Fractal Project - Due January 15, 2008

Fractal project:

This project has been adapted from a webquest designed by Sharon Swihart: http://www.manteno.k12.il.us/webquest/middle/Math/Fractals/fractalquest.htm

INTRODUCTION FRACTALS:
What IS a fractal? Is it more than an interesting shape? Who uses them and for what reason? In this project, you will find answers to these questions and begin your understanding of fractals.

TASK
Through this project you will become more familiar with fractals by exploring a variety of resources. First you will develop a working definition of fractals. Then you will move into your role of Mathematician, Historian, Application Expert and Artist to learn more. You will hand in a report answering the questions posed by each role and include some fractal work that you create.

PROCESS
You may use the supplied Web resources or do your own research to answer the questions and do the required activities. Prepare a report that includes a section for each part detailed below. Your report should include a page that lists all resources that you used.
Sources:
http://www.math.umass.edu/~mconnors/fractal/fractal.html
http://math.rice.edu/~lanius/frac/Tch_Notes/
http://math.bu.edu/DYSYS/chaos-game/chaos-game.html
PH Chapter 10 project links: pages 144,158,165,171

I. Mathematician - Your job will be to explore fractals mathematically. In your written report you should include the answers to the following:

1. What is a fractal?
2. To what branch of mathematics do fractals belong?
3. What mathematics and tools are needed to produce fractals?
4. Give an example of a formula that produces a fractal and show the fractal it produces.
5. What is fractal dimension? What formula is used to determine this? Give an example.

II. Application Expert - Your job will be to determine how fractals are used. In your written report you should include the answers to the following:

1. How are fractals used in mathematics?
2. What other fields use fractals and to do what? Give at least two examples.
3. What is an iteration and how does it apply to fractals?

III. Historian - Your job will be to investigate both the history of fractals and some of the current work being done in fractals. Your report will need to include the answers to the following:

1. How long have fractals been around?
2. Who is the "father of fractals" and when did he begin his work? Give an example of his work. (Is he still around?)
3. Who are two other mathematicians who have worked with or are currently researching fractals? Briefly describe what they are doing.

IV. Artist - Your job will be to investigate fractals as art. Generate your own fractal image either by sketching on paper or using a computer generated program. Include a description of how you generated the image. You may reproduce a known fractal like Sierpinkski’s triangle or a Koch snowflake or create your own image. Do not simply print an image from the web.