  Self-assembly is the process in which the components of a system, whether
molecules, polymers, or macroscopic particles, are organized into ordered
structures as a result of local interactions between the components themselves,
without exterior guidance. In this paper, we speak about the self-assembly of
aperiodic tilings. Aperiodic tilings serve as a mathematical model for
quasicrystals - crystals that do not have any translational symmetry. Because
of the specific atomic arrangement of these crystals, the question of how they
grow remains open. In this paper, we state the theorem regarding purely local
and deterministic growth of Golden-Octagonal tilings. Showing, contrary to the
popular belief, that local growth of aperiodic tilings is possible.
