Achim's p4

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Achim's p4
x = 11, y = 9, rule = B3/S23 2b2o3b2o$bo2bobo2bo$bob2ob2obo$2o7b2o$2bobobobo$2o7b2o$bob2ob2obo$bo2b obo2bo$2b2o3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ LOOP 4 GPS 2 THUMBSIZE 2 ]]
Pattern type Oscillator
Number of cells 40
Bounding box 11×9
Frequency class 29.0
Period 4
Mod 4
Heat 4
Volatility 0.17
Strict volatility 0.17
Discovered by Achim Flammenkamp
Year of discovery 1988
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.


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]


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]

Image gallery

The original, less compact form of Achim's p4

See also


  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. 3.0 3.1 Adam P. Goucher. "Census". Catagolue. Retrieved on October 27, 2018.
  4. Tanner Jacobi (November 8, 2014). Re: Soup search results (discussion thread) at the forums
  5. gameoflifeboy (August 21, 2015). Re: Soup search results (discussion thread) at the forums
  6. Aidan F. Pierce (April 27, 2016). Re: Soup search results (discussion thread) at the forums
  7. Jason Summers' jslife pattern collection. Retrieved on January 5, 2020.
  8. Lewis Patterson (October 17, 2010). Re: Thread For Your Accidental Discoveries (discussion thread) at the forums
  9. Matthias Merzenich (October 17, 2010). Re: Thread For Your Accidental Discoveries (discussion thread) at the forums
  10. Chris Cain (March 1, 2015). Re: Thread for your unsure discoveries (discussion thread) at the forums

External links

  • 40P4.9 at Heinrich Koenig's Game of Life Object Catalogs