I know there are many ways to crack basic ciphers were each letter is mapped to some other letter, but what ways are there to decode something that was encrypted using a cipher that changed after every letter, in a way that is based on the letter just coded?
For example, imagine using a Caesar cipher where the number of letters the alphabet was shifted over changes by $n$ after every letter coded, where $n$ is the position in the alphabet of the letter just encoded.
That would seem to null the efficacy of observing letter frequency, double letter patters, common short words, etc. How would a code like this be cracked?
Sorry, I might have been unclear. The Caesar cipher was just an example, but say that the positions shift over $f(n)$ letters instead of just $n$, how would $f(n)$ be determined?