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Author Topic: True 3D mandelbrot type fractal  (Read 272098 times)
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bugman
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« Reply #330 on: October 15, 2009, 03:40:48 AM »

I have just rendered animation with flying around 3D Nebulabrot fractal (Twinbee formula).
For faster rendering I cached all iteration data on HD. It takes about 20GB space :-) and I used 4 threads for rendering and 1 for loading data from HD in background. The bottleneck was drive speed (90MB/s) however it was much more faster than rendering without cached data.

That's great! You might also want to try the old formula. It produces some interesting-looking results:
http://www.bugman123.com/Hypercomplex/Nebulabrot0111.jpg
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David Makin
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« Reply #331 on: October 15, 2009, 03:55:27 AM »

Zooms of two Julias from the new contender for a true 3D Mandelbrot that I posted here:

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8231/#msg8231

They were rendered as here at 640*480 and 640*640 and took 14 mins and 12 mins respectively.

In both cases you can see a problem with my algorithm - the speckles are due to some points never reaching the iteration density required to be called "solid" - both these Julias almost disappear at 150 iterations or so.

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twinbee
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« Reply #332 on: October 15, 2009, 07:35:28 AM »

xenodreambuie, can you render larger versions of those objects?
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bugman
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« Reply #333 on: October 15, 2009, 07:43:22 AM »

Some really neat stuff above! I'm getting an article together to further explore the object, but I can't resist sharing one of my own zooms now. I've cut the 3D mandelbrot in half, and then I zoom into one the thin valley sections.

This is amazing Twinbee! I doubt anyone has ever made a fractal animation quite like this one!  afro
« Last Edit: October 15, 2009, 07:48:18 AM by bugman » Logged
twinbee
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« Reply #334 on: October 15, 2009, 09:18:12 AM »

Cheers, though it would look 100x better if it used proper perspective camera zooming (which I'll hopefully be sorting out soon). At the mo, it's like zooming into a 2D photograph, which is weird considering the object is 3D heh.

It'd be nice to see an anim going through the thin corridor near the beginning of the vid (ala Star Wars). Anyone up for rendering that? smiley
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xenodreambuie
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« Reply #335 on: October 15, 2009, 10:01:07 AM »

Twinbee, that is a cool animation. Here is my favourite cosine triplex variant; like a quaternion but more Gothic. This one went overnight to get reasonably clean. Inverse iteration struggles with some settings, even with MIIM. Forward iteration should produce quicker and nicer images in many cases, if not all.
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David Makin
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« Reply #336 on: October 15, 2009, 10:00:13 PM »

Twinbee, that is a cool animation. Here is my favourite cosine triplex variant; like a quaternion but more Gothic. This one went overnight to get reasonably clean. Inverse iteration struggles with some settings, even with MIIM. Forward iteration should produce quicker and nicer images in many cases, if not all.

Garth:
I've been trying and failing to reproduce your inverse renders but it appears that the divergent formula I'm using is not the exact inverse of your inverted version - here's my iteration loop where zri is x/y (complex) and zj is z (float):

            r = (magn=sqrt(magn))^@mpwr
            th = @mpwr*atan2(zri)
            ph = @mpwr*acos(zj/magn)
            zri = r*(cos(th)*sin(ph) + flip(sin(ph)*sin(th))) + cri
            zj = r*cos(ph) + cj
            magn = |zri| + sqr(zj)

Is that what you intended as the "forwards" iteration ?

