Supramolecular self-assembly of the organic semiconductor perylene-3, 4, 9, 10-tetracarboxylic diimide (PTCDI) together with Ni atoms on the inert Au(111) surface has been investigated using high-resolution scanning tunneling microscopy under ultrahigh vacuum conditions. We demonstrate that it is possible by tuning the co-adsorption conditions to synthesize three distinct self-assembled Ni-PTCDI nanostructures from zero-dimensional (0-D) nanodots over one-dimensional (1-D) chains to a two-dimensional (2-D) porous network. The subtle interplay among non-covalent interactions responsible for the formation of the observed structures has been revealed from force-field structural modeling and calculations of partial charges, bond orders and binding energies in the structures. A unifying motif for the 1-D chains and the 2-D network is found to be double N-H…O hydrogen bonds between PTCDI molecules, similar to the situation found in surface structures formed from pure PTCDI. Most interestingly, we find that the role of the Ni atoms in forming the observed structures is not to participate in metal-organic coordination bonding. Rather, the Ni adatoms acquire a negative partial charge through interaction with the substrate and the Ni-PTCDI interaction is entirely electrostatic.