Conjecture.

For every torus size <sup>n</sup> <sup>∈</sup> <sup>N</sup>, n <sup>≥</sup> 4, both the 2<sup>n</sup> � 2 fair update rules, as well as the <sup>n</sup> elementary unfair update rules with a single active cell, are a generating set for the full alternating group on 2<sup>n</sup> elements, using ECA-57.
