Labyrinth fractals are self-similar dendrites in the unit square that are defined with the help of a labyrinth set or a labyrinth pattern. In the case when the fractal is generated by a horizontally and vertically blocked pattern, the arc between any two points in the fractal has infinite length (Cristea and Steinsky in Geom Dedicata 141(1):1–17, ; Proc Edinb Math Soc 54(2):329–344, ). In the case of mixed labyrinth fractals a sequence of labyrinth patterns is used in order to construct the dendrite. In the present article we focus on the length of the arcs between points of mixed labyrinth fractals. We show that, depending on the choice of the patterns in the sequence, both situations can occur: the arc between any two points of the fractal has finite length, or the arc between any two points of the fractal has infinite length. This is in stark contrast to the self-similar case.
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机译：迷宫分形是单位正方形中的自相似树突，它们是通过迷宫组或迷宫图案定义的。如果分形是由水平和垂直方向的分块图案生成的，则分形中任意两点之间的弧线的长度都是无限的（Cristea和Steinsky在Geom Dedicata 141（1）：1-17中； Proc Edinb Math Soc 54 （2）：329-344，）。在混合迷宫形分形的情况下，使用一系列迷宫图案来构造枝晶。在本文中，我们将重点放在混合迷宫形分形点之间的弧长。我们表明，根据序列中模式的选择，两种情况都可能发生：分形的任意两点之间的弧长有限，或者分形的任意两点之间的弧长无限。这与自相似情况形成了鲜明的对比。
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