论文标题
基本分形几何形状。涉及非理性旋转的网络和地毯
Elementary fractal geometry. Networks and carpets involving irrational rotations
论文作者
论文摘要
具有开放式环境的自相似集合（分形几何形状的线性对象）主要用于晶体学数据。在这里，我们基于非理性角度的旋转，在平面中引入新的对称类别。在计算机辅助搜索中发现了没有特征方向，具有牢固联系和较小复杂性的示例。它们令人惊讶，因为旋转由有理矩阵给出，并且开放式条件的证明通常需要整数数据。我们通过对称类别和代数数来开发自相似集的分类。给出了各种二次数字字段的示例。 。
Self-similar sets with open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles. Examples without characteristic directions, with strong connectedness and small complexity were found in a computer-assisted search. They are surprising since the rotations are given by rational matrices, and the proof of the open set condition usually requires integer data. We develop a classification of self-similar sets by symmetry class and algebraic numbers. Examples are given for various quadratic number fields. .
