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Author Topic: True 3D mandelbrot type fractal  (Read 275568 times)
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Aexion
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« Reply #465 on: November 14, 2009, 06:20:56 PM »

Wow, I'm away for a couple of days, and then I miss all this!

Aexion, you've got to one of my fave fractal artists ever - I love your recent "The Hexahedral Puzzle" - it has a lovely Aztec feel about it. Still think your Sunset Castle (and Return thereof) is awesome.


Thanks a lot Twinbee!!  smiley
It's nice to be here, and BTW, your renders are absolutely amazing!
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Fractals all the way..
Incendia for 3D Fractals
Aural for Musical Fractals
ker2x
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« Reply #466 on: November 14, 2009, 06:53:49 PM »

Hi all,

I just updated the WIP3D formula, new link:

http://www.fractalgallery.co.uk/MMFWip3D.zip

Again unzip, copy all the text and paste into an open UF fractal window (also requires UF5).
This time the UPR is an example render of Pickover stalks (orbit trap) - note that "auto distances" is disabled and the solid threshold is much larger than used for solid on iteration/distance estimate.
Several more options in the formula plus some bugfixes in the analytical distance estimate methods.
This is actually named as a different formula so as not to cause compatibility issues with any renders you've already done smiley


Hi ! Thank you for sharing this.
I'm playing with incendia (which is awesome) since yesterday.

And with UF5 (demo Grin with closed eyes) and your formula.
Sadly, not good enough to understand the math behind (*sigh*) i just click here and there and found that i could do some interestring rendering with the "Truly 3D Mandelbrot". i don't know how "true" is my rendering and how it could be even close to anything related to a mandelbrot fractal but... it's nice.

I've seen the pic of "3D Mandelbrot" seen from the inside... it's truely awesome. But it look like most of 3D Mandelbrot rendering are done with custom renderer and not distributed at all... am i correct ?

Thx again !!

PS about the image below. "Truely 3D mandelbrot" after randomly playing with parameters

Edit : i finally found how to adjust parameters to have a 3D Mandelbrot, adjust accuracy and detail.
It is, mostly, all about "Solid Thresold" to be able to dive into details smiley


* keru3D-2.jpg (62.78 KB, 800x800 - viewed 1746 times.)
« Last Edit: November 14, 2009, 07:32:04 PM by ker2x » Logged

often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
(en) http://www.blog-gpgpu.com/ , (fr) http://www.keru.org/ ,
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bib
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« Reply #467 on: November 14, 2009, 08:55:46 PM »

Some vids based on the old M-true3D formula. Nice to watch but quite disappointing indeed sad
Watch the first one til the end you'll recognize the 2D M-set shape.
In the second one I tried to use some rotation to enhance the 3D impression
<a href="http://www.youtube.com/v/mIbDAunza6Q&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/mIbDAunza6Q&rel=1&fs=1&hd=1</a> <a href="http://www.youtube.com/v/uDUWEBAk8Ys&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/uDUWEBAk8Ys&rel=1&fs=1&hd=1</a>
« Last Edit: November 14, 2009, 09:00:58 PM by bib » Logged

Between order and disorder reigns a delicious moment. (Paul Valéry)
JosLeys
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« Reply #468 on: November 14, 2009, 11:11:04 PM »

On the question which factor should precede the analytical distance estimate formula :

is it
Quote
dist = 0.5*sqrt(@mpwr-1.0)*log(magn)*sqrt(magn/|dzri|)
or
Quote
dist = 0.25*@mpwr*log(magn)*sqrt(magn/|dzri|)
?

Let's change notation first : for the spherical case for any power I use DE=log(R)*sqrt(R)/(dR)/2, where dR is the derivative. So my factor is just 0.5.

To test how accurate this is, I took a Julia with seed (0,0,0) which produces a sphere of radius 1, so we now know the real distance for any point on a ray.

