混合迷宫分形中弧的维数
On the dimension of arcs in mixed labyrinth fractals
摘要：
混合迷宫分形是Cristea和Steinsky提出的单位正方形中的枝晶。最近，Cristea和Leobacher研究了分形中弧的长度。本文首先给出了一种构造混合迷宫分形的方法，该分形具有所有弧的盒维数为2的性质。随后，我们展示了如何一个特定的家庭的模式可以提供一个混合迷宫分形的任何盒计数维数之间的1和2，这也符合盒计数维数之间的任何两个不同的点的分形的弧。最后，我们将展示如何将结果扩展到更一般的设置。
英文摘要：
Mixed labyrinth fractals are dendrites in the unit square introduced by Cristea and Steinsky. They were studied recently by Cristea and Leobacher with respect to the lengths of arcs in the fractals. In this article we first give a construction method for mixed labyrinth fractals with the property that all arcs in the fractal have box counting dimension 2. Subsequently, we show how a certain family of patterns can provide a mixed labyrinth fractal of any box counting dimension between 1 and 2, which also coincides with the box-counting dimension of the arc between any two distinct points of the fractal. Finally, we show how the results can be extended to a more general setting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
