Inversions and Fractal Patterns in Alpha Plane

Abstract

In this paper, we introduce the alpha circle inversion by using alpha distance function instead of Euclidean distance in definition of classical inversion. We give some proporties of alpha circle inversion. Also this new transformation is applied to well known fractals. Then new fractal patterns are obtained. Moreover we generalize the method called circle inversion fractal be means of the alpha circle inversion. In alpha plane, we give a generalization of alpha circle inversion fractal by using the concept of star-shaped set inversion which is a generalization of circle inversion fractal.

The Alpha Distance Formulae

“…They are very suitable for new studies since it includes infinitely many metrics in which the alpha can be considered as a weight that can reflect relative importance of different criteria or dimensions. On the other hand, the derived conclusions are rather wide (for example see [6,7,9]).…”