This applet can be zoomed in on by clicking on any point on the graph. Clicking on points of activity yield the most interesting expansions. More iterations give more detail and take longer. Color choices will be applied on the next zoom. Because of the limitations of the java type double, only 12 zooms are available. Reset will start at a fully zoomed out point.
With respect to the complex function Z^2 + C this applet represents with color the number of iterations required to prove a tendency towards infinity. This tendency is proven when the magnitude of the complex function exceeds 2.0.
I first wrote this code with a complex number class. I abandoned the use of complex numbers in favor of direct computation in the interest of speed.
I tried the java bigDecimal class in order to circumvent the problem of only 12 zooms and the working code is commented out in the source. I found it to be painfully slow. Research into the bigDecimal class tells me that in the future (when the class is rewritten) the code may be viable.
The windows version of the code is hard coded with 175 iterations and uses the long double type. This allows for 22 zooms. Note that since each zoom is X4 this is 4^22 (17,592,186,044,416) magnification. Magnification for the java file is only 4^12 (16,777,216).