The claim "This makes the cipher aperiodic" should be justified. As an immediate counter, I would say that if your code runs on a physically finite machine (an however large, yet finite number of bits to store state), this strikes me as very unlikely to be theoretically true.
In cryptography, "aperiodic" means the period is computationally unreachable. We use a 256-bit state, making the probability of a collision negligible (on the order of 2^256). This is a parameter of the CVM; it could be increased to 512 bits or more if required.
This is the standard security model for all modern hash-based constructions.