Sequential Labyrinth Fractals

Abstract

This paper introduces the concept of a sequential labyrinth fractal constructed on a unit square using two sequences. It also explains how the obtained fractal differs from the classical labyrinth fractal, mixed labyrinth fractal, and supermixed labyrinth fractals. The Hausdorff and the box-counting dimension of sequential labyrinth fractals, which are constructed using convergent sequences, are also examined. Besides that, it gives the dimension of fractals on the unit square, which are generated from converging sequences, but without having the labyrinth conditions.