Title: 3D Mandelbrot Fractal Anim1 HD 720p Post by: Saquedon on December 02, 2009, 10:20:55 AM http://www.youtube.com/watch?v=XBviE3AXBbE
Watch in on Youtube for the HD version. Basically a test is did exploring 3D Mandelbulb in animation. I plan to make a full Length video with various animations of it. You can view it also here: http://www.vimeo.com/7902770 Or view and download it here: http://blip.tv/file/2912774 Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: miner49er on December 02, 2009, 09:47:48 PM Completely and utterly awesome!
I would love to see some zooms in. Do you know if the the bits between the bulbs ever show a fractal like complexity? or are the forever simple and flat regardless of number of iterations? I must start rendering some of these... Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: bib on December 03, 2009, 12:26:29 PM Completely and utterly awesome! I would love to see some zooms in. Do you know if the the bits between the bulbs ever show a fractal like complexity? or are the forever simple and flat regardless of number of iterations? I must start rendering some of these... examples of zooms : http://www.youtube.com/watch?v=LxsniUIVfEM http://www.youtube.com/watch?v=jR46hjcqQnA The "flat" parts become less flat when you increase iteration count, revealing new fractal details, but sometimes extremely stretched so not very interesting graphically. Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: miner49er on December 03, 2009, 10:53:44 PM Pretty damn cool.
That second one was really starting to get interesting just before it finished! How long did these take to render and on what hardware? Also, do any mathematicians know if the cause of the stretching artefacts are caused by the fact there is a singularity in the co-ordinate system? And if so, is there any theoretical way around the problem? Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: bib on December 03, 2009, 10:58:03 PM How long did these take to render and on what hardware? between 20 and 30 hours each on a core i7 920 Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: kram1032 on December 03, 2009, 10:58:40 PM About stretching: I could only guess...
In certain regions, the standard-Mandelbrot gets very stretched too... So my guess would be that the additional dimension kinda just increases that stretching.... Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: Tglad on December 04, 2009, 12:01:40 AM >> Also, do any mathematicians know if the cause of the stretching artefacts are caused by the fact there is a singularity in the co-ordinate system?
>> And if so, is there any theoretical way around the problem? About the best explanation I've heard is that the mapping function needs to be conformal in order to remove stretching. Z^2 is conformal, which means that if you make any tiny shape out of points in Z, then square each one, you end up with the same shape without any stretching, just scaled and rotated. There doesn't seem to be much literature about 3d conformal mappings, but here are 3 ones that I think are conformal: 1. just scaling and rotating the 3d space, e.g. x,y,z = 2(x,y,z) or x,y,z = 2(-y, x, z) 2. A certain type of toroid may be conformal 3. A mapping that looks like a cardoid swept around its main axis is also probably conformal The problem is that 1 is boring and 2 & 3 don't have an attractor at infinity... everything tends to sweep back to 0,0,0 I personally think there is a way around the problem, but the resulting bulb may not be spherical, since all spheres have a singularity.. see http://en.wikipedia.org/wiki/Hairy_ball_theorem Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: miner49er on December 04, 2009, 01:48:33 PM Thanks for the replies everyone, very very interesting.
In certain regions, the standard-Mandelbrot gets very stretched too... I've never noticed this. Unless you mean the slightly distorted mini-mandelbrots at deep)ish zoom levels? Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: bib on December 04, 2009, 02:29:44 PM Thanks for the replies everyone, very very interesting. In certain regions, the standard-Mandelbrot gets very stretched too... Maybe he talks about the long filaments. The difference with the stretched parts of the Mandelbulb is that the 2D filaments do have fractal details if you zoom deep enough. I've never noticed this. Unless you mean the slightly distorted mini-mandelbrots at deep)ish zoom levels? Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: kram1032 on December 04, 2009, 07:48:09 PM Yup, the Minimandelbrots are quite stretched in certain regions. especially from the valley in the caridote, I saw some very stretched regions.
It could be that this distortion more or less increases over the dimensions... Bib are you sure that the Mandelbulb never gets (3D) fractal details on higher iteration counts? That's also a thing of course... "growin" Mandelbrotsets start quite smooth and get more and more..... welll... fractal in the still smooth regions... Title: Re: 3D Mandelbrot Fractal Anim1 HD 720p Post by: Saquedon on December 07, 2009, 11:50:30 PM Well there are great details in the "flat" zoomed in surfaces and i've made quite a few images with them already, obviously they don't look like the 3D object anymore. I hope to publish some of those soon, for now i am working on making prints of my work available. But i didn't seem to get much detail raising the iteration count, what iteration factors are we talking ? I also found the objects got very jaggy shadows (quite noticable in black & white) which i haven't been able to solve yet. |