Achim's p4
| Achim's p4 | |||||||||
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| Pattern type | Oscillator | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Oscillator type | Billiard table | ||||||||
| Number of cells | 40 | ||||||||
| Bounding box | 11 × 9 | ||||||||
| Frequency class | 29.0 | ||||||||
| Period | 4 (mod: 4) | ||||||||
| Heat | 4 | ||||||||
| Volatility | 0.17 | 0.17 | ||||||||
| Kinetic symmetry | +c | ||||||||
| Discovered by | Achim Flammenkamp | ||||||||
| Year of discovery | 1988 | ||||||||
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- This article is about the p4 oscillator sometimes referred to as "cloverleaf". For other uses of "cloverleaf", see Cloverleaf (disambiguation).
Achim's p4 (or cloverleaf) is a period-4 oscillator that was found in a less compact form (using two sombreros) by David Buckingham in 1976. The form shown here was found by Achim Flammenkamp in 1988.[1] The rotor is two copies of the rotor of 1-2-3-4, so the oscillator is sometimes called the dual 1-2-3-4.
| The original, less compact form of Achim's p4 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
Occurrence
- See also: List of common oscillators
Achim's p4 is about the twenty-third most common naturally-occurring oscillator in Achim Flammenkamp's census.[2] On Catagolue, it is the third most common period 4 oscillator, being less common than mazing.[3] Stator variants with one[4] and three[5] bits added respectively are the fourth and eighth most common period-4 oscillators,[3] and an inflected version has also occurred naturally.[6]
| Achim's p4 forms when a traffic light + block sequence gets hit by a dot spark in a specific location and timing. (click above to open LifeViewer) |
Glider synthesis
An 8-glider synthesis of this oscillator was found by Jason Summers in September 2004.[7] In October 2010, Lewis Patterson found a predecessor of this oscillator that allows a 7-glider synthesis.[8][9] This was improved to 6 gliders by Chris Cain in March 2015,[10] and then to 5 gliders in July 2022.[11]
| The 5-glider synthesis shows an example of the required dot spark being delivered at the right time (click above to open LifeViewer) |
Trivia
One half of Achim's p4 (excluding the central row) may act as the stator component of a seminaturally-occurring variant of the T-nosed p4, or as part of the stator of a half-middleweight volcano, as found by Noam Elkies on March 15, 2000.
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See also
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.
- ↑ 3.0 3.1 Adam P. Goucher. "Census". Catagolue. Retrieved on October 27, 2018.
- ↑ Tanner Jacobi (November 8, 2014). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ gameoflifeboy (August 21, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ praosylen (April 27, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ Jason Summers' jslife pattern collection. Retrieved on January 5, 2020.
- ↑ Lewis Patterson (October 17, 2010). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (October 17, 2010). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
- ↑ Chris Cain (March 1, 2015). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
- ↑ Carson Cheng (July 4, 2022). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
External links
- Achim's p4 at the Life Lexicon
- Achim's p4 at Adam P. Goucher's Catagolue
- 40P4.9 at Heinrich Koenig's Game of Life Object Catalogs
- Patterns
- Patterns with Catagolue frequency class 29
- Natural periodic objects
- Oscillators with 40 cells
- Periodic objects with minimum population 40
- Patterns with 40 cells
- Patterns found by Achim Flammenkamp
- Patterns found in 1988
- Patterns that can be constructed with 5 gliders
- Oscillators
- Billiard tables
- Oscillators with period 4
- Oscillators with mod 4
- Oscillators with heat 4
- Oscillators with volatility 0.17
- Oscillators with strict volatility 0.17
- Oscillators with +c symmetry