Barberpole
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A barberpole is a period-2 oscillator consisting of two terminal pre-pre-blocks and a linear chain of B3c-inducing lone dots. This sequence of oscillators starting from bipole,[note 1] tripole, quadpole, pentapole, hexapole, etc. was found by the MIT group in 1970.[1]
| The first 12 barberpoles (click above to open LifeViewer) RLE: here Plaintext: here |
A barberpole of order n (where n is the number of cells that move, an integer ≥ 2) has 6+n cells (6 of which are its stator, n of which are its rotor), a square bounding box with side length 2n+1, heat 2n, and volatility n/(n+3). Any barberpole can be lengthened by the 4-glider component shown in barbershop.
The term is also used (usually in the form "barber pole") to describe other extensible sections of oscillators or spaceships, especially those (usually of period 2) in which all generations look alike except for a translation and/or rotation/reflection.
Table
| barberpole | order population bounding box |
glider synthesis | commonness | ||
|---|---|---|---|---|---|
|
2 8 5 × 5 |
4 gliders (Catagolue) | Seventh most common naturally-occurring oscillator per Achim Flammenkamp's census.[2] | ||
|
3 9 6 × 6 |
Martin Grant improved the previous 7-glider synthesis to 6 gliders on June 23, 2017.[3] goldenratio found a 5-glider synthesis in September 2020.[4] | Fourteenth most common naturally-occurring oscillator per Achim Flammenkamp's census.[2] However, in "D2_x", "D4_x", and "D8" symmetries, the tripole is more more common than both the bipole and quadpole due to it having reflectional rather than rotational symmetry. | ||
|
4 10 7 × 7 |
5 gliders (Catagolue) | Eighth most common naturally-occurring oscillator per Achim Flammenkamp's census.[2] Despite behaving the same in Conway's Game of Life as they do in HighLife (B36/S23), they are only about 2% as common in HighLife because the ship is not stable, preventing it forming when a century predecessor collides with a ship. In Grounded Life (B35/S23), it is also less common as the century reaction does not work, even though ship works. | ||
|
5 11 8 × 8 |
8 gliders (Catagolue) | First appeared naturally on March 31, 2015 in a soup submitted to Catagolue by David S. Miller.[5] | ||
|
6 12 9 × 9 |
A 7-glider synthesis was found by Carson Cheng on June 3, 2024.[6] | First appeared naturally on April 16, 2015 in a soup submitted to Catagolue by Brett Berger.[7] | ||
|
7 13 10 × 10 |
11 gliders (Catagolue) | First known appearance was on January 26, 2015 in a symmetric soup found by gameoflifeboy using apgsearch.[8] It first appeared naturally on December 11, 2018 in a haul submitted to Catagolue, making it the longest barberpole and the last 13-bit periodic object to have emerged naturally.[9] | ||
|
8 14 11 × 11 |
Goldtiger997 found a 12-glider synthesis based on a symmetric sample soup from Catagolue on April 22, 2017.[10] | Along with xp2_4l1148kgzx302, it is one of two periodic 14-bit objects which have not shown up on Catagolue in an asymmetric soup. | ||
|
9 15 12 × 12 |
14 gliders (Catagolue) | |||
|
10 16 13 × 13 |
Goldtiger997 found a 14-glider synthesis based on a sample soup from Catagolue on April 22, 2017.[10] GUYTU6J reduced this to 12 on September 29, 2021.[11] | |||
|
11 17 14 × 14 |
16 gliders (Catagolue) | |||
|
12 18 15 × 15 |
A 16-glider synthesis was found by Chris857 on December 26, 2022.[12] He then found a 14-glider synthesis on August 15, 2023.[13][14] | |||
|
13 19 16 × 16 |
18 gliders (Catagolue) | The largest barberpole so far to have occurred semi-naturally. | ||
|
14 20 17 × 17 |
19 gliders (Catagolue) | |||
|
15 21 18 × 18 |
23 gliders (Catagolue) |
Wickstretcher
On 9 March 2023, Keith Amling discovered a c/4 diagonal barberpole wickstretcher.[15]
| c/4 diagonal barberpole wickstretcher (click above to open LifeViewer) RLE: here Plaintext: here |
See also
- Pseudo-barberpole
- Quad, skewed quad and lone dot agar
- Barbershop
- List of barberpole variants (includes oscillators using barberpoles as components, as well as other related patterns)
Notes
References
- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
- ↑ 2.0 2.1 2.2 Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
- ↑ Extremeenthusiast (June 23, 2017). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Ian07 (September 21, 2020). Re: Randomly enumerating glider syntheses (discussion thread) at the ConwayLife.com forums
- ↑ gameoflifeboy (April 1, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ Carson Cheng (June 3, 2024). Re: Synthesizing Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ praosylen (April 16, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ gameoflifeboy (January 26, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ Billabob (December 11, 2018). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ 10.0 10.1 Goldtiger997 (April 22, 2017). Temp: to Soup Search Results (discussion thread) at the ConwayLife.com forums
- ↑ GUYTU6J (September 29, 2021). Re: Synthesizing Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Chris857 (December 26, 2022). Re: Synthesizing Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ shinjuku (#4873158801) (August 15, 2023). Job triggered by Adam P. Goucher at GitLab Catagolue project.
- ↑ Chris857 (August 15, 2023). Re: Synthesizing Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Keith Amling (March 9, 2023). Re: Spaceship Discussion Thread (discussion thread) at the ConwayLife.com forums
External links
- Barberpole at the Life Lexicon