A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology. We proposed a new theory that allowed us to model the most challenging cases of atomic self-assembling whose complexity prevented their modeling before. For example, the most challenging and biologically relevant case of formation of double-stranded helix polymers from a solution of monomers is successfully simulated. The self-organization is in the atomic scale resolution while a time resolution is commensurate with the typical diffusion time. These advancements are achieved due to introduction of two novel concepts, atomic fragments (fraton) regarded as interacting pseudo-particles and structural clusters that are central for the proposed construction of the model Hamiltonian as a bilinear expansion in structural clusters. Both novelties provide a self-organization of even disordered atomic distribution to a desired atomic structure of practically any complexity. Several other examples including a crystallization of the diamond and zinc-blende structures are presented.