When a continuous dynamical system admits a Markov
partition, the exponential of its topological entropy, called the
growth rate, is a weak Perron number. The Thurston set for a family
of such maps is the closure of the set of Galois conjugates of growth
rates of maps in the family. I will discuss some of the basic
geometric and topological properties of the Thurston set and a
closely related set, the Thurston Master Teapot, for the family of
superattracting real quadratic polynomials. In particular, I will
show that Thurston's Master Teapot is connected.