Barberpole

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A barberpole is any period-2 oscillator in the infinite sequence bipole, tripole, quadpole, pentapole, hexapole, heptapole, etc.

x = 137, y = 16, rule = B3/S23 2o4b2o5b2o6b2o7b2o8b2o9b2o10b2o11b2o12b2o13b2o14b2o$obo3bobo4bobo5bobo 6bobo7bobo8bobo9bobo10bobo11bobo12bobo13bobo2$2bobo3bobo4bobo5bobo6bob o7bobo8bobo9bobo10bobo11bobo12bobo13bobo$3b2o6bo$10b2o5bobo5bobo6bobo 7bobo8bobo9bobo10bobo11bobo12bobo13bobo$18b2o8bo$27b2o7bobo7bobo8bobo 9bobo10bobo11bobo12bobo13bobo$37b2o10bo$48b2o9bobo9bobo10bobo11bobo12b obo13bobo$60b2o12bo$73b2o11bobo11bobo12bobo13bobo$87b2o14bo$102b2o13bo bo13bobo$118b2o16bo$135b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 1200 AUTOSTART GPS 15 ]]
barberpoles
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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). The monopole cannot exist in regular Life due to the would-be alternating cell having 2 neighbours, allowing it to survive to evolve into a long ship.

This sequence of oscillators was found by the MIT group in 1970.[1] 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. Any barberpole can be lengthened by the reaction shown in barbershop.

barberpole order
population
bounding box
glider synthesis commonness
per Achim Flammenkamp's census[2]
notes
3b2o$2bobo2$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Bipole (Ethyl)
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RLE: here Plaintext: here
Catagoluehere
2
8
5×5
5 gliders (Catagolue) Seventh most common naturally-occurring oscillator.
4b2o$3bobo2$bobo$o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Tripole (Propyl)
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RLE: here Plaintext: here
Catagoluehere
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. 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.
5b2o$4bobo2$2bobo2$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Quadpole (Butyl)
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RLE: here Plaintext: here
Catagoluehere
4
10
7×7
5 gliders (Catagolue) Eighth most common naturally-occurring oscillator. Despite behaving the same in Conway's Game of Life as they do in HighLife, they are only about 2% as common in HighLife because the ship is not stable, preventing the reaction on the right from occurring.
bo$o$o$b3o2$4b2o$4bobo$5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 GPS 2 LOOP 10 PAUSE 3 AUTOSTART ]]
Most common way by far for quadpole to form is by a
century predecessor colliding with a ship
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RLE: here Plaintext: here
6b2o$5bobo2$3bobo2$bobo$o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Pentapole
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RLE: here Plaintext: here
Catagoluehere
5
11
8×8
9 gliders (Catagolue) First appeared naturally on March 31, 2015 in a soup submitted to Catagolue by David S. Miller.[5]
7b2o$6bobo2$4bobo2$2bobo2$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Hexapole
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RLE: here Plaintext: here
Catagoluehere
6
12
9×9
8 gliders (Catagolue) First appeared naturally on April 16, 2015 in a soup submitted to Catagolue by Brett Berger.[6]
8b2o$7bobo2$5bobo2$3bobo2$bobo$o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Heptapole (septapole)
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RLE: here Plaintext: here
Catagoluehere
7
13
10×10
12 gliders (Catagolue) First known appearance was on January 26, 2015 in a symmetric soup found by gameoflifeboy using apgsearch.[7] 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.[8]
9b2o$8bobo2$6bobo2$4bobo2$2bobo2$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Octapole
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RLE: here Plaintext: here
Catagoluehere
8
14
11×11
Goldtiger997 found a 12-glider synthesis based on a symmetric sample soup from Catagolue on April 22, 2017.[9] Along with 14P2.4, it is one of two periodic 14-bit objects which have shown up on Catagolue in an asymmetric soup.[citation needed]
10b2o$9bobo2$7bobo2$5bobo2$3bobo2$bobo$o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Nonapole (enneapole)
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RLE: here Plaintext: here
Catagoluehere
9
15
12×12
16 gliders (Catagolue)
11b2o$10bobo2$8bobo2$6bobo2$4bobo2$2bobo2$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Decapole
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RLE: here Plaintext: here
Catagoluehere
10
16
13×13
Goldtiger997 found a 14-glider synthesis based on a sample soup from Catagolue on April 22, 2017.[9] GUYTU6J reduced this to 12 on September 29, 2021.[10]
12b2o$11bobo2$9bobo2$7bobo2$5bobo2$3bobo2$bobo$o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Undecapole
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RLE: here Plaintext: here
Catagoluehere
11
17
14×14
16 gliders (Catagolue)
13b2o$12bobo2$10bobo2$8bobo2$6bobo2$4bobo2$2bobo2$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Duodecapole
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RLE: here Plaintext: here
Catagoluehere
12
18
15×15
20 gliders (Catagolue)
14b2o$13bobo2$11bobo2$9bobo2$7bobo2$5bobo2$3bobo2$bobo$o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Tredecapole (tridecapole)
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RLE: here Plaintext: here
Catagoluehere
13
19
16×16
24 gliders (Catagolue) The largest barberpole so far to have occurred semi-naturally.[citation needed]
15b2o$14bobo2$12bobo2$10bobo2$8bobo2$6bobo2$4bobo2$2bobo2$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Quattuordecapole
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RLE: here Plaintext: here
Catagoluehere
14
20
17×17
28 gliders (Catagolue)
16b2o$15bobo2$13bobo2$11bobo2$9bobo2$7bobo2$5bobo2$3bobo2$bobo$o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ]]
Quindecapole
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RLE: here Plaintext: here
Catagoluehere
15
21
18×18
32 gliders (Catagolue)

See also

References

  1. Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  2. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  3. Extremeenthusiast (June 23, 2017). "Re: Synthesising Oscillators". ConwayLife.com forums. Retrieved on June 24, 2017.
  4. Ian07 (September 21, 2020). Re: Randomly enumerating glider syntheses (discussion thread) at the ConwayLife.com forums
  5. gameoflifeboy (April 1, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  6. Aidan F. Pierce (April 16, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  7. gameoflifeboy (January 26, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  8. Billabob (December 11, 2018). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  9. 9.0 9.1 Goldtiger997 (April 22, 2017). "Temp: to Soup Search Results". ConwayLife.com forums. Retrieved on April 23, 2017.
  10. GUYTU6J (September 29, 2021). "Synthesizin Oscillators". ConwayLife.com forums. Retrieved on September 29, 2021.

External links