I'm printing the results below for a point progressing from a distance 2 from the surface of the sphere. The first column is the number of iterations, the second is the calculated DE, and the third is the real distance. As the point is still "far" away, and the number of iterations to reach bailout is low, then DE is exaggerated. (that's why an extra factor to temper DE is always needed). However, as the point gets closer, DE becomes very accurate.
The numbers are from a power 8 Julia, but I see almost exactly the same numbers for a degree 2.

power=8
start
         DE                        real distance
1 , 3.29583686625158 , 1.99999999999248
1 , 0.407849058786746 , 0.352081566866694
2 , 0.158627173103063 , 0.148157037473318
2 , 0.0711605799066145 , 0.0688434509217899
2 , 0.033810346387068 , 0.033263160968481
3 , 0.01649105643562 , 0.0163579877749456
3 , 0.00814527732540994 , 0.00811245955713247
3 , 0.00404797039654616 , 0.00403982089442678
4 , 0.00201786652103339 , 0.00201583569615593
4 , 0.00100740958383335 , 0.00100690243564117
4 , 0.000503324618422875 , 0.000503197643723752
5 , 0.000251567358870418 , 0.000251535334513164
5 , 0.000125759953482483 , 0.000125751655076556
5 , 6.28740467193265E-005 , 6.28716783381833E-005
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Buddhi
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« Reply #469 on: November 15, 2009, 04:59:28 PM »

Hi
I'm still fighting with some kind of volumetric rendering. Now it's not fixed grid. Step depends on iteration count, perspective factor (bigger step in bigger distances). Additionally for improve performance and quality I use binary searching algorithm. I think it's quite enough for this kind rendering.
Generally I have lot's of trouble to render that deep perspective view, because for acceptable performance I have to add lots of factors to each shading algorithm. Details in background are 1000 times bigger than in foreground. For the farthest elements quality of shaders are much less accurate. I made the same for more transparent details. Without this optimisation this fractal will be rendered approximately in one month. Now it is possible in 8 hours with global illumination.

Render parameters:
resolution: 1280x1280
camera target: {-1.7844592849042, 0, 0}
zoom: 10000x
max. number of iterations: 80
fog range: between 65 and 80 iteration


http://www.fractalforums.com/gallery/?sa=view;id=1058
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ker2x
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« Reply #470 on: November 15, 2009, 06:08:14 PM »

hooo fluffy \o/
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often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
(en) http://www.blog-gpgpu.com/ , (fr) http://www.keru.org/ ,
Sysadmin & DBA @ http://www.over-blog.com/
iq
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« Reply #471 on: November 16, 2009, 03:29:46 AM »

if anybody is interested, this is the full polynomial replacement for Z->Z^8+C, simplified (still one inverse square root, but that's much faster than a square root)

Code:
// Z=(x,y,z), C=(a,b,c)

float x2 = x*x; float x4 = x2*x2;
float y2 = y*y; float y4 = y2*y2;
float z2 = z*z; float z4 = z2*z2;

float k3 = x2 + z2;
float k2 = inversesqrt( k3*k3*k3*k3*k3*k3*k3 );
float k1 = x4 + y4 + z4 - 6.0*y2*z2 - 6.0*x2*y2 + 2.0*z2*x2;
float k4 = x2 - y2 + z2;

x = a +  64.0*x*y*z*(x2-z2)*k4*(x4-6.0*x2*z2+z4)*k1*k2;
y = b + -16.0*y2*k3*k4*k4 + k1*k1;
z = c +  -8.0*y*k4*(x4*x4 - 28.0*x4*x2*z2 + 70.0*x4*z4 - 28.0*x2*z2*z4 + z4*z4)*k1*k2;
« Last Edit: November 16, 2009, 05:18:55 AM by iq » Logged
cKleinhuis
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« Reply #472 on: November 16, 2009, 11:48:16 AM »

i just checked some traffic stats, it is not as much ... just 4 times more than on usual days ...

hope it will stay like this, traffic problems shouldnt occur, because of unlimited data transfer smiley
last time google featured gaston julias birthday a few gigabytes were sucked through the lines in a few hours ( back in 2006 i think )

but 270 guests dont seem to be only bots wink

yeah, congratulations all contributors this thread is going to be really really long ....

just nice to get mentioned ... me as "only" the site owner is very happy ...  wink Azn smiley grin cheesy
« Last Edit: November 16, 2009, 11:50:34 AM by Trifox » Logged

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iq
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« Reply #473 on: November 16, 2009, 12:11:09 PM »

Hi, I added some distance estimation to the raymarcher based on the G/|grad(G)|, which is the very basic definition of DE, so I have no confusion possible with unkown constant factors. It works fine, but it's still "slow" cause I compute the gard(G) numerically, but since I have the polynomials for the iterations I will be able to compute it analycally tomorrow. I have extracted the Jacobian already, which is a bit of a monster. The normal to the surface is simply n = J * z (a vector transformation), so I will have analytical normals too. In the meanwhile I think I should try David-Makin´s way of DE, which only uses 2 points (mine uses 4).

