Computational Geometry of Period-3 Hyperbolic Components in the Mandelbrot Set

Mathematics

Young-Hee Geum¹  Young-Ik Kim¹ 

[1] Department of Mathematics, Dankook University, Cheonan 330-714, Korea;

关键词: parameter space;    Mandelbrot set;    budding point;    hyperbolic component;    critical orbit;   

DOI  :  10.3390/math9192519

来源: DOAJ

【 摘 要 】

A parametric theoretical boundary equation of a period-3 hyperbolic component in the Mandelbrot set is established from a perspective of Euclidean plane geometry. We not only calculate the interior area, perimeter and curvature of the boundary line but also derive some relevant geometrical properties. The budding point of the period-$3k$ component, which is born on the boundary of the period-3 component, and its relevant period-$3k$ points are theoretically obtained by means of Cardano’s formula for the cubic equation. In addition, computational results are presented in tables and figures to support the theoretical background of this paper.

【 授权许可】

Unknown