Recursion utilizes some self similar nature of an object (some representation of the given problem) to produce some quantitative measure (output) on the object through some algorithm (utilizing the self similar nature).

Can one consider algorithms themselves as fractal description of some measurable information of the object the algorithm works on?

Has the tools used in the study of fractals provided any illuminating examples for lower or upper bounds for recursive complexity of algorithms?

I am looking for examples and references along the lines of whether algorithms can be treated as fractals and tools about fractals can be used to prove results about algorithms.