Yes, exactly, the zeros of the polynomial

If the three matrices are unitary, they inevitably lead us to the bounded norm

The words are fixed beforehand, and I would like to find out what matrices $A,B,C$ lead us to bounded norms of products

UPD: I also observed this behaviour for irrational numbers like $e$ and $\pi$.

The question is about all real irrational numbers a. The example shows that the finite differences are arranged into strings of three kinds. These strings themselves form a quasiperiodic sequence which also turns out to be composed of blocks of three types.