Self similar functions

ABSTRACT Master of Science Thesis SELF SIMILAR FUNCTIONS Derya ÇAKMAK Anadolu University Graduate School of Natural and Applied Sciences Mathematics Program Supervisor: Prof. Dr. Şahin KOÇAK 2004, 63 Pages The notion of "self-similarity" for sets is a fundamental concept of fractal geometry. But there is no agreement on the concept of "self-similarity" for functions. The condition of the self similarity of the graph of a function as a set is not a satisfactory approach for self similarity of functions. In this study we propose a new definition for self-similarity of functions on the example of the Sierpinski Gasket using the concepts of harmonic analysis on fractals. Then we have generalized the fractal interpolation theorem on intervals given by Barnsley to a fractal interpolation theorem on the Sierpinski Gasket. Keywords: Self Similar Functions, Fractal Interpolation, Harmonic Function, Contraction Mapping, Sierpinski Gasket. 11