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 ).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.

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Noel Giffin,