On circular inversions and fractals

In this thesis, the inverses of the lines and of the taxicab circles under the inversion transformation with respect to the taxicab circle has been analyzed and classified analytically. In addition, p-circle inversion and p-circle fractal examples are studied. This thesis consists of seven chapters. The first chapter contains the introduction and purpose of the thesis. In the second part, the literature research on the subject of the thesis is given. In the third chapter, basic definitions and concepts in the taxicab plane geometry are presented. In the fourth part of the thesis, the inverses of the lines under the inversion transformation with respect to the taxicab circle in the taxicab plane, and in the fifth part of the thesis, the inverses of the taxicab circles are analyzed and classified analytically. In the sixth chapter of the thesis, p-circle fractal examples are presented by examining p-circle inversions. In the last part, the conclusions and recommendations of the study are given.