Pupils explore the concept of Mandelbrot sets and Julia sets. For this Mandelbrot and Julia set lesson, students use a function integrator applet to investigate two-variable function iterations. Pupils use Julia set and Mandelbrot set...

Students are introduced to the notion of a complex number and function iteration in order to motivate the discussion of Julia sets and 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.

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.

Use a function to operate on two variables. Pupils look at operating with complex numbers as a function of two variables. The interactive squares the input and adds a constant to it. Learners visualize the resulting output and its...

Teach class members to work with rational expressions using their knowledge of fractions. The lesson plan starts with a warm-up of rational expressions at four different levels of complexity. The different levels continue throughout...

For this word problem worksheet, students solve thirty-six application problems.  These problems include: mixture problems, rate problems, age problems, and consecutive integer problems.

Students determine the relative size and distance of the planets in the solar system. They use ratios in their mathematical calculations to make models of the planets after discussing the relative sizes of the planets. They keep a...

Pupils solve word problems which involve graphing systems of equations. After discussing methods of solving word problems, the teacher demonstrates how to solve problems which involve graphing. They work together, at their desks, and...

Students investigate architecture and construction by building a home from cardboard tubes.  In this housing lesson, students collaborate in groups to plan and create buildings they can fit in made from cardboard tubes, newspaper...

Learners brainstorm pizza toppings and determine the number of possible ways to order a pizza. In this algebra lesson, students analyze and investigate geometric patterns as they relate to the concept of a variable. Learners then...

Here's an example of "What a 2 Dimensional Julia Set will look like using modern computers with their sophisticated graphical displays." Gaston Julia published his theories long before computers and as the site's author remarks, "What a...

Enter a complex value for "c" in the form of an ordered pair of real numbers. The applet draws the fractal Julia set for that seed value.

In this lesson students will explore Julia sets and the Mandelbrot set. In the process they will learn about fractals and explore complex numbers and function iteration.

Explore fractals by investigating the relationships between the Mandelbrot set and Julia sets.

This site progresses in iterations through Mandelbrot and Julia sets to explain fractals and the mathematics behind them.

This web site addresses counting and adding in fractal operations, as well as the role of the Fibonacci sequence in fractal geometry.

A simple explanation of fractals is presented, along with several diagrams including the Mandelbrot set and Julia set.

Although fractal images can be intriguingly complex, fractals are more than just pretty pictures. In this project, you'll explore the mathematical properties of the famous Mandelbrot and Julia sets. You'll learn about how these images...

The Shodor Education Foundation has as its mission: "To advance science and math education through the use of computational science, modeling and technology." At this site, Shodor's Project Interactivate offers Java-based activities for...

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.

This is an interesting site for information on chaos and fractals. Includes links to interactive activities to learn more.

Making Mathematics provides a brief explanation and a list of examples of iterations.

This site provides some links to activities and lesson plans dealing with fractals and chaos.