We study for the first time the structure of stable finite size clusters (i.e. colloidal molecules) obtained by self-assembly of cationic gold nanoparticles (i.e. atoms) mediated by a flexible polyanion. We reveal with non denaturizing techniques a striking structural transition from 1D small chains of 12 gold nanoparticles (AuNPs) with a self-avoiding conformation to 3D fractal clusters of 130 AuNPs with short-range ordering around the charge inversion threshold. Interestingly these well-defined structures are obtained by simple mixing in water without anisotropic functionalization or external forces. As a preliminary step we introduce a new synthesis pathway leading to well-defined cationic AuNPs (i.e. 'atoms') of controllable size that can be dispersed in H2O or D2O without aggregation and ligands self-assemblies. On this occasion, we point for the first time that usual procedures do not enable to eliminate cationic ligands self-assemblies that could play an undesired role in AuNPs' self-assembly through electrostatic interactions.