A \REGULAR" PENTAGONAL TILING OF THE PLANE
Conformal Geometry and Dynamics of The American Mathematical Society(1997)
摘要
The paper introduces conformal tilings, wherein tiles have spec- ied conformal shapes. The principal example involves conformally regular pentagons which tile the plane in a pattern generated by a subdivision rule. Combinatorial symmetries imply rigid conformal symmetries, which in turn illustrate a new type of tiling self-similarity. In parallel with the conformal tilings, the paper develops discrete tilings based on circle packings. These faithfully reflect the key features of the theory and provide the tiling illustra- tions of the paper. Moreover, it is shown that under renement the discrete tiles converge to their true conformal shapes, shapes for which no other ap- proximation techniques are known. The paper concludes with some further examples which may contribute to the study of tilings and shinglings being carried forward by Cannon, Floyd, and Parry.
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关键词
circle packing,. tiling,subdivision rules,conformal maps.,conformal symmetry,conformal map,conformal maps
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