open LifeViewer)
RLE: here Plaintext: here

See also


  1. "Big beacon". The Life Lexicon. Stephen Silver. Retrieved on June 14, 2011.
  2. Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  3. Mark Niemiec (1998). "Life Period-8 Oscillators". Retrieved on February 5, 2009.
  4. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  5. Adam P. Goucher. "Statistics". Catagolue. Retrieved on October 27, 2018.

External links

  • 12P8.1 at Heinrich Koenig's Game of Life Object Catalogs