Examination of traditional and v-variable fractals

In this paper, we begin in Chapter 1 by giving a brief overview of the history of fractal geometry, focusing on six of the most important mathematicians in this field. Chapter 2 explains the main definitions needed for the remainder of the paper. In Chapter 3, we clarify the process of creating fractals from iterated function systems. Chapter 4 consists of an examination of the properties of traditional fractals. Next, in Chapter 5, we examine the newly discovered V-variable fractals and their properties. Finally we consider applications and future research in the field of fractal geometry