How Do I Use This Activity?

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.

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Controls and Output

• These boxes near the bottom of the applet are where you enter a Starting Point and a Constant, C, for the quadratic function f(Z) = Z^2 + C, that you want to iterate.
  
• Whenever you change the Starting Point or Constant, press the Restart button to start a fresh graph with those values. Press the Next Step button to calculate the next iteration.
• The Graph shows the path (also called the orbit) of the starting point as it is plugged into the function. The red line is the path from the previous point to the most recent one. If the orbit path goes outside the gray circle of radius 2, the starting point is guaranteed to be an escapee.
  

  The List on the left is another way to look at the values of the function -- as ordered pairs.