Frequency Analysis

Assuming the commonly accepted reading order, the distribution of values is roughly uniform (up to some measurement error for the sample size) over all 83 values. There are 1036 total trigrams across all 9 messages. Based on this, the expected frequency of any given value for a uniform distribution is 12.482.

(add frequency plot at some point)

A way to quantify how close to a uniform distribution it is would be to use the index of coincidence. We will normalize the IoC by multiplying it by the number of distinct symbols in the ciphertext of the message (which, when taking all messages together, is 83). Uniformly distributed random text has a normalized IoC of 1.

The normalized IoC of all messages combined is 1.066.

Normalized IoCs per message are 0.958, 1.043, 0.950, 0.918, 1.025, 0.990, 1.040, 0.872, 0.928. These are all pretty close to random.

In comparison, IoC for plaintext, or text under a simple substitution cipher, is usually around 1.6 - 1.8 for English, possibly higher depending on how repetitive the text is.

Frequency analysis gives strong evidence that the eyes are not a simple substitution cipher. Further evidence comes in the form of isomorphs, which give evidence that the eyes are not monoalphabetic, but rather polyalphabetic, since only polyalphabetic ciphers can produce large numbers of isomorphs with complex patterns.