Figure eight
| Figure eight | |||||||||
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| Pattern type | Oscillator | ||||||||
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| 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 | ||||||||
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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 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 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
| 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.[4]
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Its smallest possible predecessor by population has 10 cells.[5]
| The smallest predecessor for figure eight (and also for any period-8 oscillator or constellation containing one). (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.[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
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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 Period-8 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
- 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
- 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