Curated OER
Fractals Lesson Plan
Students create fractals. In this lesson, students use a computer program to explore different types of fractals.
Curated OER
The Mandelbrot Set
Learners explore the concept of Mandelbrot sets and Julia sets. In this Mandelbrot and Julia set lesson, students use a function integrator applet to investigate two-variable function iterations. Learners use Julia set and Mandelbrot set...
Curated OER
Complex Analysis: Complex Variables
In this complex variable worksheet, students use functional iteration to find the fixed points of a function. This two-page worksheet explains the functional iteration, the Julia Set and the Mandelbrot set. Four problems are included.
Curated OER
Two-Variable Function Pump Exploration Questions
Guiding students through two variable (complex) functions, this worksheet helps them perform complex arithmetic on 6 expressions. They iterate several functions with given starting points, determining whether each is a prisoner, escapee,...
Curated OER
The Mandelbrot Set
Students explore the Mandelbrot Set. They are introduced to the concept of a complex number and function in order to motivate the discussion of Julia and Mandelbrot sets. Students investigate fractals and how they are built.
University of California
Geometry Junkyard
An interesting junkyard of geometry findings where people are free to add their own findings and sift through others' interesting additions.
Shodor Education Foundation
Shodor Interactivate: Lesson: The Mandelbrot Set
In this instructional activity students will explore Julia sets and the Mandelbrot set. In the process they will learn about fractals and explore complex numbers and function iteration.
Boston University
Fractal Geometry of the Mandelbrot Set Ii
This web site addresses counting and adding in fractal operations, as well as the role of the Fibonacci sequence in fractal geometry.
Texas Instruments
Texas Instruments: Key Curriculum Press Algebra: Project the Mandelbrot Set
Students will choose a small region on the boundary of the Mandelbrot Set and create a graph of that smaller region.
PBS
Pbs: Nova: A Sense of Scale
Students can use this interactive tool to explore a Mandelbrot set of fractals. As they increase magnification up to 250,000,000 times, they keep returning to an image similar to the one they started with.
Other
University of Edinburgh: Glossary of Introductory Computer Graphics Terms
This website, from the University of Edinburgh, provides a lengthy glossary of computer graphics terms written by Olin Lathrop, author of "The Way Computer Graphics Work". This site provides simple definitions of basic terms; no graphics...
Shodor Education Foundation
Shodor Interactivate: The Mandelbrot Set
Explore fractals by investigating the relationships between the Mandelbrot set and Julia sets.
Shodor Education Foundation
Shodor Interactivate: Two Variable Function Pump
Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form.
Mathigon
Mathigon: Alice in Fractal Land
When Alice falls down the rabbit hole, she discovers a wonderful world of mathematics: Pascal's triangle, sequences of rabbit generations, and beautiful, never-ending fractals.
Boston University
Boston University: Chaos, Fractals and Arcadia
This is an interesting site for information on chaos and fractals. Includes links to interactive activities to learn more.
Boston University
Bu: Fractal Geometry of the Mandelbrot Set
This site progresses in iterations through Mandelbrot and Julia sets to explain fractals and the mathematics behind them.
Education Development Center
Iteration
Making Mathematics provides a brief explanation and a list of examples of iterations.
Wolfram Research
Wolfram Math World: Fractals
This page briefly illustrates and discusses fractals, which are closely linked to the concept of iteration (repitition.) Site links to well known pictured fractals.
Shodor Education Foundation
Shodor Interactivate: Lesson: Fractals
This site provides some links to activities and lesson plans dealing with fractals and chaos.
Other
Eal: Fract Ed
A great resource for beginners. The site begins with a definition of iteration of functions, and proceeds from there to discuss fractal dimension.
Cut the Knot
Cut the Knot!: Interactive Mathematics: Geometry Articles, Theorems, Problems
Contains over five hundred Geometry articles, problems, puzzles, and games. Some sites relating to circles are provided within this list.
Interactive Mathematics
Interactive Mathematics: Fractals
A simple explanation of fractals is presented, along with several diagrams including the Mandelbrot set and Julia set.