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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > (new) Theories & Research > Swirl "mandelbrot"?
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Author Topic: Swirl "mandelbrot"?  (Read 1749 times)
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kram1032
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« Reply #15 on: January 19, 2010, 08:28:54 PM »
generally, those Msets can simply be generated by:
abs(z)^k*sign(z)^n
where k is for the radius change and n is for the angular... uh... frequency smiley

The 2nd one with the triangle in it is nice smiley

EDIT:
I just ran a test for the case k=2 and n=8 and it looks like this is a plane through the 8-order Mandelbulb...
I wonder if that could be true?
Could it be that the 2nd angle is equivalent to an infinite number of slices of different distances?

The correspondence would most likely be related to tan(k) or something close to that, I guess...

It renders exremely slow and is quite dark (meaning, none of the points get hit often - I'm using the buddhabrot - style technique) but it clearly looks like I'm cutting straight through an area of the 8bulb... smiley

I also tried the reversed, k=8 and n=2 which gave a totally different look and either is part of the 2nd order mbulb but doesn't look that familiar, or it could easily be that for this observation, k has to be >= n....
« Last Edit: January 19, 2010, 09:24:55 PM by kram1032 » Logged
Timeroot
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« Reply #16 on: January 20, 2010, 02:52:28 AM »
Interesting thing with the slices of M-bulbs...

I just noticed this post: http://www.fractalforums.com/ifs-iterated-function-systems/julia-ifs-example-'kissing-circles'/. Apparently, in the Escape-time IFS function by David Makin, you can add the pixel to the non-affine function after each iteration to get a general MSet for any IFS (see my previous posts). However, this is only for IFS - that is, affine functions only. The Apophysis coloring formula (when combined with with Pixel formula) allow non-affine transform. It'd be so cool if those two were combined....  smiley
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
Timeroot
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« Reply #17 on: January 21, 2010, 02:25:23 AM »
Okay, I tried it out with k and n as you specified, doesn't really look slice of the M-Bulb to me. But I don't really know it all that well anyway. What interests me is that with k=2, n=-2, you get the tricorn, and with k=2, n=-2 you get the regular M-Set (obviously). I wonder if this means the Chaosbrot fractals are just a special case of this formula.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
matsoljare
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« Reply #18 on: January 30, 2010, 05:40:13 PM »
What if you apply an absolute function to the angle? Such as, if angle is measured in radians...

abs ( (angle*2) - pi )

Or a power?
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kram1032
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« Reply #19 on: January 30, 2010, 05:59:06 PM »
I see... so no real slice...

Well, easiest way to proof it would probably be to use k as a third dimension...


I tried out squaring the angle today. It gives a strange shape^^

Wonder how that'd look like for 3D smiley
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