Abstract: We propose a new approach inspired by fractal geometry to analyze partially hyperbolic systems, which leads to several regularity jump and rigidity phenomena. Applications include a lower dimensional example theorem: for a volume preserving C^\infty partially hyperbolic diffeomorphism with contracting center on T^3,
(1). if both Holder exponents of E^s and E^c are higher than those predicted by Lyapunov exponents respectively, then f is C^\infty conjugate to a linear toral automorphism.
(2). If E^s (or E^c) has no excessive H\"older regularity, then it has a fractal graph.
