Hash functions are generally not reversible, unless you were to very carefully define the input domain. Given the "similar inputs" -> "quite different outputs"

Hash functions are generally not reversible, unless you were to very carefully define the input domain. Given the "similar inputs" -> "quite different outputs" ("avalanche") effect described here and the article, I wonder this: Is it possible to describe a given hash function as a "cyclic" function, given some kind of transformation on the input to create a matrix/tensor out of the input -- are there common methods to re-order the inputs in such a way that there are discernible "axis" that exhibit cyclic behavior? I suppose such an analysis would be a way to determine cryptographic fitness of a function, but I am only speculating.