Repeating Key

Periodic ciphers are polyalphabetic substitution ciphers where there is a repeating pattern to the alphabets used, according to a fixed key. For example, a Vigenere cipher with a repeating keyword. These types of ciphers can be solved by figuring out the key length and then applying frequency analysis to the positions which are the same modulo the key length. The key length can be estimated by calculating the periodic index of coincidence (IoC) and plotting it as a function of the period (length of the repeating key). Doing this should show a clear peak at the actual key length as well as multiples of it.

Applying this kind of analysis to the eyes does not yield any particular key length as especially promising, which makes a periodic keyed substitution unlikely.

Additionally, isomorphs are an observation of the eyes which is not consistent with a periodic cipher. We see isomorphs at a variety of distances which are relatively prime, whereas with periodic ciphers, we would instead see exact ciphertext repeats at multiples of the period. Ciphers which produce isomorphs at any distance are instead more likely to be some kind of autokey cipher, particularly ciphertext-autokey (CTAK) and generalizations of it.