  Labyrinth fractals are dendrites in the unit square. They were introduced and
studied in the last decade first in the self-similar case [Cristea & Steinsky
(2009,2011)], then in the mixed case [Cristea & Steinsky (2017), Cristea &
Leobacher (2017)]. Supermixed fractals constitute a significant generalisation
of mixed labyrinth fractals: each step of the iterative construction is done
according to not just one labyrinth pattern, but possibly to several different
patterns. In this paper we introduce and study supermixed labyrinth fractals
and the corresponding prefractals, called supermixed labyrinth sets, with focus
on the aspects that were previously studied for the self-similar and mixed
case: topological properties and properties of the arcs between points in the
fractal. The facts and formulae found here extend results proven in the above
mentioned cases. One of the main results is a sufficient condition for infinite
length of arcs in mixed labyrinth fractals.
