Pentadecathlon (or PD; plural pentadecathlons[note 1]) is a period-15 oscillator that was found in 1970 by John Conway[2] while tracking the history of short rows of cells (see one-cell-thick pattern); indeed, an orthogonal row of 10 cells evolves into this object. It is the only known oscillator that is a polyomino in more than one phase (besides the blinker).

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Pattern type Oscillator
Number of cells 12
Bounding box 16×9
Frequency class 18.6
Period 15
Mod 15
Heat 22.4
Volatility 1.00
Strict volatility 1.00
Discovered by John Conway
Year of discovery 1970


Pentadecathlon is the most natural oscillator of period greater than 3 (and indeed, the second most natural oscillator of period greater than 2) in Achim Flammenkamp's census. In fact, it is the fifth or sixth most common oscillator overall in this census, being about as frequent as the clock, but much less frequent than the blinker, toad, beacon or pulsar.[3][4] It is also the most common oscillator with a volatility of 1. The pentadecathlon is also the fifty-second most common object on Adam P. Goucher's Catagolue and by far the most common period 15 oscillator, with all other natural oscillators of that period featuring it combined with some other object.[5]

Uses of the pentadecathlon

The pentadecathlon is so called because it has a period of 15 generations. This, being a factor of 30, means that it can be elegantly used in combination with period 30 devices (based on the queen bee shuttle). Firstly, it can reflect a glider 180° as in p60 glider shuttle, and a pair of perpendicular pentadecathlons can rotate a glider 90°.

Hassling capabilities

The pentadecathlon is classified as a pulsating oscillator, since it undulates throughout its cycle. During this process, the pentadecathlon throws off multiple accessible sparks. More specifically, the oscillator produces horizontal T-nose sparks, horizontal V sparks and vertical domino sparks. Two copies of these domino sparks can be used to hassle toads in two distinct ways. The V sparks elegantly convert blocks into gliders, which forms the basis of the p30 *WSS => glider converter and aforementioned glider reflectors. This property is also exploited in numerous oscillators.


On April 11, 1997, Heinrich Koenig found a three-glider collision that produced a clean pentadecathlon. This was a surprising result at the time. Four-glider pentadecathlon recipes had been known and used for many years, so this was an unlooked-for improvement, very similar to Luka Okanishi's discovery of a three-glider synthesis of a switch engine almost twenty years later. This also makes the pentadecathlon the rarest object in Catagolue for which a 3-glider synthesis is known.

Other rules

  • In EightLife, it still functions as a period 15 oscillator, but it generates extra internal sparks.

See also


  1. The correct Ancient Greek dual and plural forms, pentadecathlo and pentadecathla,[1] are not in common use.


  1. "ἆθλον". English Wiktionary. Retrieved on 2016-06-16.
  2. Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  3. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  4. "Census Results in Conway's Game of Life". The Online Life-Like CA Soup Search. Retrieved on July 12, 2009.
  5. Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
  • 12P15.1 at Heinrich Koenig's Game of Life Object Catalogs
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