I'll let Fractint's manual explain log mapping.
" By default, Fractint maps iterations to colors 1:1. I.e. if the
calculation for a fractal "escapes" (exceeds the bailout value) after N
iterations, the pixel is colored as color number N. If N is greater than
the number of colors available, it wraps around. So, if you are using a
16-color video mode, and you are using the default maximum iteration
count of 150, your image will run through the 16-color palette 150/16 =
When you use Logarithmic palettes, the entire range of iteration values
is compressed to map to one span of the color range. This results in
spectacularly different images if you are using a high iteration limit
and are zooming in on an area near a "lakelet" ".
Above uses log mapping. I used the value given by the auto log map function (logarithmic
not square root spread). Note that in the first given the rapid cycling of the palette due to the
density of iteration bands make the figure seen almost noisy. With log mapping the mapping is