Aggregation of peptide molecules into amyloid fibrils is a characteristic feature of several degenerative diseases. However, the details behind amyloid-formation, and other self-assembled peptide aggregates, remain poorly understood. In this study, we have used small-angle X-ray scattering (SAXS), static and dynamic light scattering (SLS and DLS) as well as cryogenic transmission electron microscopy (cryo-TEM) to determine the structural geometry of self-assembled peptide aggregates in various dilute aqueous solutions. Pramlintide was used as a model peptide to assess the aggregation behaviour of an amyloid-forming peptide. The effects of adding sodium chloride (NaCl), sodium thiocyanate (NaSCN), and sodium fluoride (NaF) and the co-solvent dimethyl sulfoxide (DMSO) on the aggregation behaviour were studied. Our scattering data analysis demonstrates that small oligomeric fibrils aggregate to form networks of supramolecular assemblies with fractal dimensions. The choice of anion in small amounts of added salt has a significant impact on the size of the fibrils as well as on the fractal dimensions of supramolecular clusters. In DMSO the fractal dimension decreased with increasing DMSO concentration, indicating the formation of a less compact structure of the supramolecular assemblies.