Sombreros
| Sombreros | |||||||||||||
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| Pattern type | Oscillator | ||||||||||||
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| Number of cells | 50 | ||||||||||||
| Bounding box | 18 × 11 | ||||||||||||
| Period | 6 | ||||||||||||
| Mod | 6 | ||||||||||||
| Heat | 5.3 | ||||||||||||
| Volatility | 0.25 | ||||||||||||
| Strict volatility | 0.25 | ||||||||||||
| Discovered by | David Buckingham | ||||||||||||
| Year of discovery | 1972 | ||||||||||||
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Sombreros is a period-6 oscillator that was found by David Buckingham in December 1972.[1][2] Each half by itself is called a sombrero.
If the two sombreros are moved three cells closer to one another, the oscillator's period drops to 4 ticks and the result is just a less compact form of Achim's p4:
| Period 4 variant (click above to open LifeViewer) RLE: here Plaintext: here |
Two sombreros moved two spaces closer and staggered by one space forms a period 5 oscillator called Siesta.
| Siesta (click above to open LifeViewer) RLE: here Plaintext: here |
goldenratio found a 36-glider synthesis of a sombreros variant[c 1] in October 2020.[3]
One sombrero can be supported by two eater 1s.[4] The resulting oscillator is shown below, with a stator variant[5] that is thinner but taller:
| Stator variant of sombrero supported by two eaters[4][5] (click above to open LifeViewer) Catagolue: here |
One period-6 stabilisation of scrubber halves involves them each mutually stabilising with a single sombrero, and can be extended to a glide-symmetric wick.
| Showing two different end stabilisations (click above to open LifeViewer) Catagolue: here |
Oscillators sharing its stator
A 37-cell glide-symmetric period-16 oscillator bearing all stator cells of a lone sombrero except the two at the ends of the eaters' tails was found by Dean Hickerson in 1997 or 1998.[6]
| (click above to open LifeViewer) Catagolue: here |
In other rules
A lone sombrero[7] would function as a period-6 pipsquirter if not for the births triggered by the b3q and b3y transitions when the edges have not receded in the phase of the domino's appearance. However, interestingly, when only b3q is removed (for the rule called qlife), it becomes a period-9 pipsquirter[c 2] with a single cell of additional clearance.
| qlife p9 sombrero (click above to open LifeViewer) Catagolue: here |
References
- ↑ Robert Wainwright (March 1973). Lifeline, vol 9, page 3.
- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
- ↑ goldenratio (October 3, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ 4.0 4.1 toroidalet (November 19th, 2016). Re: Oscillator Discoveries Thread (discussion thread) at the ConwayLife.com forums
- ↑ 5.0 5.1 BlinkerSpawn (November 19th, 2016). Re: Oscillator Discoveries Thread (discussion thread) at the ConwayLife.com forums
- ↑ Dean Hickerson's "New billiard tables" oscillator collection
- ↑ Headerless RLE: 3b2ob2o$b3o3b3o$o4bo4bo$2ob2ob2ob2o$4bobo$4bobo$5bo!
External links
- Sombreros at the Life Lexicon
- 50P6.9 at Heinrich Koenig's Game of Life Object Catalogs
- Sombreros at Adam P. Goucher's Catagolue
- Sombrero at Wikipedia (name origin)
- Patterns
- Oscillators with 50 cells
- Periodic objects with minimum population 50
- Patterns with 50 cells
- Patterns found by David Buckingham
- Patterns found in 1972
- Patterns that can be constructed with 37 gliders
- Patterns that can be constructed with 30 gliders
- Oscillators
- Oscillators with period 6
- Oscillators with mod 6
- Oscillators with heat 5
- Oscillators with volatility 0.25
- Oscillators with strict volatility 0.25
- Patterns with rectangular orthogonal symmetry
- Semi-natural periodic objects