Mandelbrot to Mandelbulb - 3D Infinity

I got chills seeing this! I've always been fascinated by the Mandelbrot Set and fractals. However, I wasn't expecting the computer technology to be available for this yet. I should have known better.

This is not trivial. I think there is a lot more to learn from this than just pretty pictures. This is really seeing the Mandelbrot set. The 2D version was just a part. Just more proof that perceiving things in higher dimensions increases complexity and beauty.

What I'm still trying to wrap my head around is that the 3D Mandelbrot set is still just two dimensions on my screen. Add resolution (or time) and this is what we get. However it is the same with the 2D Mandelbrot Set. 2D pictures with resolution. It reminds me of the difference between South Park and Avatar. Both are 2D with resolution, but Avatar has exponentially more info within each frame. Does this mean perceiving higher dimensions requires observing more information within time?


[edit on 9-2-2010 by royalred]

Fractals are fascinating, to say the least!

Thanks for the links, and for the history of this most relevant of information!

Originally posted by The Soothsayer
Not trying to move the thread along a different route, nor am I trying to not contribute, for I will eventually comment, but I just have to say this...

Some of those pictures I just had to stop and stare... it was if I was being drawn in. Amazingly, a few seemed to show representations of Cambodian temple design...

Perhaps this is a glimpse into the divine.

...

Okay, now with that said. Having been involved in 3D animation and illustration, I can't even begin to fathom the time it took to fully render this... if it has even happened. It's an infinite object, rendering wouldn't stop. Every time it is zoomed, it will render more and more. To answer an earlier question, to animate it would be nigh-impossible.

Hey bro,heres a start .....en.wikipedia.org...
For programmers

The definition of the Mandelbrot set, together with its basic properties, suggests a simple algorithm for drawing a picture of the Mandelbrot set. The region of the complex plane we are considering is subdivided into a certain number of pixels. To color any such pixel, let c be the midpoint of that pixel. We now iterate the critical value c under Pc, checking at each step whether the orbit point has modulus larger than 2.

If this is the case, we know that the midpoint does not belong to the Mandelbrot set, and we color our pixel. (Either we color it white to get the simple mathematical image or color it according to the number of iterations used to get the well-known colorful images). Otherwise, we keep iterating for a certain (large, but fixed) number of steps, after which we decide that our parameter is "probably" in the Mandelbrot set, or at least very close to it, and color the pixel black.

In pseudocode, this algorithm would look as follows.

For each pixel on the screen do:
[
x0 = x co-ordinate of pixel
y0 = y co-ordinate of pixel

x = 0
y = 0

iteration = 0
max_iteration = 1000

while ( x*x + y*y

Very Cool Thread , A nice perspective , S&F bro , Keep up the nice work!!

Maybe fractals explain why history repeats itself.

I prefer to look at Mandelboobs, I could stare at them for infinity.

[edit on 9-2-2010 by harrytuttle]

Yea I'd have to agree with those that believe the universe being one never ending fractal.

As far as the Mandlebulb, thanks for posting this S+F

I was and am a huge fan of the Mandelbrot Fractal/set, and have mant pictures of the 2d version.

Haveing said this, although I find the 3d Mandelbulb to be very pleasant on the eyes, and just amazing.

I still find the animated zoom in of the 2d set to be more mind blowing than the animated zoom in of the 3d bulb. Perhaps because with the 3d set you cannot just keep going deeper and deeper like the 2d set, because sooner or later your gonna run into a wall because it's 3d.

But it's beauty is not lost on me, Comparing the 3d stalk to the 2d stalk. There's no question the 3d one is way more amazing.

But I can only imagine how much time and effort these scientists and graphics designers put into makeing the Mandelbulb. So cheers to them.

and cheers to the OP again for posting this thread, and the intial post was done very well, showing the progression, and explination of the Mandelbrot set, along with pictures for reference, and the video at the end was spectacular. Thats where I say the 2d version shines over the 3d version in a zooming in endless video format, which I just don't see how it can be done with the Mandelbulb, as said sooner or later you run into something solid

But again GREAT thread!

leave it to me to kill the mood but.....of what practical use is this so far other than to titillate the intellect, curiosity and imagination? can this be used to free the little ppl from big brother?

reply to post by ikonspyre


Nothing will free us from big brother because we don't want to be. If we did we would have banded together and done it. Were too petty and self interested. The fractal set is more about looking at existence and its nature. As a representation of infinity the 3d set is a great way of explaining the big and small and the relativity of each.

