Symmetry

There exist several concepts in cellular automata which can be labelled as symmetries:

• Static symmetry, referring to geometrical mirror and rotational symmetries preserved by any pattern in a rule;
• Minor static symmetry, referring to attributes which are not necessarily geometrical but are still preserved in the same way as those above;
• Kinetic symmetry, which refers to both spatial and temporal symmetries preserved by still lifes, oscillators and spaceships.