A method to fabricate a hierarchical graduated-branched structure that grows in a three-dimensional pattern down to fractal-branching, nano-size level is detailed. The fractal patterning is accomplished on a three-dimensional (i.e., non-planar) surface, by exposing the surface to a properly focused particle beam, which causes the spontaneous growth of graduated branches all over the surface. The structure can be fabricated with a single material and the fractal-patterning is done in a one step process. No addition of material is required for the formation of each branch. The fractal graduated branching structure can then be molded in order to produce replicas.