Browsing by Author "Rhyner, Jakob"
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Item Open Access Item Open Access Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings(1986) Gähler, Franz; Rhyner, JakobThe two main techniques for the generation of quasipcriodic tilings.,de Bruijn's grid method and the projection formalism, are generalised. A very broad class or quasi periodic tilings is obtained in this way. The two generalised methods are Shown to be equivalent. The standard calculation of Fourier spectra is extended to the whole general class of tilings. Various upplications are discussed.Item Open Access Quasiperiodic tilings : a generalized grid projection method(1988) Korepin, Vladimir E.; Gähler, Franz; Rhyner, JakobWe generalize the grid-projection method for the construction of quasiperiodic tilings. A rather general fundamental domain of the associated higher-dimensional lattice is used for the construction of the acceptance region. The arbitrariness of the fundamental domain allows for a choice which obeys all the symmetries of the lattice, which is important for the construction of tilings with a given non-trivial point-group symmetry in Fourier space. As an illustration, the construction of a two-dimensional quasiperiodic tiling with 12-fold orientational symmetry is described.