Non-deterministic phenomena are at the base of plenty of biological processes, that comprise physiological signalling, cellular communications, and biological architectures. Among them, natural surface topographies are often characterized by "chaotic" features, that are not trivial to be re-created in vitro. Recently, some methods have been proposed to resemble the hierarchical organization of the extracellular microenvironment, through the chemical preparation of randomly rough and self-affine fractal surfaces. Notwithstanding, this approach does not allow the fractal dimension to be modulated at a desired value, being moreover the self-affinity maintained just for one decade of spatial frequencies. Here, we propose the replication of in silico generated Brownian surfaces through a two-photon polymerization technique. Thanks to the direct laser writing of the desired patterns, we were able to obtain highly reproducible self-affine (in a range of two spatial frequency decades) structures characterized by the desired pre-determined Hurst exponents. Rat mesenchymal stem cells were moreover cultured on the obtained substrates, highlighting interesting phenomena concerning cell adhesion, cytoskeleton conformation and actin polymerization, strictly depending on the fractal dimension of the surfaces.