Limit-(quasi)periodic point sets as quasicrystals withp-adic internal spaces

Mathematical Quasicrystals with Toric Internal Spaces, Diffraction and Rarefaction

Aperiodic crystals viewed as Delone sets of points on the real line, having an average lattice, are studied as congruence model λ-sets (physical space is Euclidean and the equivalent of the internal space is toric) in the context of cut-and-congruence λ-schemes, a new concept. When windows are finite point sets, the fractal rates of occupancy, at infinity, of the affine lattices associated with...

Visualizing point sets, fractals, and quasicrystals using raster techniques

Algorithms for creating a natural Voronoi tiling associated with point sets are developed. These algorithms provide additional information about the tiling which can be readily visualized. Images created in this way can be quite striking. We illustrate the application of the algorithms on fractals, lattices, and quasicrystals.

Ultrametric sets in Euclidean point spaces

Finite sets S of points in a Euclidean space the mutual distances of which satisfy the ultrametric inequality (A;B) maxf (A;C); (C;B)g for all points in S are investigated and geometrically characterized. Inspired by results on ultrametric matrices and previous results on simplices, connections with so-called centered metric trees as well as with strongly isosceles right simplices are found. AM...

Triangulating Point Sets in Orbit Spaces

Twin - peak quasiperiodic oscillations as an internal resonance ( Research Note )

Aims. Two interrelated peaks occur in high-frequency power spectra of X-ray lightcurves of several black-hole candidates. We further explore the idea that a non-linear resonance mechanism, operating in strong-gravity regime, is responsible for these quasi-periodic oscillations (QPOs). Methods. By extending the multiple-scales analysis of Rebusco, we construct two-dimensional phase-space section...