Today's post is of two examples of log versus regular palette mapping. 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 =
  9.375 times.
     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" ".
  Log mapping is particularly useful in deep zooms when the iteration values are high
and the density of iteration  with the rapid cycling of the palette produces
an effect that is almost noisy. Go to http://maxitersfractalfollies.blogspot.com
 for the original gifs and two resampled jpgs. Note that for fract355.gif the autolog map value
 of 102 calculated by Fractint  was increased to 140. To generate the fractals with regular mapping
set the x screen "log palette" value to 0.

fract355.gif       { ; logmap hi
                     ; blank
                     ; calctime   0:00:43.34
                     ; created Aug 08, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=mandel
  center-mag=-0.13784252841051350/+0.84680655314023390/86407.5
  params=0/0 float=y maxiter=3600 inside=0 logmap=140
  colors=00000000200400600800A00C00E00G00I00K00M00O00Q00S00U00W00Y00_00a00\
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  J90I90H80G80F70E70D60C60B50A509408407306305204203102101
  }
 
fract356.gif       { ; auto log map
                     ; blank
                     ; calctime   0:11:41.79
                     ; created Aug 08, 2010
                     ;  Fractint Version 2004 Patchlevel 9
  reset=2004 type=mandel
  center-mag=-0.13784212640222090/+0.84680532340393120/2.941708e+007/1/-17\
  7.499999933515994/-6.95950524293165174e-008 params=0/0 float=y
  maxiter=12000 inside=0 logmap=595
  colors=w0dv0bt0ar0_q0Zo0Xm0Wl0Uj0Ti0Rg0Qe0Pd0Nb0M`0K_0JY0HX0GV0ET0DS0BQ0\
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  }