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Author Topic: Interesting Mandelbrot variant  (Read 938 times)
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rollercoaster158
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« on: June 12, 2012, 02:04:40 AM »

While messing around with my newly installed copy of Ultrafractal, I was editing the formula for the Mandelbrot set. Most of my variants were blank screens but then I came across a strange result. I changed the equation from Z=Z^2+C to Z=Z^Z+C. This was out of curiosity, to see what it would look like if the value Z was squared to was different for every pixel. Expecting a chaotic mix of different multibrots, I was surprised to see this:



I don't know if it's been discovered before, but a quick Google of the formula turns up nothing related to it. There are some interesting parts of this fractal, see for yourself:



(Yes, I did use MS Paint to label those. I have yet to obtain a decent image editing program so it will have to do. The following pictures are closeups of 1, 2, and 3 respectively.)


It does get a little chaotic, but I'm pleased with it. If you zoom in further, the mess settles out into mandelbrot-like spirals and shapes (sort of).


That arrow is strange. I wonder how it is made by this formula.



This is what the arrow is pointing at, there's nothing cool to see here. It goes on like that forever.

Anyway, here are my questions:

1. Has this been discovered before?
2. If the value that z is being multiplied by changes frequently, shouldn't there (theoretically) be a mini-brot of every value Z can be squared to in here?
3. Is there a way to make a 3d representation of this?
4. If it hasn't already been discovered, what would you name it? I have no idea what to call it.

rollercoaster158
« Last Edit: June 12, 2012, 02:06:40 AM by rollercoaster158 » Logged
David Makin
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« Reply #1 on: June 12, 2012, 11:52:32 AM »

Erm, yes - most things have.

In this case to render it properly you need to increease the bailout - the magnitude of 2 proof is not valid for *any* formula.

Here is what z^z+c looks like with a bailout of 256...

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11782
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11783
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11784

Params are with the 3rd image -- except that I also change the UF default z^p+c to do z^z+c so it'll only render corectly if you do the same wink
Of course anyone doing so needs to remember to change it back again after !!
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DarkBeam
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« Reply #2 on: June 12, 2012, 12:32:41 PM »

Go to OPTIONS / UPDATE FORMULA COLLECTION wink There are millions of new formulas. Many made by the guy that answered your question crazy eyes in mmf-whatever cheesy

Mine are in lgn-whatever wink police You must use them everyday snore

 grin
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Alef
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« Reply #3 on: June 12, 2012, 06:39:46 PM »

If I 'm correct, this is one of classical fractints formulas. Probably should be in UF database in Fractint compatibility files.

Try EM files, too. And LKM (Or was they IKM tongue stuck out)
http://formulas.ultrafractal.com/
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rollercoaster158
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« Reply #4 on: June 13, 2012, 05:16:27 PM »

OK, it seems that I have a lot to learn about Ultrafractal. I just got it, and I'm still exploring the help files. Thanks for the help.
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