**
**# Exploring Fractals

### by

#### Department of Mathematics and Statistics

University of Massachusetts
Amherst

<> This World Wide Web project commenced in July 1994. It is is
based
on a curriculum, entitled "Exploring Fractal Dimension," developed
by Mary
Ann Connors and Anna Rose Haralampus at an
NSF funded Institute for High School Mathematics Teachers at Georgetown
University July - August, 1991. Its revision entitled
"Exploring Fractals: From Cantor Dust to The Fractal Skewed Web" has
been edited by Mary Ann Connors 1994, 1995, 1996, 1997, 1998, 1999,
2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010,
2011, 2012, 2013, and 2014.<>

© Copyrighted 1994,1995,1996,1997,
1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 and 2015 by Mary
Ann
Connors.

All rights reserved.
### Exploring Fractal Dimensions of Strictly Self-Similar Fractals:

Cantor Dust to the Fractal Skewed Web

**What is a fractal?**

A *fractal * is a geometric shape which

- is self-similar and
- has fractional (fractal) dimension.

**An introduction**

So,
what are fractals?

**What does it mean for a shape
to be self-similar**

Strictly
Self-similar shapes

**What is dimension?**

How
do we assign dimension to an object intuitively?

**What is the dimension of a
geometric object?**

Mathematical
Interpretation

**Dimension of a Fractal**

Non-integer
and integer dimensions

**Investigations**

Questions
and Answers.

**Generating Fractals**

Strictly
Self-similar Fractals

**Teacher Information**

Instructions

**Sources**

Sources for Exploring Fractals

Some Interesting Links for Further Exploration.

Last updated: September 5, 2014

Updated by: Dr.
Mary Ann Connors

© Copyrighted 1994,1995,1996,1997,
1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 and 2015 by Mary
Ann
Connors.

All rights reserved.

<>If you wish to use any of the text or images in **Exploring
Fractals**
please contact its author Mary Ann Connors at the following address.

Thank you.

Dr. Mary Ann Connors
*email: mconnors@math.umass.edu
*

or

email: mconnors@westfield.ma.edu

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“Exploring Fractal Dimension, Area and Volume” is published in the
2010 MAA Notes # 76, The Beauty of
Fractals: 6 Different Views edited by Denny Gulick and Jon
Scott, the Mathematical Association of America,pp. 51-61. http://www.maa.org/ebooks/notes/NTE76.html

"Fractals", a modified version of Exploring Fractals, is
a Case Study in the Calculus/Math Modules published by PWS Kent.