created by Kevin Glaser

Manchester Regional High School

Introduction | The Task | The Process & Resources | Conclusion | HyperText Dictionary

You have entered a world of strange and unusual shapes with a name that somehow seems fitting: FRACTALS. The name itself seems to conjure up images of small broken pieces and that is what these fascinating figures seem to look like. What IS a fractal? Is it more than an interesting shape? Who uses them and for what reason? In this WebQuest you will find answers to these questions and begin your understanding of fractals.

Through this WebQuest you will become more familiar with fractals by exploring a variety of resources. First you will develop a working definition of what a fractal is as a group. Then you will move into your roles of Mathematician, Historian, Application Expert and Artist to learn more. Finally, you will come together as a group to share what you have learned. You will hand in a written report containing at least four pages (one from each member of your team) and any activities required by your role. Finally, you will present what you have learned to the class using a PowerPoint Presentation.

In this WebQuest you will be working together in groups of four. Each of the four members will have a distint job: either a Mathematician, Historian, Artist, or Application Expert. As a member of the group you will explore Webpages from people all over the world who care about Fractals. Because these are real Webpages we're tapping into, not things made just for schools, the reading level might challenge you. Feel free to use an online dictionary (dictionary.com) or one in your classroom.

You'll begin with everyone in your group getting some background before beginning the work your job entails.

Use the Internet information linked below to answer the basic questions of who? what? where? when? why? and how? Be creative in exploring the information so that you answer these questions as fully and insightfully as you can.

- Fractals Lesson - A fractals unit for elementary and middle school students.
- Exploring Fractals - This website continues general and more advanced information about fractals.
- The Fractal Microscope - This website contains information about supercomputing and fractals.
- Sprott's Fractal Gallery - A gallery of fractal art.
- Fractals Theme Page - This website contains information relevant to the teaching of fractals and curriculum.
- The Math Forum Home Page - A forum for users to ask mathematics related questions.
- Spanky Other Images - Another Gallery of Fractal Art.
- Mathematics Archives - This website contains several different links to websites and articles pertaining to websites.

INSTRUCTIONS:

1. Individuals or pairs from your larger WebQuest team will explore one of the roles below.

2. Read through the files linked to your group. If you print out the files, underline the passages that you feel are the most important. If you look at the files on the computer, copy sections you feel are important by dragging the mouse across the passage and copying / pasting it into a word processor or other writing software.

3. Note: Remember to write down or copy/paste the URL of the file you take the passage from so you can quickly go back to it if you need to to prove your point.

4. Be prepared to focus what you've learned into one main opinion that answers the Big Quest(ion) or Task based on what you have learned from the links for your role.

## Mathematician

Use the Internet information linked below to answer these questions specifically related to role, job or perspective #1: Mathematician: Your job will be to explore fractals mathematically. Your results, first in written form, should include answers to the following:

1. To what branch of mathematics do fractals belong?

2. What mathematics and tools are needed to produce fractals?

3. Give an example of a formula that produces a fractal and show the fractal it produces.

4. What is fractal dimension? What formula is used to determine this? Give an example.

## Historian

Use the Internet information linked below to answer these questions specifically related to role, job or perspective #2: 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. In what other fields are fractals being used and to do what? Give at least two examples.

3. What is an iteration and how does it apply to fractals?

4. Go to 'A Fractals Lesson' and do one of the activities found there to generate your own fractal. Include it as part of your report.

## Application Expert

Use the Internet information linked below to answer these questions specifically related to role, job or perspective #3: 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.

## Artist

Use the Internet information linked below to answer these questions specifically related to role, job or perspective #4: Artist Your job will be to investigate fractals as art. You will need to include the following in your report:

1. Are fractals mathematics or are they art?

2. What medium is used to produce fractals?

3. Who are some fractal artists? (Name at least three.) Are they artists or mathematicians?

4. Visit a fractal art gallery and bookmark at least two fractal drawings you like. Include a description of them or put their URL's in your written report and make a link to them in your PowerPoint presentation.

You have all learned about a different part of Fractals. Now group members come back to the larger WebQuest team with expertise gained by searching from one perspective. You must all now answer the Task / Quest(ion) as a group. Each of you will bring a certain viewpoint to the answer: some of you will agree and others disagree. Use information, pictures, movies, facts, opinions, etc. from the Webpages you explored to convince your teammates that your viewpoint is important and should be part of your team's answer to the Task / Quest(ion). Your WebQuest team should write out an answer that everyone on the team agrees with.

You and your teammates have learned a lot by dividing up into different roles. Now's the time to put your learning into a letter you'll send out for real world feedback. Together you will write a letter that contains opinions, information, and perspectives that you've gained. Here's the process:

1. Begin your letter with a statement of who you are and why you are writing your message to this particular person or organization.

2. Give background information that shows you understand the topic.

STATE THE TASK / QUEST(ION) AND YOUR GROUP'S ANSWER.

3. Each person in your group should write a paragraph that gives two good reasons supporting the group's opinion. Make sure to be specific in both the information (like where you got it from on the Web) and the reasoning (why the information proves your group's point).

4. Have each person on the team proofread the message. Use correct letter format and make sure you have correctly addressed the email message. Use the link below to make contact. Send your message and make sure your teacher gets a copy.

Your Contact is:the designated contact

This WebQuest is designed to introduce you, the middle school or high school student, to a field of mathematics that may be totally unfamiliar to you. It is my hope that you will have as much fun exploring these fascinating figures we call fractals, their history and their source as I did. I hope also that it may inspire you to continue to learn and explore, not only fractals, but also the many other interesting fields of mathematics that exist.

Content by Kevin Glaser, qheven@yahoo.com http://www.kn.sbc.com/wired/fil/pages/webfractalske.html Last revised Sat Mar 27 7:34:19 US/Pacific 2004 |