The formulization of the intrinsic metric on the added sierpinski triangle

Due to its relationship with nature, one of the most important features of fractals, that have applications in many disciplines, is self-similarity. Thanks to this feature, especially on some classical fractals, the intrinsic metric can be described with the help of code representations of points. Recently, intrinsic metrics are formulated on self-similar sets such as the Sierpinski triangle, box fractal, Sierpinski tetrahedron and mod-3 Sierpinski triangle via the code representations. In this thesis, the intrinsic metric on the added Sierpinski triangle will be constructed by using the code representation of the points. The difference between this fractal and the other fractals given the intrinsic metric formulas in the literature formulas is that the contraction coefficients of the related iterative function systems are different. With this feature, it is the first theoretical study that formulates the intrinsic metric with the help of code representations. In addition, using this intrinsic metric formula, some geometric properties of the added Sierpinski triangle are given and compared with the related geometric properties of the Sierpinski triangle. Finally, using this formula, some topological sets are obtained by the code representations of points on the added Sierpinski triangle.