The Mandelbrot Set model displays a set of points, c, in the complex plane that keep the function, z² + c, bounded.  The function is generated by starting with value of c and an initial value for z, and generating the resulting complex number from the function z² + c.  The result of the function them becomes the new z to be substituted back into the function.  This process is repeated until it is clear the function is bounded or unbounded by the initial choice of c.  By click-dragging in the plot you can magnify the selected region of the Mandelbrot set.  You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting "Open Ejs Model" from the pop-up menu item.  

Ejs Mandelbrot Set model was created using the Easy Java Simulations (Ejs) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_chaos_MandelbrotSet.jar file will run the program if Java is installed.  Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models.  Additional Ejs models for Newtonian mechanics are available.  They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

Please note that this resource requires at least version 1.5 of Java (JRE).