Fractals, Multifractals, and Thermodynamics

The basic concept of fractals and multifractals are introduced for pedagogical purposes, and the present status is reviewed. The emphasis is put on illustrative examples with simple mathematical structures rather than on numerical methods or experimental techniques. As a general characteriza­tion of fractals and multifractals a thermodynamical formalism is introduced, establishing a connec­tion between fractal properties and the statistical mechanics of spin chains.