Java Number Cruncher
Program 162
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:

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 dropdown list.  Or, press the Random button to generate a random value for c. Only 510% of random values produce interesting fractal images, so you may need to press this button repeately.
 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.