Mathematics Project Abstract
COMPUTER EXPLORATIONS OF FRACTALS
Presenter:
Daniel Gulotta, Illinois Mathematics and Science Academy, 1500 West Sullivan Road, Aurora, IL 60506; dgulotta@imsa.edu
Advisor:
Steven Condie, Ph.D., Mathematics, Illinois Mathematics and Science Academy, 1500 West Sullivan Road, Aurora, IL 60506; scondie@imsa.edu; 630-907-5967
Abstract:
Fractals are everywhere. Clouds, trees, coastlines, mountains, capillaries, and galaxies exhibit self-similar structures. Despite their great complexity, these structures can be understood and recreated using mathematics. Many fractal phenomena appear in simple equations that lend themselves to computer experiments. Such experiments can lend crucial insight into the nature of fractals. In this presentation, we will discuss the iterative processes that give rise to fractals. We will examine the recursive functions that correspond to different types of fractals and look at how a computer can use them to quickly and accurately generate fractal images. We will observe some images to see what information they convey about the structure of fractals. This will allow us to make conjectures about these structures.