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-- Mike Condron

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What's New

Magnet Zoom Mistake

The big news of this issue is that the previous Magnet Fractal deep zoom was a bit of a mistake. A huge mistake, in fact. This is terribly embarrassing! Much of the cool new stuff I had thought I found in the magnet fractal turned out to be an artifact of an error in the arithmetic functions in the software that makes the videos.

I have kept that video on the web site, and on YouTube, but only as a reminder to be more careful. Some people have graciously accepted it as it is, in its own right, despite its inaccurate depiction of the structure of this fractal. That is very kind, and I appreciate all the nice comments about that video. But the main mission of this project is to render the fractals accurately, faithfully, with as little fluff and enhancement as possible -- "Letting the shapes speak for themselves." So software-induced artifacts, no matter how interesting, are just not what I am all about here.

Floating Point

The source of the bogus structures in the Magnet Fractal video was an overflow in the multiplication function in the high-precision math code. The details are spelled out on a special Technical page dedicated to describing this very intense and complicated project. Now, I have written a top-notch set of floating-point arithmetic functions, and a new high-speed assembly language division function that lets me render this type of fractal about 7X  faster than before, with no artifacts.

New Still Images

As part of the testing of the new floating-point functions, a large number of images were generated, many of which are much deeper zooms into the magnet fractal than have ever been created. Also a few into the Nova fractal were made as well.

Multi-X Metaphase Variation

Completely independent of the magnet fractal debacle is this really cool animation inspired by Stardust4Ever (see YouTube or DeviantArt) and his very nice extension of the "Metaphase" concept originally discovered by Paul Derbyshire in the late 1990s. This video continues the progression of doublings of X-like structures within ovoid enclosures, which really resemble chromosomes in a cell at the metaphase of cell division, which is what inspired the name. In principle the number of "chromosomes" can be doubled ad infinitum, but I've stopped here at 32 X structures after 5 progressive doublings.

With a final frame size of 5e-119, this animation is a serious deep zoom in its own right, independent of the metaphase motif.

Looking Forward

A new Magnet Fractal video is certainly mandated. It wont' have the weird, artifactual structures that the last one did, but it will be a very cool deep zoom into something nobody has ever seen before.

The still images of the Nova fractal are absolutely going to be the subject of a deep zoom soon.

The type 2 Magnet Fractal is also fertile ground. HPDZ is aware of only one existing zoom into this fractal, and it was not very deep. This is a much more comlicated mathematical formula, but I believe the new hardware and software are up for this challenge.

Eventually, the secant videos may be something worth deep zooming, but this will require a set of transcendental floating point functions, and that is not to be taken lightly.

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