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Author Topic: True 3D mandelbrot type fractal  (Read 263007 times)
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twinbee
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« Reply #495 on: November 17, 2009, 08:17:11 AM »

Wow, it's all there - the eyes, nose, beard and hair!

Hi Jules, have you tried rendering large/raytraced images of the 3D set you found, and maybe higher powers too? If you know the boolean function (accepting x,y,z, and outputting true or false - i.e. in the set or not), it'd be interesting to see the output.
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David Makin
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« Reply #496 on: November 17, 2009, 09:36:56 AM »

I thought mine was fast, but 2 seconds!!! Right, I see you're from the year 2050 then? wink

Lycium's right - my server was dying (10k hits per hour), but I managed to get a lot of the content over to Amazon S3 - a great solution for bandwidth at commodity prices. This thread is linked from Slashot too. Surprised to hear only 4x as many visitors (Trifox, you must get 2500 per hour ordinarily wink )

Congrats all cheesy

I'm also getting a knock on effect - yesterday over 600 unique visitors, 2,113 page hits, 26,271 overall hits and a whopping 817MB of bandwidth used - I'm actually hoping it'll drop off a little otherwise I'll have to either remove at least the .mov files or fork out for some alternate space or a greater bandwidth limit (currently 15 GB/month).
Edit: Should have said my normal unique visitors per day (say last month) was around 40.

« Last Edit: November 17, 2009, 09:39:31 AM by David Makin » Logged

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bib
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« Reply #497 on: November 17, 2009, 09:43:28 AM »


Excellent quality! smiley
Why can't you install a special cooling system on your GPU?
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Between order and disorder reigns a delicious moment. (Paul ValÚry)
bib
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« Reply #498 on: November 17, 2009, 09:45:46 AM »


Definitely humans are designed to find patterns.


lol

did you notice in my zoom that the shape in the last frame looks like an alien skull?
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Between order and disorder reigns a delicious moment. (Paul ValÚry)
cbuchner1
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« Reply #499 on: November 17, 2009, 11:59:26 AM »

Hi everbody.

I've been following this thread with great interest.

Let me bring to your attention that nVidia's Optix SDK (raytracing) has a "julia" sample where they apply the DE method to raytrace a Julia set. Frame rates are interactive on decent graphics chips. I believe it should be simple enough to modify this SDK sample to render a Mandelbulb instead. The maths is currently still a little over my head, but maybe someone of you wants to have a go at it.

Using this raytracing SDK has the nice advantage that implementing various surface properties (including reflection and refraction) is a breeze. Maybe one could even render the entire fractal transparently like a crystal (don't know if the DE method works for rays passing through the fractal though).

The Optix SDK is available free of charge (only filling in a short questionnaire is required before getting to the download) and they support are Windows and Linux in 32bit and 64 bit flavours - however nVidia do require Quadro FX or Tesla cards to run the code. This is an arbitrary limitation by nVidia and there are tools on the net to patch out that requirement. While it may not be legally sound to redistribute patched binaries, I think it's unproblematic to do some testing with it.

UPDATE: I stripped down that SDK sample to render nothing but the quaternion Julia set (the animated chrome ball is gone, so is the floor consisting of moving cubes).  I can now rotate the Julia set in a VGA sized window pretty much smoothly on a low-end GPU (nVidia GT220, I get 15-30 FPS). Let's hope it stays that way when I switch to the Mandelbulb. My next step would be to adapt the DE formula as given in this thread, but I am not sure if I can do that on my own.
« Last Edit: November 17, 2009, 06:01:44 PM by cbuchner1 » Logged
JosLeys
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« Reply #500 on: November 17, 2009, 12:21:55 PM »

Thanks Inigo for the tip on using an orbit trap to mimic ambient occlusion lighting.
Here is a power 7 in Ultrafractal. The orbit trap makes a big difference.


Ultrafractal takes about two and a half minutes to produce this. I'm a bit less envious of the two-second GPU  versions now that I hear that they produce a fire hazard  evil

I'm glad Dave volunteered to test the second derivative distance formula. It's a bit of a monster, and probably too expensive, but I wonder how it performs.
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bib
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« Reply #501 on: November 17, 2009, 12:45:35 PM »

I'm also getting a knock on effect


Me too smiley
Usually my videos on Youtube get less then 50 hits after a few weeks. But the 3D Mandelbrot Power 6 zoom got almost 2000 hits in 2 days!
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Between order and disorder reigns a delicious moment. (Paul ValÚry)
kram1032
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« Reply #502 on: November 17, 2009, 04:14:02 PM »

Hi smiley
I talked to Twinbee about this on deviantart and he told me to come here, so here I am.
Hi lycium. cheesy

I had one idea for why the standard Mandelbrotset behaves that assymmetric in this 3D-Variant.
Most likely, that is, because it already does so in the 2D-Version.
Well, nearly.
In the 2D-Version, z▓+c produces only mirror-symmetries and relative to the zero-point, inside the caridode, one could say, it features "single-axial radial symmetry"
z│+c features double mirror symmetries or "2-axial radial symmetry"
z4+c features 3-axial radial symmetry and so on

zn+c in general features an (n-1)-axial radial symmetry.

As things get twisted into higher dimensions, things with only one axis of symmetry start to look odd. they twist in a rather strange way and that happened to the z▓+c-variant.

Though, I have a couple of ideas:
Right now, you basically use two totally unrelated angles and transform them in one and the same way to get your results.
What if you actually search for a relation between them?
One way to do this would be to interpret the two angles as complex unit vectors.

your formula for the angles then would be:

(r,theta,phi)n =
(rn,2*pi*cos(arg(z))*n,2*pi*sin(arg(z))*n)

Other relations could be thinkable... though I only can give an example which probably does not work directly.
http://www.wolframalpha.com/input/?i=sqrt%28%28x%29^2%2B1%2F%28x%29^2%29%3D2
the idea here is that one angle always has to be the inverse of the other angle. But as the angles are real-valued, so that complex solutions wouldn't work, you only get four different values to work with.

