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bugman
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« on: November 25, 2009, 11:39:46 PM » |
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Here is a summary of some different 3D Mandelbrot set formulas for your convience. I have tried to include a second order and 8th order rendering for each formula presented here. Additional formulas are welcome.
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« Last Edit: December 18, 2009, 08:53:31 AM by bugman »
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bugman
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« Reply #1 on: November 25, 2009, 11:40:36 PM » |
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« Last Edit: December 18, 2009, 08:54:34 AM by bugman »
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bugman
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« Reply #2 on: November 25, 2009, 11:41:02 PM » |
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« Last Edit: December 18, 2009, 08:55:36 AM by bugman »
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bugman
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« Reply #3 on: November 25, 2009, 11:41:18 PM » |
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« Last Edit: December 18, 2009, 08:56:03 AM by bugman »
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David Makin
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« Reply #4 on: November 26, 2009, 04:34:07 AM » |
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Hi Paul, you might want to try normalising that last one to 1 before multiplying by the magnitude - if the magnitude of the trig is zero then use (1,0,0) multiplied by the magnitude.
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ZsquaredplusC
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« Reply #5 on: November 26, 2009, 05:56:37 AM » |
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Thanks for all these. That is the sort of summary I requested back in the original thread. This will really help others looking for formula info.
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dougfractal
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« Reply #6 on: November 27, 2009, 01:22:56 AM » |
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This is the method that I used to create my 3D versions  |
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TedWalther
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« Reply #7 on: November 27, 2009, 03:17:03 AM » |
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This is the method that I used to create my 3D versions
<Quoted Image Removed>
Doug, I don't know enough math to follow that; could you turn it into a formula so I can see how new x,y,z values are created? Ted |
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dougfractal
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« Reply #8 on: November 27, 2009, 03:31:22 AM » |
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« Last Edit: November 27, 2009, 03:43:15 AM by David Makin »
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bugman
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« Reply #11 on: December 18, 2009, 08:56:58 AM » |
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Thanks for pointing that out. I made the correction.
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cbuchner1
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« Reply #12 on: December 18, 2009, 03:39:02 PM » |
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I am getting confused as to why I cannot reproduce the exact same shapes of 3D mandelbulbs when I plug above formulas into a voxel generator. I do apply the exact same iterative formulas in a spherical coordinates, yet the voxel representations of the bulbs look distinctly different (especially apparent for power 2).
I am beginning to think that maybe a 3D raymarching approach based on Hubbard Duady does not really give the "correct" result. Could anyone verify this hypothesis or prove it wrong?
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jehovajah
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« Reply #13 on: December 19, 2009, 03:22:24 PM » |
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Couple more formulae for you paul. (x,y,z) 2 = (  ) left hand version. (x,y,z) 2 = (  ) right hand version. Do you want the correct vx versions as well? |
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« Last Edit: December 19, 2009, 03:45:05 PM by jehovajah »
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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M Benesi
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« Reply #14 on: February 06, 2010, 09:54:09 PM » |
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I've added 4 new formulas, starting in post 114 of this thread: http://www.fractalforums.com/3d-fractal-generation/truerer-true-3d-mandelbrot-fractal-(search-for-the-holy-grail-continues)/msg12604/#msg12604 They definitely don't strictly stick to the accepted Mandelbulb format, but they are all 3d fractals (not simply "regions inside level sets for 3d fractals" (quoted from an unnamed source, haven't asked permission to use their name) like the previous formulas I posted in the thread). Images are in the thread. As it is, some of them are pretty cool and have really neat fractal symmetry (I like Type B (not Mandelbulb B) the most). Zooming into the point (front) of type B higher order Z^8++ is pretty fun. If you think they are appropriate for this thread, go ahead an import them. May have a mod move them over here and put a link to this thread from that one.... or whatever. matt |
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May 05, 2010, 03:17:07 PM
2d/3d conformal formulas for a tetrahedral projection Mandelbrot
The 3D Mandelbulb
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