On the computation of some code sets of the added Sierpinski triangle

Abstract

In recent years, the intrinsic metrics have been formulated on the classical fractals. In particular, Sierpinski-like triangles such as equilateral, isosceles, scalene, added and mod$-3$ Sierpinski triangle have been considered in many different studies. The intrinsic metrics can be defined in different ways. One of the methods applied to obtain the intrinsic metric formulas is to use the code representations of the points on these self-similar sets. To define the intrinsic metrics via the code representations of the points on fractals makes also possible to investigate different geometrical, topological properties and geodesics of these sets. In this paper, we investigate some circles and closed sets of the added Sierpinski triangle and express them as the code sets by using its intrinsic metric.