A different way to get nice angular relations might be via the riemann-sphere.
Taking the radius as is but looking at where the iteration would have been found on the riemann-sphere, express it as the two angles (the radius of 1, as said is overwritten by the resulting radius) and plot the new position accordingly.
Though, as on the bottom of that sphere, you have zero and on the top you have infinity, this might lead to a different kind of distortion. - 3D but not as spherical as the original intention^^


A very exotic variant would be a weird clifford algebra without any real part.

Something like
i*i=-j
j*j=-e
e*e=0
i*e=j
j*e=i
i*j=e
i*j*e=e*e=0

no idea if that would actually describe something usable but it might be worth a try smiley
Also, for that, you would probably need to figure out, if it at all works, how it works:
is j*i=i*j or not? Grin with closed eyes

Ok, those where some random quick ideas. I hope, you like them Grin with closed eyes
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flok
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« Reply #503 on: November 17, 2009, 04:39:54 PM »

Hi,

I've been experimenting a little with Daniel's formula. After a few hours of experimenting I somewhat succeeded in implementing the formula in Java with Povray-scene output being generated.

Put all of it on my website: http://vanheusden.com/java/3dmand/

First results are not as impressive as some (well, most) of the pictures I saw in this forum but maybe with some texture-changes or so (or higher detail rendering) it might be fun to play with it.
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bugman
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« Reply #504 on: November 17, 2009, 05:52:27 PM »

Akkara Leith pointed out to me the reason why some people are not getting the same formulas for my higher order non-trigonometric formulas. The reason is because I was using atan(y/x) instead of atan2(y,x) for my definition of theta. I have gone back and changed this to my original posts:
http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8426/#msg8426
http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8470/#msg8470
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bugman
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« Reply #505 on: November 17, 2009, 05:53:18 PM »

.


* WhiteZ Formulas.gif (15.58 KB, 946x527 - viewed 1787 times.)
« Last Edit: November 17, 2009, 10:16:20 PM by bugman » Logged
bugman
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« Reply #506 on: November 17, 2009, 06:02:10 PM »

I am continuing to play with inverse Julia sets using the MIIM method. I was quite impressed with xenodreambuie's inverse Julia sets using this method. Earlier on this thread, he presented an interesting method for finding n▓ valid roots for any nth order formula. When I tried to implement this method, I found that sometimes some of the roots were still invalid, but with some minor modifications, I was able to consistently get all 16 unique valid roots for the 4th order formula. Here is an example of the 4th order inverse Julia set using MIIM. I still haven't implemented soft shading yet with my point cloud renderer, but I hope to add that soon.


* 560.jpg (222.75 KB, 560x560 - viewed 1185 times.)
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JColyer
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« Reply #507 on: November 17, 2009, 06:25:37 PM »

Hey all, I've been dabbling in fractals since I first saw the Beauty of Fractals book way back in the day.  I'm a programmer by trade but not a math geek - so most of the formulas are way over my head.  Once I see it in code I'm cool.  I just found this site/thread from the /. link yesterday about the 3d Mandelbulb, which has got me going again.  I've noticed from browsing around that a lot of folks seem "down" on Quaternions as being too smooth and boring, but I think that they're wrong.  It's all about what's on the inside, not the outside... sorry about the crappy JPG's forum limits...



* quaternion_0.27334_0.jpg (244.68 KB, 1243x928 - viewed 1183 times.)

* quaternion_0.32_0.043_0_0_2.jpg (196 KB, 1243x928 - viewed 1147 times.)
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cbuchner1
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« Reply #508 on: November 17, 2009, 09:55:41 PM »

My next step would be to adapt the DE formula as given in this thread, but I am not sure if I can do that on my own.

 tease

Some early raytracing code for Mandelbulbs requiring the Optix SDK and CUDA tool kit to be found in this posting. Optix is an API for raytracing on CUDA capable graphics chips. It will run at interactive frame rates on a GTX260 graphics cards and better, however a binary patch is required to enable Optix on anything but Tesla and Quadro Fx cards (use google to find such hackery).

Dependencies are the Optix SDK by nVidia and the CUDA toolkit V2.3 or later - both available for free for Windows and Linux. Because .zip files can't be attached here, find the source code on the nVidia forums (need to register to download the attachment)

http://forums.nvidia.com/index.php?showtopic=150985&view=findpost&p=952165

Still, I am still very dissatisfied with the shading and lighting - it is hard to make out any surface detail. But it does ressemble the 8th order Mandelbulb. In my version I'd rather call it an ugly barnacle ball. But I am onto something. I only hacked on this for about 4 hours. I am still having issues with some transparently appearing pixels where there should be a solid. Also the way the surface normals are determined give the shading a weird and grainy look.

Let me know if my iteration formulas and parameters look correct. I mostly copied the approach by JosLeys in posts #355 and #397.

I'd love to learn how to implement the orbit traps correctly to simulate global illumination.

Christian
« Last Edit: November 17, 2009, 09:58:40 PM by cbuchner1 » Logged
fractalrebel
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« Reply #509 on: November 17, 2009, 10:27:41 PM »

Dave,

I set iterations to 1000 and bailout to 100. It really doesn't give much more detail than with your rendering. I guess we are still in search of the elusive highly detailed 3D-Mandelbrot. All of my current stuff is now in the UF database in reb.ulb.


* 4DMaandel.jpg (67.73 KB, 640x512 - viewed 1283 times.)
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