Pulsar

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Pulsar
2b3o3b3o2$o4bobo4bo$o4bobo4bo$o4bobo4bo$2b3o3b3o2$2b3o3b3o$o4bobo4bo$o 4bobo4bo$o4bobo4bo2$2b3o3b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ THUMBSIZE 2 GPS 2 ]]
Pattern type Oscillator
Number of cells 48
Bounding box 15 × 15
Frequency class 12.1
Period 3
Mod 3
Heat 42.7
Volatility 0.73
Strict volatility 0.73
Rotor type Pulsar
Discovered by John Conway
Year of discovery 1970

Pulsar (rarely referred to as Cambridge pulsar CP 48-56-72[note 1]) is a large but surprisingly common period-3 oscillator. It was found by John Conway in March 1970.[1]

Extensions

The rotor of a pulsar consists of four mutually stabilizing quadrants; alternate arrangements exist for any odd multiple of 4 (for the version with 12 copies, see quasar). A closely related oscillator — the pulsar quadrant — includes just the external "horns" of the rotor and can be stabilized on its own.

Two other oscillators, the bracket pulsar and cross, can be extended in much the same way.

x = 42, y = 15, rule = B3/S23 32bo3bo$2b3o3b3o21bo3bo$32bo3bo$o4bobo4bo18b2o3b2o$o4bobo4bo5bo2bo8bob o3bobo$o4bobo4bo5bo2bo5b5o5b5o$2b3o3b3o6b2o2b2o$15b3o4b3o$2b3o3b3o$o4b obo4bo14b5o5b5o$o4bobo4bo2b3o4b3o5bobo3bobo$o4bobo4bo4b2o2b2o8b2o3b2o$ 18bo2bo10bo3bo$2b3o3b3o7bo2bo10bo3bo$32bo3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 4 LOOP 3 ZOOM 12 ]]
The pulsar (left), cross (center) and bracket pulsar (right) (click above to open LifeViewer)
RLE: here Plaintext: here

Commonness

Main article: List of common oscillators

Despite its size, pulsar is the fourth most common oscillator (and the most common of period greater than 2) in Achim Flammenkamp's census; the only oscillators more common are blinker, toad, and beacon.[2] It is by far the most common period 3 oscillator, being about 45,000 times more common than jam.[3] Overall, the pulsar is the twenty-first most common object on Adam P. Goucher's Catagolue.[4]

Compared to Catagolue's typical 16 × 16 soups, the pulsar is 30% more common in 8 × 8 soups and 14% more common in 10 × 10 soups; this is probably because a pulsar is more likely to survive if there is nothing around it.

A pulsar-on-pentadecathlon is the largest object to have occurred in the B3/S23/C1 census as of January 2022, with 100 cells in its maximum phase.[5][4]

The smallest pattern by population that evolves into a pulsar has seven cells; there are several of these.

Construction

Pulsar can be constructed with 3 gliders; there are multiple known syntheses.[6][note 2]

x = 41, y = 33, rule = B3/S23 30bo5bo$30bo5bo$30b2o3b2o2$26b3o2b2ob2o2b3o$bo7b2o17bobobobobobo$b2o6b obo18b2o3b2o$obo6bo$30b2o3b2o$28bobobobobobo$26b3o2b2ob2o2b3o2$30b2o3b 2o$30bo5bo$30bo5bo16$24b3o$24bo$25bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 450 THEME Book ZOOM 10 X -2 Y -4 AUTOSTART GPS 12 T 0 PAUSE 3 T 8 PAUSE 1 T 87 PAUSE 1 T 152 PAUSE 1 T 209 PAUSE 1 T 230 PAUSE 1 LOOP 231 ]]
A three-glider synthesis[6] (click above to open LifeViewer)
x = 30, y = 14, rule = B3/S23 19b3o3b3o2$17bo4bobo4bo$bo15bo4bobo4bo$2bo14bo4bobo4bo$3o16b3o3b3o2$ 19b3o3b3o$17bo4bobo4bo$17bo4bobo4bo$17bo4bobo4bo2$2o2b2o13b3o3b3o$2o2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 450 THEME Book ZOOM 10 X -4 Y 0 AUTOSTART GPS 12 T 0 PAUSE 3 T 16 PAUSE 1 T 50 PAUSE 1 T 54 PAUSE 1 T 78 PAUSE 1 T 90 PAUSE 1 LOOP 91 ]]
A Blockic one-glider seed for the pulsar[6][7] (click above to open LifeViewer)

See also

Notes

  1. The numbers refer to the populations of the three phases. The Life pulsar was indeed discovered at Cambridge, like the first real pulsar a few years earlier.
  2. There are 77 matches for the pulsar in the octo3g database (out of 464746 lines). There are also 404 matches in the octo3obj database (out of 3421907 lines), and 99 matches in the octohash database (out of 455380 lines). If all collisions with at least one occurrence of pulsar in the ash are included, then there are 632 results in the octo3g database (including three collisions with two pulsars in the ash), 4833 results in the octo3obj database (including 53 results with two pulsars in the ash) and 551 results in the octohash database (including two collisions with two pulsars in the ash).

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. Adam P. Goucher. "Census". Catagolue. Retrieved on October 27, 2018.
  4. 4.0 4.1 Adam P. Goucher. "Statistics". Catagolue. Retrieved on September 22, 2010.
  5. gameoflifeboy (April 20, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  6. 6.0 6.1 6.2 The 1 period 3 oscillator buildable from 3 gliders at Mark D. Niemiec's Life Page (download pattern file: lg/48pu.rle)
  7. knightlife (June 23, 2013). Blockic Seeds (discussion thread) at the ConwayLife.com forums

External links