Complimentary Microworld: Fractals and the Mandelbrot Set
Click the Hyperlink above to visit the Microworld in your Browser.
Author: Jim Swift

This 12 page Microworld is an interactive introduction to Fractals and the Mandelbrot set. It steps through the construction of that set, developing the notion of complex iterated maps, and provides many exercises that can illustrate the basic ideas. The book is accompanied by a number of dazzling pictures that support exploration of well-known properties of the Mandelbrot set, and that lead the reader to investigate some mysterious connections with the Fibonacci sequence.

There are three kinds of pages in this Microworld.

  • Descriptive material giving background information and/or instruction about the interaction on a following page. This includes Windows Help that you may pop up on each page.
  • Interactive pages that give you the opportunity to explore hypotheses about the Mandelbrot iteration, and observe how these iterations go, step-by-step. Along thw way, you will learn a little about complex numbers and Fractals.
  • Exercise pages where you can practice what you have learned on the interactive pages.

Return to the listing of MathwrightWeb Microworlds

Once you download our free Mathwright32 Reader above, then simply click Get This Microworld, and it will be downloaded to your machine and installed in a directory there. You may find it whenever you want to view it, by going to the Start, Programs, Mathwright32 Reader menu.

To visit our Microworlds in your browser, it must be able to read ActiveX controls. Microsoft Internet Explorer 4.0 Browser (or later) is so equipped. You should check that the Security Settings under Tools, Internet Options, Security for the Internet, Custom Level has:

  • "Run ActiveX Controls and Plugins" set either to enable or prompt.
  • "Initialize and Script ActiveX Controls not marked as safe" set either to enable or prompt.
- James E. White, Ph.D. , Library Director,
author of this website, Mathwright 2000, MindScapes,
MathwrightWeb, and Mathwright32

 

Mathwright Visualization Studio free demonstration Microworld:

Fractals and the Mandelbrot Set

 

This 10 year old work began life in 1993 as a WorkBook for IBM's Toolkit for Interactive Mathematics. It exemplifies the goals of structured discovery learning so well that we have translated it without change to our Microworld format so that you may view it either in your browser or offline. It is one of our new free Visualization Studio Microworlds in the Math Cafe, and readers are invited to check it out before joining the Library to get a glimpse of what is possible with Mathwright.

There is much that has been said about the Mandelbrot iteration and its intriguing and colorful Fractal display. Jim Swift found something new to say, that he formulates as a conjecture for readers to pursue. The book steps through the strategy of complex iteration, so that the reader can get a clear visual understanding of the structure of the set. Once he sets the stage for his conjecture, he asks the reader to navigate the "bays" of the fractal design:

to discover in it the successive terms of the famed Fibonacci sequence! Now that is an unexpected connection indeed! But it is perhaps not a surprise that Fibonacci found his way to the unexpected Fractal shores of a future magical sea.

The Microworld features a new capability of Mathwright (available since version 2.10, May 12, 2003) that makes use of Windows Help to give pop-up information about each page if the reader desires it. This is new for MathwrightWeb, but was part of the original WorkBook.

 

 

 

 

 

 

 

 

 

 

 

 

 

Requires the Java MathwrightWeb ActiveX Control to read in your Browser.
For proper viewing, be sure to use Version 2.10 or later, dated May 12, 2003


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Library members, download the free Mathwright32 Reader, then press

For proper viewing, be sure to use Version 2.10 or later, dated May 12, 2003