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arXiv · 1310.7781

A new multidimensional slow continued fraction algorithm and stepped surface

Maki Furukado·Shunji Ito·Asaki Saito·Jun-ichi Tamura·Shin-ichi Yasutomi
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Abstract

We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling substitutions) for any stepped surface for any cubic direction.

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Maki Furukado, Shunji Ito, Asaki Saito, Jun-ichi Tamura, Shin-ichi Yasutomi. 2013-10-29. A new multidimensional slow continued fraction algorithm and stepped surface. https://arxiv.org/abs/1310.7781

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