You can check out the wikipedia page on Hausdorff dimension.
Hey, I was just wondeirng if anyone has ever come across a formal definition of self similarity. I'm playing around with simple, self-similar objects, and I need to know if I can just say ' this object is self similar' (provided that its similarity is obvious enough), or if I need to prove self similarity. I've tried to find definitions of this concept on the interent, yet I've not found any formal definition. Usually, people state that an object A is self similar iff the structure completly or approximiitly preserved in a small part of it.