Fractal structures displaying self-similarity provide the idea to produce materials incorporating multiple length scales simultaneously. Here we report the formation of fractal-like structures from self-assembling dipeptide derivatives, Fmoc-Phe-Tyr- phosphate (FPTP) and Fmoc-Phe-Tyr (FPT). Upon addition of alkaline phosphatase, FPTP solution is converted to FPT, and forms hydrogel with nanofiber network. When FPT solution is deposited on a silicon film, fractal structures are observed after drying from scanning electron microscopy image. More interestingly, FPTP which cannot form hydrogel in solution also assemble into fractal pattern on solid film. We study the effects of pH and building block concentration on the structure morphology. The fractal dimension of the patterns is measured using standard method. The formation process of fractal structures from diffusion-limited cluster-cluster aggregation is discussed. The present work will provide a molecular design concept for the construction of complex materials and patterns.