Complexity function and forcing in the 2D quasi-periodic Rauzy tiling |
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Authors: | V G Zhuravlev A V Maleev |
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Institution: | (1) Vladimir State Pedagogical University, pr. Stroiteleĭ 11, Vladimir, 600024, Russia |
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Abstract: | The quantitative characteristics of the long-range translational order in the 2D quasi-periodic Rauzy tiling (complexity function and forcing depth) have been investigated. It is proved that the complexity function c(n) is equal to the number of figures in the n-corona grown from a seed composed of three figures of different types. The complexity function c(n) is found to be additive. A relationship between the jumps in the maximum forcing depth and large incomplete particular expansions in a chain fraction of irrational angles of rotation of a unit circle, which determine the growth of geodetic chains, is established. |
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