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:
- 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:
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 repeatedly.
- 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.