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DeepZooming with FractInt

FractInt now has this amazing capability to zoom into unbelievable depths, with precision up to 1600 decimal digits.   So you can now look for new and unique fractal regions at previously unheard of scale.   The trick is not to get carried away with just zooming in, where you can get lost in infinite whorls of self-similarity, but to carefully step from minibrot to minibrot, looking for new levels of complexity and detail.   I took a shot at it and produced the following image.   I thought that the fine filigree structure was fascinating.

Deep Zoom image

The region is in a spiral, but not too deeply and the precision is about 18 decimal digits.   It is not even seriously testing the arbitrary precision math, but the full size image still managed to take about 3 weeks to compute on my 486DX/66 computer.   This is primarily due to the high iteration limit and the image resolution of 1024x768 for the full-size image.   It was my first attempt to achieve the dubious honour of watching FractInt inform me that my image took too long to compute.   I did not quite succeed.   I was about three days short of the required lapsed time, but I seriously taxed my own limits in creating it.   That is a long time to wait for one image.   Hat's off to those with the personal fortitude to explore deeper and wait longer.

Wes Loewer <>, the one who programmed the arbitrary precision math routines into FractInt, has sent me his deepest zooming effort.   It is a 1.0e1500 zoom into a self similar region at the very top of the Mset in the region of (0.0, 1.0).

Top 1500s image

This version is a GIF87a format and I use it here as it is a much smaller file due to a better compression with a reduced palette than the original GIF89a version that contains the FractInt information.   The two images are almost identical and the only reason to download the GIF89a version would be to load it into FractInt and keep zooming or to actually see FractInt report an image that took 7 weeks, 2 days, 8 hours, 15 minutes, 33.50 seconds of actual running time to compute on a 486sx/25 system.   It was calculated using a boundary trace mode that help reduce the calculation time.   Only about 20% of the pixels in this image needed to be computed using this algorithm of a FractInt .PAR entry:

      top-mag1500      { ; a really really deep zoom        Wesley Loewer
                         ; highly self similar
                         ; took over 1200 hours at 320x240 on a 486sx/25
        reset=1920 type=mandel passes=b center-mag=0.0/1.0/1e+1500
        maxiter=15000  }

Learn more about Wes's efforts in exploring self-similarity in the M-set in this area and view a couple of .FLI animations he has created.   [NEW]

Horizontal Hold image

I used Dewey Odhner's <> original parameter file of the Horizontal-Hold image to generate this fractal.   It caused a reasonable amount of consternation on the sci.fractals UseNet Newsgroup.   Noone had seen anything quite like this before and some people thought that FractInt's deepzooming feature was broken.   This was modified slightly from the original.   It uses 1-pass mode with periodicity turned off and has a different palette, but it should give you an idea why we were all concerned.

Horiz. Hold image

Bengt Månsson <> backed out a little bit and found this reassuring geometric structure nearby and we all relaxed again.

See more of Bengt's Deepzooming Adventures into the Mset.

Another version of the horzontal-hold image was created by Serge Moes <>

big Horiz. Hold image

The thumbnail image to the right links to Serge's fullsize 1024x768 version done with Dewey's original colour scheme.   He says it took about 10 days on his 486DX2 computer.

Kerry Mitchell, <> created a deepzoom fractal from this area as well.   I will include the text and the parfile that he sent me along with the image.

Zoom 256 image

Here is my first attempt at a deepzoom fractal.   It is a Mandelbrot midget on the spike (negative real axis), that was carefully chosen.   If you look at the midget at -1.75, you will see that it is associated with the number 3.   That is, this midget causes the band of dwell = 3 to dip down toward the axis, and the main cardioid for this midget has periodicity = 3.   In a similar fashion, the midget in this deepzoom is associated with 256.   It took over 37 hours to compute on a 486DX50, at 320x240 resolution and single pass mode (although the image is symmetric).

      two56      { ; dwell 256 midget by Kerry Mitchell
        reset=1930 type=mandel passes=1 float=y inside=0 periodicity=0
        210971806586916814/0.0/7e+305 params=0/0 maxiter=8192
        Cs`Cs<12>EFsCGsCIs<14>Cks<14>CFF  cyclerange=0/255  }

Spider Web image

Here is another interesting DeepZoom image by Dewey Odhner <> that has a bit of history.   This is a deepzoom image into the Mandelbrot using 63 decimal digits of precision.   The thumbnail leads to a 1024x768x256 image of 195-k bytes.   Dewey started this fractal and posted the partial image on the net when it was 2/3 completed after expending approximately 2343 hours of calculation time on a 486/33 computer.   The following .PAR file, which was posted to the UseNet Newsgroup, shows a calculation time of 2413 hrs, 22 min, 56.14 seconds.

      spidrweb   { ; (c) by Dewey Odhner.  Public domain.  26 Jun 1995
                   ; time=2413:22:56.14 on a 486/33 at 1024x768x256
                   ; Video=SF7 using FractInt 19.20
        reset=1920 type=mandel passes=1 float=y inside=0 maxiter=65535
        144784316302197739437/4.4e+058 params=0/0 logmap=yes
        CIscU<2>mbU  }

Charles Crocker <> picked up the image and finished it in about 70 hrs on a Pentium 90 system and sent it on to me.   This is about a factor of 20 increase in performance.   Not insignificant!   It turns a calculation that was going to take hundreds of days into something tolerable.

Both Charles and I were a little curious as to how Dewey found this minibrot.   When calculation times are this long, random zooming is no longer a workable method.   He must have some technique for isolating the buds.   I queried him on this and here is his reply:

"I found the spidrweb minibrot by looking at areas around larger minibrots and learning to recognize where they occur, what the areas tend to look like as you look on smaller buds and closer to the tip of the bud.   I tried to find the largest minibrot within that distance of the bud tip."

Frank Gentges has contributed a few images and some documentation on his deepzooming explorations into the Horizontal Hold area.

These and other more ambitious deepzooms can be found in this collection of email's and parfiles gleaned from the sci.fractals UseNet Newsgroup.

Minoru Morikawa <> in Japan, has provided three small deepzoom images into the tip of the Mset:

m1280cm imageThe m1280cm image:   small M with period 1280.   mag 10^1539.   preview mode.

m1280pa imageThe m1280pa image:   the right side of the above small M.   mag 10^1542.   preview mode.

m320paf imageThe m320paf image:   the right side of small M with period 320.   mag 10^386.  320*200 mode.

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