Activity Description 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.

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Julia Sets

Place in mathematics curriculum:

• practice students' arithmetic skills
• practice students' point plotting skills
• introduce students to complex numbers
• investigate the notions of Julia sets, prisoners and escapees
• motivate the Mandelbrot set

This activity allows the user to investigate the Julia sets associated with functions f(Z) = Z^2 + C for any complex number C=(a,b) in the circle of radius 2. This activity would work well in groups of two to four for about twenty-five minutes if you use the exploration questions and ten minutes otherwise.

Preparations for this activity:

• give implicit directions on what they are to do. For example "Today we are going to find out about prisoners, escapees, and complex numbers by using the Julia set activity as well as the Two Variable Function Pump and the Julia set worksheet..."
• answer the question "What is a prisoner and what is an escapees?"
• discuss complex numbers, and how to plot points