# Exploring Fractals

## Mary Ann Connors

#### 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, 2014, 2015, 2016, 2017 and 2018.

© Copyrighted 1994,1995,1996,1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017 and 2018 by Mary Ann Connors.

### 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

1. is self-similar and
2. 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

Generating Fractals
Strictly Self-similar Fractals

Teacher Information
Instructions

`SourcesSources for Exploring Fractals Some Interesting Links for Further Exploration.`

Last updated: January 11, 2018

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, 2015, 2016, 2017 and 2018 by Mary Ann Connors.

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.