An oscillator is in its canonical form if the stator contains no state 1 cells and the casing only contains state 5 cells. Note that the canonical form does not necessarily have the smallest possible population.
For example, the P6 MW emulator on the left is not in its canonical form, since there are four state 1 cells in the stator, and the casing contains cells other than state 5 cells. The canonical form of the P6 MW emulator is the one on the right, despite having a slightly higher population.
While not part of the definition of a "canonical form", if the function is the same, states 4 and 2 are preferred over states 15 and 16.
Separating oscillators using canonical forms
The canonical form can be used to separate seemingly connected parts of oscillators. The canonical form of the toaster and middleweight volcano (on the left) are the forms on the right, which are obtained by converting all state 1 cells in the bushing to state 4, removing the casing, and using state 5 cells to prevent unwanted births:
canonical forms in StateInvestigator (click above to open LifeViewer)
After separating out the rotor from the bushing, it is apparent that they actually consist of multiple rotors that are not connected by state 1 cells (left). Since the main usage of the toaster and middleweight volcano only uses the sparking end, the other parts can be removed, resulting in the reductions on the right.