Fabulous Fractals and Difference Equations

Fabulous Fractals and Difference Equations


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

Lesson Feedback


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.

Additional Online Resources

Presentation of the Chaos Game

A site full of materials useful for middle and high school students, sponsored by the Community Learning Network

An interactive lesson on fractals

An interactive lesson on patterns in fractals

An interactive lesson on fractals: infinity, self-similarity and recursion

An interactive lesson on fractals and the Chaos Game