Fractal Geometry

An Internet-Based Treasure Hunt

Introduction

Fractals are geometric figures, but they have different properties than classical shapes such as triangles, rectangles, or circles. Few objects in nature have the form of a rectangle or triangle, but many are shaped like fractals. Whether they are generated by computer or nature, fractals are dazzlingly beautiful. This treasure hunt will help you to gain an awareness of this amazing branch of living geometry.

Questions

1. What is a fractal?
2. Who created the term "fractal" and when was it created?
3. Describe at least three ways that fractal geometry different from traditional Euclidean geometry.
4. How do iteration and recursion relate to fractal geometry?
5. What does is mean when a fractal is described as being self-similar? Give an example of self-similarity in nature.
6. What kind of dimension do fractals have?
7. What is unusual about the perimeter of the Koch Snowflake? Does its area exhibit the same unusual properties?
8. Name four well-known fractals.
9. List three examples of fractals in nature.
10. Go to self-similarity and fractals and answer questions #1-4.

Internet Resources

• Fractal Overview
• Why Study Fractals?
• Self-Similarity
• Fractals and Self-Similarity
• Natural Fractal
• Mandelbrot Set Zoom
• Fractal Dimension
• Fractal Geometry
• Fractal Music Lab
• Apollonian Gasket
• Dictionary

"Mathematics, rightly viewed, possesses not only truth but also supreme beauty”

Images

• Cygnus Software Gallery
• Alice Kelley Gallery
• Jos Leys Fractals
• Infinite Art of Kerry Mitchell and Janet Parke
• Hidden Dimension Fractals
• Fractal Factory
• Mathemagic Images
• Barbara Rubin's Fractal Art
• Gumbycat's Fractals
• Fractal World
• Fractal Dimentia
• QMI Fractal Gallery
• 3D Fractals Gallery
• Elements of Design
• Chaffey High School Fractal Links
• Sarah Scotland's Fractal Gallery
• Fractal Daydreams

Interactive Explorations

Animations and Movies

• Sierpinski Zoom
• Sierpinski Pyramid
• Broccoli
• Binary Tree
• Ternary Tree
• The Fractal Movie Theater

The Sierpinski Triangle

The Sierpinski Carpet

Jurassic Fractal

Go to Studying Mandlebrot Fractals and investigate the fractal. Follow instructions #1-3. Answer questions #4-7.

Requirements

1. Using the internet resources, answer questions 1-10.

2. Do the interactive explorations and answer the questions in the Mandlebrot Exploration.

3. View the images, select your favorite one, and print it.

4. View the animations and movies.