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dc.contributor.authorChen, Jin-Yuen_US
dc.contributor.authorChen, Yu-Jieen_US
dc.contributor.authorHu, Wen-Gueien_US
dc.contributor.authorLin, Song-Sunen_US
dc.date.accessioned2017-04-21T06:56:04Z-
dc.date.available2017-04-21T06:56:04Z-
dc.date.issued2016-02en_US
dc.identifier.issn0022-2488en_US
dc.identifier.urihttp://dx.doi.org/10.1063/1.4941734en_US
dc.identifier.urihttp://hdl.handle.net/11536/133542-
dc.description.abstractThis investigation completely classifies the spatial chaos problem in plane edge coloring (Wang tiles) with two symbols. For a set of Wang tiles B, spatial chaos occurs when the spatial entropy h(B) is positive. B is called a minimal cycle generator if P(B) not equal empty set and P(B\') = empty set whenever B\' not subset of B, where P(B) is the set of all periodic patterns on Z(2) generated by B. Given a set of Wang tiles B, write B = C-1 boolean OR C-2 boolean OR ... boolean OR C-k boolean OR N, where C-j, 1 <= j <= k, are minimal cycle generators and B contains no minimal cycle generator except those contained in C-1 boolean OR C-2 boolean OR ... boolean OR C-k. Then, the positivity of spatial entropy h(B) is completely determined by C-1 boolean OR C-2 boolean OR ... boolean OR C-k. Furthermore, there are 39 equivalence classes of marginal positive-entropy sets of Wang tiles and 18 equivalence classes of saturated zero-entropy sets of Wang tiles. For a set of Wang tiles B, h(B) is positive if and only if B contains a MPE set, and h(B) is zero if and only if B is a subset of a SZE set. (C) 2016 AIP Publishing LLC.en_US
dc.language.isoen_USen_US
dc.titleSpatial chaos of Wang tiles with two symbolsen_US
dc.identifier.doi10.1063/1.4941734en_US
dc.identifier.journalJOURNAL OF MATHEMATICAL PHYSICSen_US
dc.citation.volume57en_US
dc.citation.issue2en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:000371620000053en_US
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