In principle, Fred's Fractal Factory and Viewer can support many different kinds of fractal calculation. In fact, they only support Mandelbrot Escape Time calculation in the current release. Eventually, other fractals such as Julia sets will be supported.

The Mandelbrot Escape Time calculation assigns a integer value labelled MandelEscapeTime(x, y) to each point in the (x, y) plane, where x and y are real numbers.

Consider the sequence of complex values Z with sequence index n:

• Z(n+1) = Z(n)*Z(n) + C where Z(0) == (0, 0) and C == (x, y).

The cartesian magnitude of Z(n) which we designate as |Z(n)| is calculated iteratively for values of n = 1, 2, 3, .. MaxIterations:  

• If on the q'th iteration we find that |Z(q)| > Escape Radius, then we assign q to MandelEscapeTime(x, y), which completes the calcuation of MandelEscapeTime(x, y) .
• If |Z(n)| <=  Escape Radius for all n in the range 1..MaxIterations, then MandelEscapeTime(x, y) is assigned MaxIterations .

The canonical value that is usually used for Escape Radius is 2.0, but the Factory lets you set it to values ranging from 2.0 to 1000.0 .

The Factory allows you to set MaxIterations to values ranging from 1 to 65000.