论文标题
三角迷宫分形
Triangular labyrinth fractals
论文作者
论文摘要
我们定义并研究了一类称为三角形迷宫分形的分形树突。对于构造，我们使用由两个三角形模式组成的三角迷宫模式系统：白色和黄色。相应地，我们有两个分形：白色和一个黄色的分形。这里研究的分形是自相似的，并且适合图形构造的框架。 The main results consist in showing how special families of triangular labyrinth patterns systems, defined based on some shape features, can generate exactly three types of dendrites: labyrinth fractals where are all nontrivial arcs have infinite length, fractals where all nontrivial arcs have finite length, and fractals where the only arcs of finite length are line segments parallel to a certain direction.我们还研究了弧线的切线。该论文的灵感来自对过去十年中研究单元正方形中迷宫分形的研究。在三角形的情况下，由于创伤形状的几何形状，为了获得结果，需要一些新的技术和思想。
We define and study a class of fractal dendrites called triangular labyrinth fractals. For the construction, we use triangular labyrinth patterns systems that consist of two triangular patterns: a white and a yellow one. Correspondingly, we have two fractals: a white and a yellow one. The fractals studied here are self-similar, and fit into the framework of graph directed constructions. The main results consist in showing how special families of triangular labyrinth patterns systems, defined based on some shape features, can generate exactly three types of dendrites: labyrinth fractals where are all nontrivial arcs have infinite length, fractals where all nontrivial arcs have finite length, and fractals where the only arcs of finite length are line segments parallel to a certain direction. We also study the existence of tangents to arcs. The paper is inspired by research done on labyrinth fractals in the unit square that have been studied during the last decade. In the triangular case, due to the geometry of traingular shapes, some new techniques and ideas are necessary in order to obtain the results.
