AI Summary & Key Takeaways
AI InsightFinally, we give several geometrical properties of this fractalby using the intrinsic metric formula.
📌 3 Key Takeaways
Abstract
To formulate the intrinsic metrics by using the code representations of the points on the classical fractalsis an important research area since these formulas help to prove many geometrical and structural properties of thesefractals. In various studies, the intrinsic metrics on the code set of the Sierpinski gasket, the Sierpinski tetrahedron, andthe Vicsek (box) fractal are explicitly formulated. However, in the literature, there are not many works on the intrinsicmetric that is obtained by the code representations of the points on fractals. Moreover, as seen in the studies on thissubject, the contraction coefficients of the associated iterated function systems (IFSs) are the same for each fractal. Inthis paper, we define the intrinsic metric formula on the added Sierpinski triangle, whose IFS has different contractionfactors, by using the code representations of the points of it. Finally, we give several geometrical properties of this fractalby using the intrinsic metric formula.