Java Number Cruncher
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 drop-down list.
- 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.
- 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.