论文标题
混合迷宫分形
Mixed labyrinth fractals
论文作者
论文摘要
迷宫分形是Cristea和Steinsky最近的工作中引入和研究的自相似分形。在本文中，我们定义和研究更多的通用对象，称为混合迷宫分形，通常不是自相似，并且是通过使用迷宫模式序列来构造的。我们表明，混合的迷宫分形是枝状分形和研究特性，在与前夫物相关的图形和分形相关图中的弧形中的路径的特性，例如路径长度和盒子计数弧度和弧形长度。我们还考虑了与混合迷宫分形有关的更多一般对象，对弧长的两个猜想进行了两个猜想，并与广义Sierpinski地毯的最新结果建立了联系。
Labyrinth fractals are self-similar fractals that were introduced and studied in recent work by Cristea and Steinsky. In the present paper we define and study more general objects, called mixed labyrinth fractals, that are in general not self-similar and are constructed by using sequences of labyrinth patterns. We show that mixed labyrinth fractals are dendrites and study properties of the paths in the graphs associated to prefractals, and of arcs in the fractal, e.g., the path length and the box counting dimension and length of arcs. We also consider more general objects related to mixed labyrinth fractals, formulate two conjectures about arc lengths, and establish connections to recent results on generalised Sierpinski carpets.
