  These notes give examples of how suitably defined geometrical objects encode
in their fractal structure thermal critical behavior. The emphasis is on the
two-dimensional Potts model for which two types of spin clusters can be
defined. Whereas the Fortuin-Kasteleyn clusters describe the standard critical
behavior, the geometrical clusters describe the tricritical behavior that
arises when including vacant sites in the pure Potts model. Other phase
transitions that allow for a geometrical description discussed in these notes
include the superfluid phase transition and Bose-Einstein condensation.
