Studying Mandelbrot Fractals


NOTE: Use of Internet Explorer 5.0 is recommended.

What is a fractal?

Alan Beck in What Is a Fractal? And who is this guy Mandelbrot? writes:
    "Basically, a fractal is any pattern that reveals greater complexity as it is enlarged. Thus, fractals graphically portray the notion of 'worlds within worlds' which has obsessed Western culture from its tenth-century beginnings."

1. Click on the button Col+ or Col- to change the colors of the fractal image.

2. Now that you have the colors set to your liking, it is time to investigate the fractal itself!

3. Using the mouse, draw a small rectangle on the fractal image. Click on Go and watch as the smaller section of the image is redrawn to fill the fractal screen.

4. What do you notice? How do the images compare? Click on the Out button to revisit the first image and the In button to return to the enlarged image.

5. Continue going into the fractal image. What do you observe?

6. It has been stated that fractals have finite areas but infinite perimeters. Do you agree? Why?/Why not?

7. Notice the values for x, y, w, and h. How do they change as you move closer and closer to the fractal image?

applet authored by José Luis Abreu

Why study fractals?

Why Study Fractals? by Cynthia Lanius provides an excellent tutorial, Making A Fractal: The Sierpinski Triangle.

Other sites with information about fractals:

Chopping Broccoli
How to make a fractal, examples of students' fractals, What's So Hot About Fractals, notes for teachers, and links to relevant math history resources.

Geometry Junkyard - Fractal Pile
A collection of usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other stuff related to discrete and computational geometry - some serious and much also entertaining.

Math Forum Fractal Links
A comprehensive listing of fractal sites on the web.

Mathland - Fractals by Ivars Peterson
It's possible to convert Pascal's triangle into eye-catching geometric forms. For example, one can replace the odd coefficients with 1 and even coefficients with 0. Continuing the pattern for many rows reveals an ever-enlarging host of triangles, of varying size, within the initial triangle. In fact, the pattern qualifies as a fractal. The even coefficients occupy triangles much like the holes in a fractal known as the Sierpinski gasket.

Fractal FAQ
A FAQ posted monthly to sci.fractals, a Usenet newsgroup about fractals; mathematics, and software, aimed at being a reference about fractals, including answers to commonly asked questions, archive listings of fractal software, images, papers that can be accessed via the Internet, and a bibliography for further readings. The FAQ does not give a textbook approach to learning about fractals, but a summary of information from which you can learn more about and explore fractals.

Tons of Links to Fractals - Chaffey High School
An extensive list of sites dealing with fractals ranging from images and animations to programs.

What is a Fractal? - Sarah Seastone
A short description (with illustrations of the Mandelbrot Set) of fractals, paraphrased from Chapter 1, "A Mathematical and Historical Tour," of Robert Devaney's, A First Course in Chaotic Dynamic Systems.

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