Pulsar
| Pulsar | |||||||||
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| 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 | 0.73 | ||||||||
| Kinetic symmetry | *c | ||||||||
| Rotor type | Pulsar | ||||||||
| Discovered by | John Conway | ||||||||
| Year of discovery | 1970 | ||||||||
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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 and interactions
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.
| The pulsar (left), cross (center) and bracket pulsar (right) (click above to open LifeViewer) RLE: here Plaintext: here |
Arms
There exists a heptomino, that acts as a p3 oscillator partial but can mutually stabilise with a quadrant of the pulsar's nucleus, replacing a standard horn in its blinker phase to comprise an "arm" and causing it to undergo a different period-3 evolutionary sequence. Due to its interference with the quadrant's nucleus, only a single arm may exist per quadrant. Despite an arm requiring the flipping of only six cells' states in this phase, no arm variant has occurred naturally, assumedly due to the pulsar's fragility. However, the two variants with two arms in D2_+1 symmetry,[note 2] and the variants with four arms in D4_+1 and C4_1 symmetry,[note 3] have occurred seminaturally.
The same heptomino can also mutually support a quadrant from a different orientation, replacing another quadrant as one of its two supports, allowing two distinct two-quadrant half-pulsars with arms.
| All pulsar arm variants (click above to open LifeViewer) |
| The cis- and trans- forms[note 4] of the half-pulsar with arms (click above to open LifeViewer) |
Dependent oscillators
| Two can support a highly volatile small period-3 oscillator that contains a tub in one phase (as seminaturally occurred in tetramer form[note 5]) (click above to open LifeViewer) Catagolue: here |
Occurrence
- See also: 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.
The pulsar-on-pentadecathlon I is the largest object to have occurred in the B3/S23/C1 census as of July 2023, with 100 cells in its maximum phase, and with its first known natural occurrence on Catagolue in April 2015.[5][4]
The smallest pattern by population that evolves into a pulsar has seven cells; there are several of these.[note 6]
Construction
Pulsar can be constructed with 3 gliders; there are multiple known syntheses.[6][note 7]
A direct Herschel-to-pulsar factory was found by yoleo in October 2023.[7]
| A three-glider synthesis[6] (click above to open LifeViewer) |
| A Blockic one-glider seed for the pulsar[6][8] (click above to open LifeViewer) |
| H-to-pulsar factory[7] (click above to open LifeViewer) |
In other rules
In Pedestrian Life (B38/S23), the pulsar is about 400 times less common than in Life because the pre-pulsar does not evolve into it. However, there are new predecessors, making it still the most common period-3 oscillator.[9]
| A pulsar evolving from a pre-traffic light and a pi heptomino in Pedestrian Life (click above to open LifeViewer) |
As a more extreme example, the pulsar is about 1500 times less common in Grounded Life (B35/S23) than in Life because the pre-pulsar does not evolve into it, instead evolving to a common alien oscillator. Furthermore, there are very few predecessors at all, accounting for the extreme increase in rarity. Despite all of these, it still the most common period-3 oscillator.
| An 8-cell pre-pulsar predecessor from Life is a p4 oscillator in Grounded Life (click above to open LifeViewer) |
On the other hand, in EightLife (B3/S238), the pulsar is 170 times more common than in Life because the pi-heptomino evolves into it.[10]
| A pulsar evolving from a pi heptomino in EightLife (click above to open LifeViewer) |
See also
Notes
- ↑ 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.
- ↑ variant 1, variant 2
- ↑ D4_+1 variant, C4_1 variant
- ↑ cis- form, trans- form
- ↑ tetramer form
- ↑ An example is 3bo$o5bo$b2ob2o!, which evolves into another 7-cell predecessor after one tick.
- ↑ 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
- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
- ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
- ↑ Adam P. Goucher. "Census". Catagolue. Retrieved on October 27, 2018.
- ↑ 4.0 4.1 Adam P. Goucher. "Statistics". Catagolue. Retrieved on March 1, 2023.
- ↑ gameoflifeboy (April 20, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ 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)
- ↑ 7.0 7.1 yoleo (October 17, 2023). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums
- ↑ knightlife (June 23, 2013). Blockic Seeds (discussion thread) at the ConwayLife.com forums
- ↑ Adam P. Goucher. "census/b38s23/C1". Catagolue. Retrieved on March 19, 2023.
- ↑ Adam P. Goucher. "census/b3s238/C1". Catagolue. Retrieved on March 26, 2023.
External links
- Pulsar at the Life Lexicon
- Pulsar at Adam P. Goucher's Catagolue
- Pulsar at Heinrich Koenig's Game of Life Object Catalogs
- Patterns
- Patterns with Catagolue frequency class 12
- Natural periodic objects
- Oscillators with 48 cells
- Periodic objects with minimum population 48
- Patterns with 48 cells
- Patterns found by John Conway
- Patterns found in 1970
- Patterns that can be constructed with 3 gliders
- Oscillators
- Oscillators with period 3
- Oscillators with mod 3
- Oscillators with heat 42
- Oscillators with volatility 0.73
- Oscillators with strict volatility 0.73
- Oscillators with *c symmetry
- Oscillators with rotor Pulsar
- Sparkers
- Sparkers with period 3
- Weak sparkers
- Extendable oscillators