As I said I can't seem to reproduce your inverse renders but I do get some interesting Julias - will post some 640*480 renders shortly smiley
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xenodreambuie
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« Reply #337 on: October 16, 2009, 12:43:17 AM »

Dave, you're right. That is the correct forward formula. I had assumed that the inverse worked with independent roots for phi and theta, simply because the pictures looked nice and made sense, but that turns out to be wrong. What I've been getting is two redundant roots, and missing the other two. I hope the correct Julias are better! I can easily fix my formula for the quadratic case, and have to check the general solution. What is surprising is that I had tried an 8th degree Julia and it looked pretty similar to Lycium's render, so I took that as a sign that it was likely correct.
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David Makin
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« Reply #338 on: October 16, 2009, 01:14:39 AM »

Dave, you're right. That is the correct forward formula. I had assumed that the inverse worked with independent roots for phi and theta, simply because the pictures looked nice and made sense, but that turns out to be wrong. What I've been getting is two redundant roots, and missing the other two. I hope the correct Julias are better! I can easily fix my formula for the quadratic case, and have to check the general solution. What is surprising is that I had tried an 8th degree Julia and it looked pretty similar to Lycium's render, so I took that as a sign that it was likely correct.

I don't suppose you can work out a "forward" method for your erroneous version ? - the Julias are rather nice smiley
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David Makin
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« Reply #339 on: October 16, 2009, 02:14:09 AM »

Zooms of two Julias from the new contender for a true 3D Mandelbrot that I posted here:

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8231/#msg8231

They were rendered as here at 640*480 and 640*640 and took 14 mins and 12 mins respectively.

In both cases you can see a problem with my algorithm - the speckles are due to some points never reaching the iteration density required to be called "solid" - both these Julias almost disappear at 150 iterations or so.

Apologies - it wasn't algorithm error, it was user error, I simply hadn't set the minimum step distance low enough smiley
Am just re-rendering corrected images.
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xenodreambuie
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« Reply #340 on: October 16, 2009, 02:30:58 AM »

Dave, for a forward method of my erroneous Julias, I think it just needs to map values with the missing roots over to the other roots. Try this: after computing phi and theta; if phi>pi/2, add pi/2 to both phi and theta (before multiplying by @mpwr.)

Edit: I doubt that will work. My analysis of the inverse iteration problem was too hasty.
« Last Edit: October 16, 2009, 02:56:48 AM by xenodreambuie » Logged

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David Makin
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« Reply #341 on: October 16, 2009, 03:33:08 AM »

Garth: OK !

Here are the new candidate Julias rendered properly:



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David Makin
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« Reply #342 on: October 17, 2009, 01:28:46 AM »

Finally had a go at some Julia's using Garth's version of the triplex formula:

http://www.fractalforums.com/gallery/?su=user;u=141;cat=95
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xenodreambuie
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« Reply #343 on: October 17, 2009, 01:38:34 PM »

Excellent, Dave! I had managed to replicate that form with an inverse formula, but wasn't sure if it was right. I have it working for quadratic and expect to make it work for other powers. I've also solved the inverse trig version of the z=-rsin(phi) one. It's much cleaner for some settings because it has no singularities or instabilities.

For the forward version of my alternative triplex, try this:
ph = acos(zj/magn)
if ph>pi/2 then ph = pi-ph  // or whatever the UF equivalent is
ph =  @mpwr*ph

Compared with the proper cos triplex, my alternative has two of the correct roots and two wrong, and misses two correct ones. So for the ones that are missing, you need to change phi to the wrong roots instead.
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David Makin
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« Reply #344 on: October 17, 2009, 05:01:49 PM »

Excellent, Dave! I had managed to replicate that form with an inverse formula, but wasn't sure if it was right. I have it working for quadratic and expect to make it work for other powers. I've also solved the inverse trig version of the z=-rsin(phi) one. It's much cleaner for some settings because it has no singularities or instabilities.

For the forward version of my alternative triplex, try this:
ph = acos(zj/magn)
if ph>pi/2 then ph = pi-ph  // or whatever the UF equivalent is
ph =  @mpwr*ph

Compared with the proper cos triplex, my alternative has two of the correct roots and two wrong, and misses two correct ones. So for the ones that are missing, you need to change phi to the wrong roots instead.

Thanks and thanks for the details for that "forward" version - will try it later smiley

In the meantime here's a Julia animation using the "correct" forwards cos triplex:

<a href="http://www.youtube.com/v/1VVFo97so8U&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/1VVFo97so8U&rel=1&fs=1&hd=1</a>
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