Between discrete and continuous: cellular automata and laplacian on the Sierpinski gasket

We will introduce and study some discrete dynamical models intrinsically related to "continuous" ones.
In particular, the following topics will be addressed.
A. Cellular automata and related dynamical systems. Fractals through celluar automata. The game of "Life".
B. Sierpinski gasket, laplacian on the Sierpinski gasket as a limit of ``discrete laplacians''. Spectrum of the laplacian and
harmonic functions on the Sierpinsky gasket.