Magnet Fractal Zoom

[HPDZ]

NOTE: This animation is likely full of artifacts due to a bug in my arithmetic code (see my subsequent posts). So, while it's fun to watch, it does not represent the actual magnet fractal's structure. I will leave the original posting here, but the comments below are not correct. My apologies!



Does anyone still watch plain old 2D zooms anymore?  

After building a new fractal rendering system with a Core i7 980X, I was feeling the need to take on a big computational challenge, but my software isn't going to do 3D animations any time soon. So I decided to make a deep (modestly deep, around 6e-29) zoom into the Magnet Fractal Type I. As far as I know, there is only one other Magnet Fractal animation, and it's not very deep, so this is something unique.

I found a few interesting features as I scoped out the plans for this animation:

• This fractal is not connected. Artifact! Unlike the Mandelbrot set, it has isolated subsets that are not connected to each other. Yet, it is not a "dust" of isolated disconnected individual points.
• This fractal is not simply connected. Also unlike the Mandelbrot set, it has more than one was to get from one point to another. This is highlighted as this video zooms into a region where a spiral arm is touching a flower structure.
• At the end, a "Mandelbar" structure appears. Artifact! I have never seen this happen before except in fractals that have a complex conjugate explicitly in their forumla. Locally, around this end point, the Magnet formula must look like a complex conjugate.

Visit http://www.hpdz.net/Animations/MagnetFractal.htm for full details and high-quality videos. A few technical details, including the formulas (which are very well-known) are at http://www.hpdz.net/StillImages/MagnetFractals.htm

And of course I posted it to YouTube as well:
<a href="http://www.youtube.com/v/V30l7BycdPM&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/V30l7BycdPM&rel=1&fs=1&hd=1</a>

[gussetCrimp]

You wrote:

> Does anyone still watch plain old 2D zooms anymore?

Yes! I'm a fan of yours. About a week after you posted the Seattle animation here, suddenly there were several comments and questions in the thread, which I think you probably missed. Anyway these new zooms are great. I also went and looked at the terrifying pictures of your new system at the HPDZ site. Regards, Gus

p.s. how do you know the Magnet Fractal is disconnected--couldn't the filaments just be really, really, really thin?

[HPDZ]

You have a good point about the filaments being really thin. Still, the impression I get is that the mini-sets are disconnected, since there's no visible alteration in the background colorings leading up to them. A subjective argument, to be sure, but that is the beginning of discovery. I will try to work on a reasonable distance estimator type of formula for this and verify.

It's also been suggested in a private message that the disconnected Julia sets and the Tricorn fractal at the end are artifacts -- I am looking into this.

[HPDZ]

OK. It's starting to look like this video is a blooper! OMG! I am so embarrassed!!! 

It's not clear exactly what the problem is yet, but the disconnected Julia-like sets that have the tricorn at their centers are probably not real. It seems there is an error in the arithmetic code. This is an extremely subtle error, since this has been tested pretty carefully (although obviously not carefully enough!) and I can draw the overview of the Magnet fractal wtih this code and it's fine, and the Julia-like (artifactual?) sets do not look like random garbage, which is what you usually get when there's a code bug. My intuition tells me it's a subtle loss of precision error related to how I've coded division of complex numbers, but I am just guessing at this point. So far all I have done is verified that Chaos Pro and Ultra Fractal do not demonstrate the same disconnected sets that this video shows.

So, while this animation is certainly something fun to watch, it may not represent "reality" (whatever that is).

At any rate, the good news is that when I figure out what is going wrong here, my code will be better. That may take a few weeks, since real life is extremely demanding right now.

Let this be a lesson: The tricorn showing up really made we wonder -- I had never seen it before in any fractal whose formula didn't have a complex conjugate. I am all for setting aside instinct and intuition in favor of empirical facts, but sometimes what we think are empirical facts are based on faulty reasoning ... or faulty computer code! Fortunately, someone with better reasoning skills than me insisted that this indicated a flaw. And it was hard to set my ego aside and pursue this, but I'm glad I did. If the end result is of general interest, I will publish here what went wrong once I fix it.

[HPDZ]

I have figured out what the problem here is. I was not correctly trapping overflow conditions in my multiplication code.

I am using a fixed-point multi-precision number system with one 32-bit "digit" to the left of the decimal point. Overflow conditions are easy to create when dividing by small numbers in this kind of system, and I was not properly testing for this condition.

My code at the present time cannot even draw an overview representation of the magnet fractals, now that I've got this error trapping working properly, let alone a deep zoom. So this video is mostly bogus, and the disconnected Julia sets and mini-tricorn at the end are artifacts of allowing the overflow condition to propagage through the iterative process undetected. 

It's amazing that this error actually yielded a convincing fractal image. Most arithmetic code errors yield total garbage.

Sorry to everyone for this screw-up. 

[regfre]

What is Program?

[regfre]

I not found artifacts

[HPDZ]

The program is my own software, a little thing I started about 9 years ago and have been slowly modifying ever since.

The artifacts are the isolated Julia sets. They start to appear in this video at about 1:00 from the beginning, where the first disconnected Julia set appears. Everything from then on is zooming into an artifactual entity, something that does not exist in the true magnet fractal. I have confirmed this by zooming into similar areas with my own software, areas that do not require high-precision math, as well as by using Ultra Fractal and Chaos Pro.

[regfre]

You do not plan to distribute your program?

I was looking for artifacts in UltraFractal and not Founded.(((

[HPDZ]

My program is really not suitable for public distribution. It's more like an experiment set up on a lab bench, not at all a stable, well-functioning commercial product. I think this little debacle with the disconnected Julia sets and the mini-tricorns proves that!

You won't find these artifacts in UltraFractal because UF's math code is full floating point arithmetic internally (as far as I know), so what it draws is the real fractal, not the artifactual things you see in this video. These artifacts are created by overflow conditions in my math code, which is designed to be very fast, but does not do certain things well. The magnet fractals require that those things be done, and my code really should have been signaling that errors were happening, but the testing I built in to detect these error conditions was not careful enough, and some errors were getting through undetected.

[Mrz00m]

@HPDZ :     WANT HDPLZ:}