We perform molecular dynamics (MD) simulations of the self-assembly process of pseudoisocyanine dye molecules with amphiphilic substituents (amphi-PIC). The spontaneous aggregation of cyanine molecules into large molecular J-aggregates with optical functionality has drawn attention for many decades already, but the shape and molecular structure of the aggregates remain issues of debate, as current imaging techniques still lack molecular scale resolution. Our MD simulations for amphi-PIC predict the existence of aggregates with the shape of either a single-walled cylinder or a ribbon. We characterize the internal structure of these aggregates using the π-π stacking and the average orientation of the long axis of the amphi-PIC molecule's chromophore. The molecular arrangement obtained exhibits much disorder, which may explain the wide absorption band observed for aggregates of amphi-PIC. We show that changing the counterion of the positively charged amphi-PIC dye can change the equilibrium aggregate shape. In addition, we demonstrate that the cylindrical aggregates attract each other and form bundles.