"Z not Z" Fractal Applet
Directions: Use the mouse to drag the images around. The keyboard arrow keys also do this. The mouse wheel or the page up and page down keys can be used to zoom in and out. Press the right mouse button to freeze and unfreeze the current fractal on the left. The buttons labeled "up" and "down" scroll through the palette, changing the coloring. This is a preliminary version and should hopefully be improved soon.
The program iterates the function cz(χ(-1,1)(re(z))+iχ(-1,1)(im(z)), where χ(-1,1) is the characteristic or indicator function of the interval (-1,1). That is, χ(-1,1)(x) is 1 if x is in the interval (-1,1), and 0 otherwise. The image on the right is an index set for these fractals. It is related to these fractals in the same way that the Mandelbrot set is related to Julia sets. Most of the interesting stuff happens near the outside boundary of the yellow region.
