# Fabulous Fractals and Difference Equations

Laura Zager
Ropes and Gray Law Firm
Boston, Massachusetts, U.S.A.

Lesson vetted and approved by CPALMS

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Presentation of the Chaos Game
http://www.jcu.edu/math/vignettes/ChaosGame.htm

A site full of materials useful for middle and high school students, sponsored by the Community Learning Network
http://www.cln.org/themes/fractals.html

An interactive lesson on fractals
http://www.shodor.org/interactivate/lessons/PropertiesOfFractals/

An interactive lesson on patterns in fractals
http://www.shodor.org/interactivate/lessons/PatternsInFractals/

An interactive lesson on fractals: infinity, self-similarity and recursion
http://www.shodor.org/interactivate/lessons/InfinityRecursion/

An interactive lesson on fractals and the Chaos Game
http://www.shodor.org/interactivate/lessons/FractalsAndTheChaos/

#### Yes, it is okay to put this

December 19, 2011 at 6:53 am

Yes, it is okay to put this video on Facebook. Glad you like it. I will tell Dr. Zager.

#### درس رائع جدا كذلك تقديم رائع

December 18, 2011 at 12:28 pm

درس رائع جدا

كذلك تقديم رائع من قبل المعلمة

هل نستطيع ان ننشر هذا الفديو في صفحات الفيس بوك؟

#### Amazing! Many thanks. I'm

November 13, 2011 at 8:45 pm

Amazing! Many thanks. I'm going to run this as a launching point for my Grade 9 enrichment class in Vancouver, Canada.

#### Yes, it is okay to put this

December 19, 2011 at 6:53 am

Yes, it is okay to put this video on Facebook. Glad you like it. I will tell Dr. Zager.

#### درس رائع جدا كذلك تقديم رائع

December 18, 2011 at 12:28 pm

درس رائع جدا

كذلك تقديم رائع من قبل المعلمة

هل نستطيع ان ننشر هذا الفديو في صفحات الفيس بوك؟

#### Amazing! Many thanks. I'm

November 13, 2011 at 8:45 pm

Amazing! Many thanks. I'm going to run this as a launching point for my Grade 9 enrichment class in Vancouver, Canada.