Fractal Sets and Boundary Theory

We discuss how the boundary concept can be used to describe fractal sets. Two examples illustrate this: 

1. Polynomial endomorphisms of C2 and their Julia sets; 

2. Self-similar fractals, particularly the Sierpinski gasket. 

The boundaries used are Shilov-Martin-Furstenberg-Poisson boundaries. We will show some pictures of the fractal sets arising in 1, which show many features that are still not quite well understood.