About the paper
coauthor 
LigiaLoreta Cristea 
language 
English 
published in 
Fractals, 27, No. 08 (2019) 
page 
1950131 
DOI 
10.1142/S0218348X19501317 
supported by 
FWF, project P28991N35 
Abstract
We deﬁne and study a class of fractal dendrites called triangular labyrinth fractals. For
the construction we use triangular labyrinth pattern systems, consisting 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 selfsimilar, and fit into the framework of
graph directed constructions. The main results consist in showing how special families of
triangular labyrinth patterns systems, which are defined based on some shape features,
can generate exactly three types of dendrites: labyrinth fractals where all nontrivial
arcs have inﬁnite length, fractals where all nontrivial arcs have finite length, or fractals
where the only arcs of ﬁnite lengths are line segments parallel to a certain direction. We
also study the existence of tangents to arcs. The article 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 triangular shapes, some new techniques and ideas
are necessary in order to obtain the results.
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