Julia Sets
Description
This MATLAB GUI iterates the quadratic map f(z) = z2+ c, where z and c are complex numbers. The (filled in) Julia set is the set of initial conditions z0 such that successive iterates z1 = f(z0), z2 = f(z1), ..., zn+1 = f(zn), ... remain bounded.
Points in the Julia set are shown in dark blue. Points z0 outside the Julia set are color-coded according to how fast successive iterates of z0 go to infinity.
How to use the GUI
The sliders at the bottom allow you to change the real and imaginary parts of the parameter c.
The Iterations slider allows you to set the number of successive iterations used in deciding whether points belong to the Julia set.
The Resolution panel controls the number of points actually plotted in the picture. You have to keep in mind that a higher resolution will lead to a nicer picture, but the code will be slower.
You can zoom in on any part of the picture by clicking and dragging the mouse to define a rectangular region to be magnified. The code keeps track of successive magnifications.
You can then zoom out by repeatedly clicking on the Back button. The Reset button takes you back to the default view.
Download
To download the GUI, right click on each of the links below, and save the corresponding files into a directory. Set the MATLAB path to that directory and then type Julia_Sets at the MATLAB prompt.
Type help Julia_Sets at the MATLAB prompt if you need to be reminded of how to use the GUI.
GUI developed by Joceline Lega, Spring 2008.