16-2 Julia Set Fractal Image

This program creates fractal images by plotting Julia sets derived from iterating complex functions of the form z^2 + c, varying z over the complex plane for a given value of c. For each complex point z that is not in the set, the “escape velocity” of the point’s orbit is represented by a shade of gray — the more iterations, the darker the shade. For each point z that is in the set, its color is determined by the modulus of the final computed orbit value.

To run the demo:

  1. Enter the real and imaginary parts of the complex value c, and then press the Manual button. Some values of c that generate interesting fractal images include:
RealImaginaryImage
0.30900264-0.0339787Claws
0.33843684-0.4211402Snowflakes
-0.39850140.5848901Turtles
-0.8184639-0.2129812Serpents
-0.33462120.6340579Amoebas
-0.55304040.5933997Sparklers

You can choose one of these from the drop-down list.

  1. Or, press the Random button to generate a random value for c. Only 5-10% of random values produce interesting fractal images, so you may need to press this button repeatedly.
  2. Because the fractal images are recursive, you can use the mouse to drag a rectangle around an area of an image that you want to zoom into.

The original Java Applets do not run in modern browsers, but you can download the Java code and run it locally on your desktop. Check back for JavaScript and Python versions - coming soon!

Downloads

Download Demos in Java