  In this paper, we present numerical and experimental evidence of directional
wave behavior, i.e. beaming and diffraction, along high-order rotational
symmetries of quasicrystalline elastic metamaterial plates. These structures
are obtained by growing pillars on an elastic plate following a particular
rotational symmetry arrangement, such as 8-fold and 10-fold rotational
symmetries, as enforced by a design procedure in reciprocal space. We estimate
the dispersion properties of the waves propagating in the plates through
Fourier transformation of transient wave-fields. The procedure identifies, both
numerically and experimentally, the existence of anisotropic bands
characterized by high energy density at isolated regions in reciprocal space
that follow their higher order rotational symmetry. Specific directional
behavior is showcased at the identified frequency bands, such as wave beaming
and diffraction. This work expands the wave directionality phenomena beyond the
symmetries of periodic configurations (e.g., 4-fold and 6-fold), and opens new
possibilities for applications involving the unusual high-order wave features
of the quasicrystals such as superior guiding, focusing, sensing and imaging.
