Figure eight

Figure eight
2o$2obo$4bo$bo$2bob2o$4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ GPS 4 THUMBSIZE 3 ZOOM 30 HEIGHT 400 ]]
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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
Strict volatility	1.00
Discovered by	Simon Norton
Year of discovery	1970
Rules Outer-totalistic rules B3/S23 – B378/S237 Important rules Conway Life # of rules 23 = 8 Isotropic rules B3-jky/S2-e3acinq – B2ci34cikqtyz5-k6-n78/S234-jknqr5-aci6-e7
Glider synthesis Fewest gliders 4 Catagolue-generated RLE synthesis Uploaded synthesis RLE figureeight_synth.rle
Pattern files Plaintext figureeight.cells RLE figureeight.rle
Identifiers apgcode xp8_gk2gb3z11 Pentadecathlon ID 12P8.1

Figure eight (or less frequently, big beacon or lemniscate) is a period-8 oscillator found by Simon Norton in 1970. 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.

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 a p64 pi-heptomino hassler; the latter two are shown below in Gallery. It is also the key component in the p8 bouncer.

• 

  One of the phases of the oscillator, which led to both of its names

Construction

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 ]] #C [[ THEME Book ZOOM 12 GPS 10 AUTOSTART T 0 PAUSE 3 T 24 PAUSE 1 LOOP 25 ]]

The reaction of the 4-glider 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 4-glider synthesis.

A four-object 21-cell one-glider seed for figure eight with bounding box 14 × 14 is known.

x = 46, y = 44, rule = B3/S23 34bo$34bobo$34b2o6$17bo$18b2o$17b2o$31bobo$31b2o$32bo5$40b3o$40b3o$40b 3o$43b3o$43b3o$43b3o15$3o$2bo$bo$4b2o$3bobo$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 400 THEME Book ZOOM 10 X 4 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 88 PAUSE 2 LOOP 89 ]] An alternate 5G synthesis (click above to open LifeViewer)

x = 30, y = 14, rule = B3/S23 bo9b2o$2bo7bo2bo$3o8bobo$12bo$24b2o$24b2obo$28bo$7b2o16bo$2o4bo2bo16bo b2o$2o5b2o19b2o3$4b2o$4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 400 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 3 T 56 PAUSE 2 LOOP 57 ]] A 4-object 1G seed (click above to open LifeViewer)

Occurrence

See also: List of common oscillators

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. On Catagolue, it is the most common period 8 oscillator, being more common than blocker.

Figure eight occurs in final patterns of two out of the collisions catalogued in the octo3obj database.

Gallery

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 ZOOM 14 AUTOSTART ]] Caterer on figure eight, the smallest known p24 oscillator by population (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 30, y = 30, rule = B3/S23 2o26b2o$2obo22bob2o$4bo20bo$bo26bo$2bob2o18b2obo$4b2o18b2o2$9b2o8b2o$ 9bobo6bobo$11bo6bo$9bobo6bobo$9b2o8b2o7$9b2o8b2o$9bobo6bobo$11bo6bo$9b obo6bobo$9b2o8b2o2$4b2o18b2o$2bob2o18b2obo$bo26bo$4bo20bo$2obo22bob2o$ 2o26b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 32 THUMBSIZE 2 ZOOM 8 HEIGHT 400 AUTOSTART ]] A p64 pi-heptomino hassler that is supported by the domino sparks of the figure eight (click above to open LifeViewer) RLE: here Plaintext: here

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

• Period-8 sparkers
• Pulsator

External links

• Figure-8 at the Life Lexicon
• Figure-8 at Adam P. Goucher's Catagolue
• 12P8.1 at Heinrich Koenig's Game of Life Object Catalogs