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Author Topic: 3D image of the Mandelbrot Set  (Read 27661 times)
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« Reply #45 on: November 21, 2006, 11:56:21 PM »

hmm, that's an interesting question... on the one hand, i wouldn't really expect uf to be that much faster than java since most java implementations have just-in-time compilation, which has been tuned for a number of years and i suspect uf's scripting is interpreted*; on the other hand i'll bet uf has built in functions for dealing with complex numbers and quaternions (which will be a real boon for you given what i said in your cubic/quintic mandelbrot set thread), which will use fast c/c++ routines internally. depending on the mix of native vs scripted operations the results can go very much either way...

unfortunately there are too many complicating factors for a direct comparison, for example support code around the basic execution, like java's display classes or uf's gui rendering code.

* if it's actually compiled to machine code then it boils down to the efficiency of said compiler versus java's ridiculously conservative/safe execution (eg array bounds checking etc).

Obviously  UF would be handle the Zoom, Perspective, coloring of the formula. I think i would swap to UF.
« Reply #46 on: November 22, 2006, 12:02:26 AM »

Or (if you mean what I think you mean) you can use my "Solid-3D" formulas from mmf.ufm - these allow you to cut a 3D fractal to up to 6 rectangular planes and/or to a sphere plus you can colour the fractal using lighting or using any "inside" colouring method.

If you mean rendering successive images closer to the "inside" then you can of course do that too.

If you want to know how to code a more optimum 3D algorithm for UF than my "Solid-3D" ones let me know as that's what I'm working on when I get chance - it's already massively faster but lacks the bells and whistles such as full phong shading, shadows and the option to use any UF colourings.

Hey, all three options are of high intrerest!

But actually i had no occasion to try the present methods. I am into the progress of oving to UF...

« Reply #47 on: December 04, 2006, 02:12:37 PM »

Thank you David Makin for you'r first two post's, They where verry usefull.
David Makin
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Makin' Magic Fractals
« Reply #48 on: December 05, 2006, 12:06:04 AM »

Thank you David Makin for you'r first two post's, They where verry usefull.

You're welcome  smiley

The meaning and purpose of life is to give life purpose and meaning.

"Makin' Magic Music" on Jango
« Reply #49 on: December 25, 2006, 04:11:07 AM »

Julesruis that's quite obviously cheating
all of the other ways look better than that, it's just a 2D shape spun around one axis, like a lathe
look on Ultrafractal, there are several formuli for doing it in diffrent ways.

Actually the image is a quaternion version of the Mandelbrot formula Z=Z*Z+Z the rotated appearance is natural to the set. Give it a try on your favorite Quaternion software.

I've run a sample animation of a slight modification to the formula Z=Z*Z+Zo where Zo is the original starting point being evaluated not the result of the last iteration.

It's not a great animation, but good enough to see the potential:
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« Reply #50 on: June 16, 2017, 12:03:53 PM »

what happens when you introduce a complex term to the exponent in z=z^2+c so that it's z=z^(2+ix)+c using the principal value expansion?  Nothing pretty but some interesting log scaling

* acf1.gif (250.46 KB, 640x480 - viewed 351 times.)
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