Figure eight
Figure eight  
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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  1.00  
Kinetic symmetry  xk  
Discovered by  Simon Norton  
Year of discovery  1970  
 
 
 

Figure eight (or less frequently, big beacon^{[1]} or lemniscate) is a period8 oscillator found by Simon Norton in 1970.^{[2]} With 12 cells in its smallest phase, it is the smallest known period 8 oscillator, ahead of 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 Ttetson (period 8), sailboat (period 16), caterer on figure eight (the smallest period24 oscillator), and a p64 piheptomino hassler; the latter two are shown below in Gallery. It is also the key component in the p8 bouncer.
Construction
The reaction of the 4glider synthesis of figure eight (click above to open LifeViewer) RLE: here Plaintext: here 
A diagonally symmetric collision between two gliders and a teardrop, which costs two gliders, produces a figure eight cleanly, leading to its 4glider synthesis.
A fourobject 21cell oneglider seed for figure eight with bounding box 14 × 14 is known.^{[4]}


Its smallest possible predecessor by population has 10 cells.^{[5]}
The smallest predecessor for figure eight (and also for any period8 oscillator or constellation containing one). (click above to open LifeViewer) 
Occurrence
 See also: List of common oscillators
Figure eight is the tenth most common naturallyoccurring oscillator in Achim Flammenkamp's census, being less common than the great onoff but more common than the spark coil.^{[6]} On Catagolue, it is the most common period 8 oscillator, being more common than blocker.^{[7]}
Figure eight occurs in final patterns of two out of the collisions catalogued in the octo3obj database.^{[8]}
Gallery


In other rules
In B35i8/S23, a teardrop evolves into a figure eight.
In B3/S234q8, a the oscillator has period 9 instead of 8, with an extra phase that consists of a diagonal 4×3 grid.
See also
References
 ↑ "Big beacon". The Life Lexicon. Stephen Silver. Retrieved on June 14, 2011.
 ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
 ↑ ^{3.0} ^{3.1} Life Period8 Oscillators at Mark D. Niemiec's Life Page (download pattern file: 12/12fg.rle)
 ↑ ^{4.0} ^{4.1} Re: One Glider Seeds (discussion thread) at the ConwayLife.com forums
 ↑ Nick Gotts (June 8, 2019). Re: Systematic survey of small patterns (discussion thread) at the ConwayLife.com forums
 ↑ 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 October 27, 2018.
 ↑ The headerless RLEs of the two collisions are 2b2o$2b2o3$4b2o2b2o$2o2b2o2b2o2b2o$2o9b2o$13bo$7b2o$7b2o! and 3b2o$3b2o2b2o$7b2o4$bo5b2o$obo3bo2bo$obo4b2o$bo$9bo$8b2o$8bobo!
External links
 Figure8 at the Life Lexicon
 Figure8 at Adam P. Goucher's Catagolue
 12P8.1 at Heinrich Koenig's Game of Life Object Catalogs
 Patterns
 Patterns with Catagolue frequency class 23
 Natural periodic objects
 Oscillators with 12 cells
 Periodic objects with minimum population 12
 Patterns with 12 cells
 Patterns found by Simon Norton
 Patterns found in 1970
 Patterns that can be constructed with 4 gliders
 Oscillators
 Oscillators with period 8
 Oscillators with mod 8
 Oscillators with heat 16
 Oscillators with volatility 1.00
 Oscillators with strict volatility 1.00
 Oscillators with xk symmetry
 Sparkers
 Sparkers with period 8
 Domino sparkers
 Moderate sparkers