Molecular self-assembly is a ubiquitous phenomenon in which individual atoms or molecules set up an ordered structure. It is of high interest for understanding the biology and a variety of diseases at the molecular level. In this work, we studied the self-assembly of tyrosine molecules via extensive molecular dynamics simulations. The formation of structures by self-assembly was systematically studied at various concentrations, from very low to very high. The temperature was kept constant, at which, in our former studies, we have already observed well-formed self-assembled structures. Depending on the concentration, the system displays a wide range of different structures, ranging from freely scattered monomers to very well formed four-fold structures. Different regimes of concentration dependence are observed. The results are proved by calculating the moments of inertia of the structures and the number of hydrogen bonds formed. Free energy landscapes calculated for the number of hydrogen bonds versus the number of contacts within a criterion provide insights into the structures observed.