Ron Mak @ Apropos Logic
Publications and books by Ronald Mak

Java Number Cruncher

Program 16-2

Julia Set Fractal Image

This applet 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:

    Real Imaginary Image
    0.30900264 -0.0339787 Claws
    0.33843684 -0.4211402 Snowflakes
    -0.3985014 0.5848901 Turtles
    -0.8184639 -0.2129812 Serpents
    -0.3346212 0.6340579 Amoebas
    -0.5530404 0.5933997 Sparklers

    You can choose one of these from the drop-down list.
  2. 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 repeately.
  3. 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.