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A new approach to study coordination shells and coordination sequences of quasiperiodic graphs is suggested. The structure of the coordination shells in the vertex graph of a Penrose tiling is described. An asymptotic formula for its coordination numbers is obtained. An essentially different behaviour of the coordination numbers for even and odd shells is revealed.

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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.