Balazs Barany (BME): How to measure the size of fractals?

According to Benoit B. Mandelbrot, "A fractal is a mathematical or natural shape made of parts similar to the whole in some way." In this talk, we will consider a mathematical model of fractals, namely the self-similar sets. These sets are generated by a set of contracting similarity functions, called Iterated Function System (IFS). We will study some of their basic properties. Since these sets can have very complicated structure, in the problem of measuring the size, one of the important task is the dimension. We will see some methods how to calculate the dimension of self-similar sets.