Date of Award

Spring 2003

Document Type

Thesis

Department

Mathematics, Engineering & Computer Science

First Advisor

Holly Zullo

Second Advisor

Jack Oberweiser

Third Advisor

Cheryl Conover

Abstract

Video games are an integral pastime of current youths. Initially, popular video games were created in a two-dimensional scene. As the field of computer technology has advanced, the ability to create realistic three-dimensional games has become available. Now, nearly every video game is three-dimensional and the desire for two-dimensional games has dwindled. Modem video game developers face the issue of creating realistic simulations of world objects in their games to compete with fierce competition. Often, if a video game can create a stunning sense of realism, it can awe its viewers and push them to purchase a video game based on graphics alone. The need to incorporate realistic simulations of our world extends beyond video games and into fields such as movies, simulators, and art.

In any computer programming production, programmers must be able to develop quickly in this market of rapid application development. Efficient programmers strive to find a general solution to a programming issue rather than a specific solution. Programmers look to find a way to code computers to solve a problem for all cases, rather than for just one case. If this general solution is found, it can be used to speed up the computer programming process, saving time. Modem game programmers are faced with many more problems in programming in the three-dimensional sense as opposed to the two-dimensional. One of these problems is the issue of how to create life-like structures such as landscapes, trees, rocks, rivers, vegetation and more. Even more specifically, video game developers need to create these structures in real time. This kind of question pushes modem “reality” modelers and programmers to turn to mathematics. Common mathematical solutions to these problems include Fourier Synthesis, Fractal Geometry, and Perlin Noise. My research was focused on methods in Fractal Geometry. Due to the Fractal Geometry of nature itself, Fractal Geometry proves to be excellent for creating realistic models of many structures in our world. This research focuses on many methods for the creation of realistic world structures through repetitive processes programmed using mathematical techniques. This work intends to give the reader an overall view of the technique of Fractal Geometry, its history and its generation. I will show many Fractal images as well as explain mathematical methods for their generation. Fractal images are an example of the beauty of visualizing mathematics. Because Fractal Geometry is expressed through the visualization of images, many of my personal attempts with their mathematics will be implemented on the computer. In programming, my focus is to provide the reader with a walkthrough of Fractals applied. That is, I will not only explain an algorithm, but I will explain how to encode these algorithms to achieve the results. All examples of code are written in C++ computer code.

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