In the meanwhile, I made a little nice trick with orbit traps, to add color and occlusions for free. The following image (reduced from 1280x720) takes around 2 seconds to render. I expect to have it realtime soon (I'm rendering a video tonight with motion blur, it should be ready by tomorrow)


http://iquilezles.org/trastero/f8p2.jpg

There seem to be some ambient occlusion in there, but there isn't. The trick is to use an orbit traps to fake it. Like in the 2D case, you can define a 3D geometric trap and track the orbit of Z relative to this trap. I used a simple point trap in the origin and use it´s distance to extract a fake occlusion term. It looks like thisÑ


http://iquilezles.org/trastero/f8p3.jpg

There is no global illumination, or raycasting of the hemisphere nor a shadow ray in it or anything. So for those with "simple" raytracers that cann´t do/afford GI, this is a nice trick to increase realism (if that´s your goal at all).

I used three more line traps to add coloring to the surface, which is nicer that doing simple color=position or color=perlinnoise(position), as the orbit trap patterns naturally follow the shape of the fractal, so the features in the structure get colored in a logical manner.

I don´t know how much the analytic gradient(G) will help, but it should in theory be a x3 gain. Will continue to inform.

In the meanwhile, I was having some thoughts. The polynomial version of formulas really highlight how "asymmetric" the formulas are. I wonder if the holly grail of the true 3d M-Set shouldn´t have a bit more even formulas for x,y,z... Not completely symmetric, but at least something more reasonable?

JosLeys, so in the end which of the formulas is the correct one for DE?
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bib
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« Reply #474 on: November 16, 2009, 12:18:12 PM »

The following image (reduced from 1280x720) takes around 2 seconds to render. I expect to have it realtime soon (I'm rendering a video tonight with motion blur, it should be ready by tomorrow)

2 seconds, waaaooo!
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iq
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« Reply #475 on: November 16, 2009, 12:28:04 PM »

another image I took before launching the video render:

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twinbee
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« Reply #476 on: November 16, 2009, 12:37:22 PM »

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
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iq
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« Reply #477 on: November 16, 2009, 12:42:44 PM »

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

no, no, not at all, I wish I did something special to take credit for that speed, but it´s not the case. It's simply that GPUs happen to be super fast today, so even when directly progamming the brute force thing in opengl it just runs fast.
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David Makin
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Makin' Magic Fractals
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« Reply #478 on: November 16, 2009, 12:46:56 PM »

The following image (reduced from 1280x720) takes around 2 seconds to render. I expect to have it realtime soon (I'm rendering a video tonight with motion blur, it should be ready by tomorrow)

I both hope and assume that's 2 seconds using the GPU ?
Can anyone please send me £2000 so I can get a new system ? (this P4HT is a dinosaur - only an ATI X600 too) cheesy
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cKleinhuis
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« Reply #479 on: November 16, 2009, 12:49:18 PM »

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

to be true, i am lazy and just checked the forum stats, it has an enormous count of online users for today: more than 1000.
i will check server logs tonight to give extra information ( in the fractalforums.com news thread )

enjoying it, and i have to agree with iq and twinbee that the "smearing" looks a bit odd at the renderings, but on the other hand they look for me like a hint.
so, it occurs that ~80% of the formula might be like we expect, but on the radial sections around some degrees ( could be 4 disconnected sections ) where the smearing
occurs it is somehow "not correct" but i am optimistic, because it is only a little part of the formula which might be changed to get fractal borders anywhere on
the object. in fact this object is constructed from "fractal" and "euclidian" regions ....

dup dee dup, keep it on ! enjoy this thread more from day to day!  afro afro afro
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divide and conquer - iterate and rule - chaos is No random!
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