  We investigate the general features of renormalization group flows near
superconformal fixed points of four dimensional N=1 supersymmetric gauge
theories with gravity duals. The gauge theories we study arise as the
world-volume theory on a set of D-branes at a Calabi-Yau singularity where a
del Pezzo surface shrinks to zero size. Based mainly on field theory analysis,
we find evidence that such flows are often chaotic and contain exotic features
such as duality walls. For a gauge theory where the del Pezzo is the Hirzebruch
zero surface, the dependence of the duality wall height on the couplings at
some point in the cascade has a self-similar fractal structure. For a gauge
theory dual to CP^2 blown up at a point, we find periodic and quasi-periodic
behavior for the gauge theory couplings that does not violate the a-conjecture.
Finally, we construct supergravity duals for these del Pezzos that match our
field theory beta functions.
