Fractal topologies, which are statistically self-similar over multiple length scales, are pervasive in nature. The recurrence of patterns at increasing length scales in fractal-shaped branched objects, e.g., trees, lungs, and sponges, results in high effective surface areas, and provides key functional advantages, e.g., for molecular trapping and exchange. Mimicking these topologies in designed protein-based assemblies will provide access to novel classes of functional biomaterials for wide ranging applications. Here we describe a computational design approach for the reversible self-assembly of proteins into tunable supramolecular fractal-like topologies in response to phosphorylation. Computationally-guided atomic-resolution modeling of fusions of symmetric, oligomeric proteins with Src homology 2 (SH2) binding domain and its phosphorylatable ligand peptide was used to design iterative branching leading to assembly formation by two enzymes of the atrazine degradation pathway. Structural characterization using various microscopy techniques and Cryo-electron tomography revealed a variety of dendritic, hyperbranched, and sponge-like topologies which are self-similar over three decades (~10nm-10µm) of length scale, in agreement with models from multi-scale computational simulations. Control over assembly topology and formation dynamics is demonstrated. Owing to their sponge-like structure on the nanoscale, fractal assemblies are capable of efficient and phosphorylation-dependent reversible macromolecular capture. The described design framework should enable the construction of a variety of novel, spatiotemporally responsive biomaterials featuring fractal topologies.