Beluchenko's p13 is a period-13 oscillator found by Nicolay Beluchenko on January 4, 2009. In terms of its 34 cells, it is the smallest known period 13 oscillator. It gives sparks, allowing for the construction of non-trivial higher-period oscillators as seen in a later section.
There are three ways in which two of these can share a common block, all of which are shown below. Jason Summers also discovered that four of these oscillators can be combined to create a statorless oscillator (i.e., where none of the cells are alive in all phases), making it the first such oscillator known with a prime period greater than two.
Beluchenko's p13 first appeared semi-naturally in March 2016, in a symmetric soup submitted to Catagolue.
The oscillators below are listed due to being the smallest known ones by population, while also satisfying the condition that at least one cell oscillates at the full period.
- 34P13.1 at Heinrich Koenig's Game of Life Object Catalogs