Fellow Fractalers:

well, after several weeks of vacation, computers humming, here are some GIFs that show what deep zooming can get you into.

Back in July, Dewey Odhner put up a fractint parameter file Horiz.Hold on sci.fractals that zoomed way into the Mandelbrot set to a magnification of 3.3e+242. The resulting image seemed bizarre, unlike any seen in the Mandelbrot set.

Had we discovered that the continuous nature of mathematics we had assumed been wrong. Was it instead, ultimately quantum like, and we were seeing the effects of math quanta? Was the arbitrary precision math in fractint somehow broken? Inquiring minds wanted to know.

Wes Loewer, author of the arbitrary math routines wondered and admited to his stomach churning at the thought of having a bug. Then he zoomed out and found more familiar patterns. Tim Wegner, major contributer to fractint found the pattern weird but for lack of computer time couldn't dismiss it as a bug although doubting it.

That was back in July. Before leaving on a vacation trip I put some fractint computations up on my machines. After returning, I could not bear to stop the work. A number of saves were done in the interim with restarts toward the answer. Now on the first of September, 3 GIF files seem to show the picture of what is going on. The GIF files are right out of fractint so the parameters are still imbeded for zooming and calculation.

(Meanwhile, a crowd of fractint enthusiasts gathers just outside the door to sci.fractals and mumbles "pinch'em" "pinch'em". What is this all about. Wait... "Pinch him, Pinch him." I still don't understand what this is all about, I'm wide awake, this isn't a dream, is it? These fractals are for real! Oh..... "Pentium, Pentium". Yeh, does make you think about that doesn't it.)

HHA.GIF is the original Dewey Odhner .par file at 1024x768 that caused so much question. Magnification was 1.58e+243 and compute time was 332 hours on a 486DX50.

HHB.GIF is a zoom out that shows the mini-Mandelbrot in some detail at a resolution of 1280x1024. Magnification was 3e+240 and compute time was 465 hours on a 486DX2-66.

HHC.GIF is a zoom back in with a bit of the lake on the left side of the same mini-Mandelbrot seen in HHB.GIF. The pattern of HHA.GIF is evident but much of the detail is still obscured in moire interference patterns as the lines converge closer and closer. Resolution was 1024x768, magnification was 6e+241 and compute time was 703 hours on a 486DX50.

Nonetheless, the nature of this area becomes evident in these three views. Thanks to Dewey Odhner, Wes Loewer, Tim Wegner and the Stone Soup group and of course Jay Hill who inspired deep zooms for making such an exotic tour so easy to take.

Frank Gentges AK4R gentges@itd.nrl.navy.mil

For reference, here is Dewey Odhner's PAR file....

Horiz.Hold         { ; by Dewey Odhner. Public domain.
reset=1920 type=mandel
center-mag=-1.9999999999999999999999999999999999999999999999999999999999\
999999999999999999999999999999999999999999999999999999999999996416785918\
148134530430458843562012392471211940405947277366380516671161895619483871\
9021305389817240974903756614325041160443974/0/3.3e+242
params=0/0 float=y maxiter=3000 inside=0
}

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