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Quasiperiodic plane tilings based on stepped surfaces. (English) Zbl 1370.52066
Summary: Static and dynamic characteristics of layerwise growth in two-dimensional quasiperiodic Ito–Ohtsuki tilings are studied. These tilings are the projections of three-dimensional stepped surfaces. It is proved that these tilings have hexagonal self-similar growth with bounded radius of neighborhood. A formula is given for the averaged coordination number. Deviations of coordination numbers from its average are quasiperiodic. Ito–Ohtsuki tiling can be decomposed into one-dimensional sector layers. These sector layers are one-dimensional quasiperiodic tilings with properties like Ito–Ohtsuki tilings.

MSC:
52C23 Quasicrystals and aperiodic tilings in discrete geometry
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