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Hyperuniformity is a property of certain heteroneous media in which densityfluctuations in the long wavelength range decay to zero. In reciprocal spacethis behavior translates into a decay of Fourier intensities in the range nearsmall wavenumbers. In this paper quasiperiodic tilings constructed by wordconcatenation are under study. The lattice is generated from a parameter givenby its continued fraction so that quasiperiodicity emerges for infinite whenirrational generators are into consideration. Numerical simulations show aquite regular quadratic decay of Fourier intensities, regardless of the numberconsidered for the generator parameter, which leads us to formulate thehypothesis that this type of media is strongly hyperuniform of order 3.Theoretical derivations show that the density fluctuations scale in the sameproportion as the wavenumbers. Furthermore, it is rigorously proved that thestructure factor decays around the origin according to the pattern $S(k) \simk^4$. This result is validated with several numerical examples with differentgenerating continued fractions.

Hyperuniformity of quasiperiodic tilings generated by continued fractions