3.6 Decomposition
You'll remember that most fractal types are calculated by iterating a
simple function of a complex number, producing another complex number,
until either the number exceeds some pre-defined "bailout" value, or the
iteration limit is reached. The pixel corresponding to the starting
point is then colored based on the result of that calculation.
The decomposition option ("decomp=", on the <X> screen) toggles to
another coloring protocol. Here the points are colored according to
which quadrant of the complex plane (negative real/positive imaginary,
positive real/positive imaginary, etc.) the final value is in. If you
use 4 as the parameter, points ending up in each quadrant are given
their own color; if 2 (binary decomposition), points in alternating
quadrants are given 2 alternating colors.
The result is a kind of warped checkerboard coloring, even in areas that
would ordinarily be part of a single contour. Remember, for the M-set
all points whose final values exceed 2 (by any amount) after, say, 80
iterations are normally the same color; under decomposition, Fractint
runs [bailout-value] iterations and then colors according to where the
actual final value falls on the complex plane.
When using decomposition, a higher bailout value will give a more
accurate plot, at some expense in speed. You might want to set the
bailout value (in the parameters prompt following selection of a new
fractal type; present for most but not all types) to a higher value than
the default. A value of about 50 is a good compromise for M/J sets.