In this paper we propose a new way to determine the permeability of many sedimentary rocks using fractal analysis of pore-scale geometry. We present experimental evidence that the fractal properties of sedimentary rocks evolve due to fluid-rock interactions that occur during diagenesis. A numerical model of pore-mineral, reaction-limited growth is constructed to study this evolution. Model results indicate a quantitative relation between fractal dimension and crystal growth rates at the pore-grain interface. The model and experiments together suggest that the state of diagenetic alteration, as well as the permeability of many sedimentary rocks, can be partly assessed from measurements of pore geometry alone and that trends in diagenesis and transport properties are linked via the evolving pore structures.