Achim's p4

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Achim's p4
Achim's p4 image
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 1994
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. 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.[1] On Catagolue, it is the third most common period 4 oscillator, being less common than mazing.[2]


In October, 2010 Lewis Patterson found a predecessor of this oscillator that allows a 7-glider synthesis.

Image gallery

The original, less compact form of Achim's p4

See also


  1. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  2. Adam P. Goucher. "Census". Catagolue. Retrieved on October 27, 2018.

External links

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