LCP Sets And Fractals

• Main Authors: Lin Feng-Mei, 林鳳美
• Other Authors: Mau-Hsiang Shih
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/42161927326500259366

碩士 === 中原大學 === 數學研究所 === 86 === The word "fractal" was initiated by Benoit Mandelbrot in the late 1970s, and Mandelbrot's definition of the fractal is a set whose Hausdorff dimension isnot an integer. LCP sets arise in deterministic constructions of curves self-similarities under changes in scale and the Sierpinski Gasket. The purpose of this thesis is study the Koch Snowflake Curve, the Koch Island Curve, the PeanoCurve, the Self-Intersection Curve, and the Sierpinski Gasket. Above four curves and the Sierpinski Gasket are constructed in section 3 and section 4. Let us mention that different approaches of the curves and Sierpinski Gasket can also be found in H. Jurgens and D. Saupe[3] and M. F. Barnsley[4]. The real limit functions of the LCP sets appear in parametrizing various fractal-like objects for example the Koch Snowflake Curve, the Koch Island Curve, the Peano Curve, the Self-Intersection Curve and the Sierpinski Gasket. In this thesis, we shall use "limit function" technique to construct certain fractals.