Activity Description 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 introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.

Shodor Interactivate utilizes JavaScript technology, you must enable it to effectively use our site.

If you wish to leave JavaScript disabled, you may attempt to view the activity. Here is some additional information about this activity that may not be accessible without JavaScript.

Two Variable Function Pump

Place in mathematics curriculum:

This activity can be used to:

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

This activity allows the user to step through plotting a two-variable function, and to judge whether a given starting point is a prisoner or an escapee, in order to understand complex numbers and Julia sets.

This activity would work well in mixed ability groups of three to five for about forty minutes if you use the exploration questions and twenty 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 Two-Variable Function Pump activity and it's worksheet..."
• answer the question "What is a prisoner and what is an escapee?"
• discuss complex numbers, and how to plot points