The self-assembled structures possess superior stability, biocompatibility and mechanical strength, and their study can provide insight into the use of creating novel biomaterials. Atomic force microscopy (AFM) images of single-stranded DNA (ssDNA) nanostructures show that well-ordered organization, high homogeneity, and molecular dimensions fractal-shaped fibers formed on a gold substrate covered with self-assembled monolayers (SAMs) of 1-hexadecanethiol (HDT). The nanoscaled architectures of ssDNA on HDT/Au changed remarkably following the process of diffusion-limited cluster aggregation (DLA) over time. The ssDNA fibers prefer to form on hydrophobic SAMs instead of hydrophilic SAMs, and the ssDNA has to have complementary regions in their sequences. This method might not be used only for the construction of fractal patterns, but also for the design and fabrication of functional DNA-based, self-assembled materials that exhibit self-similarity at multiple length scales.