turkmath.org

The notion of ''fractals'' was introduced by Mandelbrot in the description of nature.''Self-similarity'' is very important in the study of such sets and most classical fractal sets constructed by many mathematicians have the self-similarity in some sense. In this talk, I will give the basics of self-similar sets and explain the topological structures of them. Then I will define a self-similar structure which is a purely topological description of a self-similar set. Finally, I will state and prove a thorem which gives a characterization of ''minimality'' of a self-similar structure.