Still lifes

Those who count still lifes according to their cell counts make a distinction between genuine still lifes and pseudo- ones. First of all, an island is a group of cells that are interconnected orthogonally or diagonally. A stable pattern can consist of several islands.

Now, if a stable pattern's islands can be partitioned into two non-empty sets, in such a way that each set is a stable on its own right, the pattern is a pseudo-still-life. If no such partition is possible, the pattern is a still life.

Matthew Cook pointed out on September 1998 that it is possible for a stable pattern to be partitionable into three sets but not into two, or into four sets but not into two or three. (It's never necessary to partition it into more than four sets, because of the Four Color Theorem.)

What are the smallest known still lifes that have these characteristics? Here are the current record-holders:

Still life partitionable into three sets but not into two (32 cells).

(Gabriel Nivasch, July 2001)

Still life partitionable into four sets but not less (34 cells).

(Gabriel Nivasch, July 2001)