\section{Executive Summary} 
This Interactive Qualifying Project explores the overlap between the subjects of fractals and art.  We sought to find out how mathematics could be involved in the process of creating art and to explore the humanistic side of fractals.  To do this, we explore several different kinds of fractals, explain their mathematical definition, and show how they could be used to generate aesthetically beautiful images.  Then we explore the sociological side of fractal art, and we analyze the psychology behind the aesthetic beauty found in several pieces of fractal art.

This report begins with a brief introduction to the topic of fractals and then addresses the question of whether fractals can be considered a form of art.  At this point, we establish the goal for this project: to prove that fractal art is a new form of art.  Proceeding from this point, we give a general mathematical background of some of the mathematical details of several kinds of fractals, including the Mandelbrot and Julia sets, iterated function systems, and L-Systems.  Then we describe the concept of fractal dimension, and demonstrate how to calculate the dimension of several example fractals.  Using this infromation, we explore how the concept of fractal dimension can be applied to works of art.

From this point the report delves into more humanistic issues. It
is interesting to generate classic fractals such as the Koch curve and 
Sierpinski gasket, but how can we use fractals to create truly beautiful art?
We show how fractals can be used to generate music, and we discuss the artistic value of such music. 
Next, we explore the relationship between art and society.  Theories of
how society is reflected in art are discussed, and we try to answer the question,``What does fractal art say about our society?''  Finally, we apply existing psychological studies about the perception of art to a few pieces of work by fractal artists, to show that many of the same qualities found in traditional art can also be found in fractal art.


