3.4 Distance Estimator Method
This is Phil Wilson's implementation of an alternate method for the M
and J sets, based on work by mathematician John Milnor and described in
"The Science of Fractal Images", p. 198. While it can take full
advantage of your color palette, one of the best uses is in preparing
monochrome images for a printer. Using the 1600x1200x2 disk-video mode
and an HP LaserJet, we have produced pictures of quality equivalent to
the black and white illustrations of the M-set in "The Beauty of
Fractals."
The distance estimator method widens very thin "strands" which are part
of the "inside" of the set. Instead of hiding invisibly between pixels,
these strands are made one pixel wide.
Though this option is available with any escape time fractal type, the
formula used is specific to the mandel and julia types - for most other
types it doesn't do a great job.
To turn on the distance estimator method with any escape time fractal
type, set the "Distance Estimator" value on the <Y> options screen (or
use the "distest=" command line parameter).
Setting the distance estimator option to a negative value -nnn enables
edge-tracing mode. The edge of the set is display as color number nnn.
This option works best when the "inside" and "outside" color values are
also set to some other value(s).
In a 2 color (monochrome) mode, setting to any positive value results in
the inside of the set being expanded to include edge points, and the
outside points being displayed in the other color.
In color modes, setting to value 1 causes the edge points to be
displayed using the inside color and the outside points to be displayed
in their usual colors. Setting to a value greater than one causes the
outside points to be displayed as contours, colored according to their
distance from the inside of the set. Use a higher value for narrower
color bands, a lower value for wider ones. 1000 is a good value to
start with.
The second distance estimator parameter ("width factor") sets the
distance from the inside of the set which is to be considered as part of
the inside. This value is expressed as a percentage of a pixel width,
the default is 71. Negative values are now allowed and give a fraction
of a percent of the pixel width. For example: -71 gives 1/71 % of the
pixel width.
You should use 1 or 2 pass mode with the distance estimator method, to
avoid missing some of the thin strands made visible by it. For the
highest quality, "maxiter" should also be set to a high value, say 1000
or so. You'll probably also want "inside" set to zero, to get a black
interior.
Enabling the distance estimator method automatically toggles to floating
point mode. When you reset distest back to zero, remember to also turn
off floating point mode if you want it off.
Unfortunately, images using the distance estimator method can take many
hours to calculate even on a fast machine with a coprocessor, especially
if a high "maxiter" value is used. One way of dealing with this is to
leave it turned off while you find and frame an image. Then hit <B> to
save the current image information in a parameter file (see Parameter
Save/Restore Commands (p. 30)). Use an editor to change the parameter
file entry, adding "distest=1", "video=something" to select a high-
resolution monochrome disk-video mode, "maxiter=1000", and "inside=0".
Run the parameter file entry with the <@> command when you won't be
needing your machine for a while (over the weekend?)
To reproduce images made prior to version 16.0, it is necessary to set
several parameters from the command line or using <G>. First, set
"release=1510", then set "olddemmcolors=y". To obtain the fine strands
it is necessary to set the "width factor" to a large negative value,
such as -32000.