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We prove discrete-to-continuum convergence of interaction energies defined onlattices in the Euclidean space (with interactions beyond nearest neighbours)to a crystalline perimeter, and we discuss the possible Wulff shapes obtainablein this way.  Exploiting the "multigrid construction" of quasiperiodic tilings (which is anextension of De Bruijn's "pentagrid" construction of Penrose tilings) we adaptthe same techniques to also find the macroscopical homogenized perimeter whenwe microscopically rescale a given quasiperiodic tiling.

Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings