Fractals: Math or Art???

Introduction:

In this activity you will be exploring Geometric fractals and their connections to math, art, and nature.  What is a fractal? Is it more than an interesting shape? Who uses them and for what reason? In this Web Quest you will find answers to these questions and begin your understanding of fractals.

The Task:

Working with a partner your task will be to investigate Fractal Geometry on the Internet.

Make a presentation that includes the following:

• Definition of a fractal
• At least 3 reasons why we study fractals
• Definition of iteration
• Common properties of all fractals
• List five types of fractals
• Identify the father of fractals
• Identify 4 fractals of nature
• Your explanation to the question - Fractals: Math or Nature?
• Your favorite fractal 

Construct a fractal by:

• Folding paper to create a Jurassic Park Fractal
• Folding paper with a computer to create a Jurassic Park Fractal
• Using Sierpinski's Triangle and triangular grid paper 
• Using Sierpinski's Triangle and Geometers Sketchpad

Resources:

Use the following sites to help you find the information that you need.

The Process: 

Establish you and your partners roles.

Presentation

• Visit the sites listed above to help you with your presentation
• While visiting each site keep in mind what you are looking for - take notes
• Presentation must include at least one technology component - (ex: Power Point, word processing program if writing a paper, Internet for graphics etc.)
• Use fractal galleries to help you find your favorite fractal -- then  be sure to save the image to disk

Fractal Construction - Jurassic Park

• Visit the paper folding site
• Use a 1" x 11" strip of paper to make your fractal
• Follow the instructions on the site to fold the fractal
• Using a chart, encode the fractal to the 5th iteration
• Using grid paper - draw the first 4 iterations of the fractal (each member of your group will need to turn a copy in to me)

Fractal Construction - Sierpinkski Triangle

• Visit the Sierpinkski Triangle site
• Print the triangle grid sheet (each member of the group will need to do this - and turn it in when completed)
• Follow steps 1-4
• Use your own creativity when coloring your completed Sierpinkski Triangle
• Make the Sierpinkski Triangle using Java
• Take the Sierpinkski quiz and e-mail me the results - (each member of the group will need to do this)

Evaluation: 

Your project will be graded on the following criteria: (you may want to print rubric)

  Presentation

  Constructed Fractals

  On Line Activities

  Conclusions

Conclusion:

This Web Quest was designed to introduce you to a field of mathematics that may be totally unfamiliar to you.  I hope this lesson has stimulated an interest in Fractal Geometry and an awareness of the connections between mathematics, art, and nature.  I invite you to  continue to learn and explore  not only this fascinating topic but also the many other interesting math fields that exist.

Last Updated:  June 12, 2006

Questions? Comments? Contact Kim Hall