  We investigate the complete phase diagram of the decoupled world-sheet theory
of (P,Q) strings. These theories include 1+1 dimensional super Yang-Mills
theory and non-commutative open string theory. We find that the system exhibits
a rich fractal phase structure, including a cascade of alternating
supergravity, gauge theory, and matrix string theory phases. The cascade
proceeds via a series of SL(2,Z) S-duality transformations, and depends
sensitively on P and Q. In particular, we find that the system may undergo
multiple Hagedorn-type transitions as the temperature is varied.
