We introduce and study mixed triangular labyrinthic fractals, which can be seen as an extension of (generalized) Sierpiński gaskets. This is a new class of fractal dendrites that generalize the self-similar triangular labyrinth fractals studied recently by the authors. A mixed triangular labyrinthic fractal is defined by a triangular labyrinthic pattern and an infinite sequence of triangular labyrinth patterns systems, whereas one triangular labyrinth patterns system is sufficient for generating a self-similar triangular labyrinth fractal. Moreover, a labyrinthic pattern is more general than a labyrinth pattern, and the idea is that the use of many different patterns provides objects with a “richer” structure. After proving that these non-self-similar fractals are dendrites, we study the growth of path lengths in graphs associated with iterations. We prove geometric properties of the fractals, some of which have rather “local” character and on the other hand occur at sites distributed “all over” the fractals.

我们介绍和研究混合三角形迷宫分形，它可以看作是（广义）Sierpiński 垫圈的扩展。这是一类新的分形树突，它概括了作者最近研究的自相似三角形迷宫分形。混合三角形迷宫分形由三角形迷宫图案和三角形迷宫图案系统的无限序列定义，而一个三角形迷宫图案系统足以生成自相似三角形迷宫分形。此外，迷宫图案比迷宫图案更通用，其想法是使用许多不同的图案可以为对象提供“更丰富”的结构。在证明这些非自相似分形是树突之后，我们研究了与迭代相关的图中路径长度的增长。