Others far more educated in mathematics will explain it better but ultimately the implications of this has less to do with opression then it does enlightening people and getting them thinking about things, perhaps in a different way than they are used to. It is the only way we progress.

Cheers

I can't believe I've never heard of these 'fractals' before. I'm intrigued!

I've always had this feeling that the universe in some way boiled down to circles and spirals. I feel like string theory fits in here somewhere as well...

Corkscrews to me are a good representation of this concept as well... the way the spiraling screw appears to infinitely move forward so long as someone's turning it.

The question is, who's turning the "corkscrew" that is the cosmos?

[edit on 9-2-2010 by Jack Squat]

I'm confused about the concept that the Universe or anything in nature is a representation of a fractal.

Pareidolia is clearly in play here. Some things in nature resemble a fractal but nothing in nature is a fractal. Patterns don't repeat when you break down natural objects. Each smaller element is unique which makes this whole fractal universe idea a red herring. Does it not?

Absolutely wonderful thread.

Thanks Evasius.

Springer...

Originally posted by ikonspyre
leave it to me to kill the mood but.....of what practical use is this so far other than to titillate the intellect, curiosity and imagination? can this be used to free the little ppl from big brother?

Good question. But I'm sure Pythagoras didn't realize all the applications for a²+b² = c².

I would imagine the process they used to get from the original 2D object to the 3D object could be applied somewhere else. Just an idea. It always takes time to see the applications.

It's also proof that our knowledge of math, computers and technology is growing rapidly. I didn't think anyone would be able to do this for quite some time. And they just did it!

Even if the application for now is only art, don't underestimate that. Appreciation of art is one of the few things the "powers that be" can not take from you.

Yer very interesting how the 3D Mandelbrot set gives of such organic looking structures. But is it art or science?

Thanks for the detail Evasius!

It's nice to have the mandlebrot set back in focus, and even more detailed in 3D!

Fractals are Creation. Fractals are Evolving Creation, creating evolution.

They are everywhere you look when you start looking. Even yourself, a fractal of your mother, a fractal of the earth, of the universe...

what is the universe a fractal of i wonder?

Originally posted by Blaine91555
I'm confused about the concept that the Universe or anything in nature is a representation of a fractal.

Pareidolia is clearly in play here. Some things in nature resemble a fractal but nothing in nature is a fractal. Patterns don't repeat when you break down natural objects. Each smaller element is unique which makes this whole fractal universe idea a red herring. Does it not?

It's confusing because you, like all of us, are thinking of it in terms of your view of reality. Both the 2D and 3D versions of the Mandlebrot Set are really both 2D with resolution (resolution could also be thought of as time, so it is really 3D, 2 spacial/ 1 temporal) The difference is the 3D Mandlebulb includes more info within a time frame.

The Universe that we observe is 3D plus time. So 4D. It's hard to see the fractal nature because we haven't fully grasped the 4D world we perceive. We have a pretty gud idea about the 3 spacial dimensions but we have barely scratched the surface of time and higher spacial dimensions.

Terrence McKenna always posited that one of the "uses"for the trance he so loved was to try to"bring something back'' and I must say,this is as close to IT as can be.This induces conversation and NOVEL words of description.

Originally posted by RogerT
has anyone managed to animate this?

www.neave.com...

Check out that link...

It does not go on forever, but it is pretty fun to play around with and it illustrates the concept well enough that you can imagine what an infinite one would be like.

far---------out, and ------farrrrrrrrrrr in!

now who amongst you prints T shirts? what a wealth of designs to choose from.

if i had any spare time i'd crank up the carousel.

all my life i've seen two streams of consciousness on this planet. one descending and one ascending. i believe we become aware of fractals as our consciousness increases.

what further beauty awaits us!

Starred and flagged for sure!

I'm sitting on my University's campus right now with my iPod on shuffle. Interestingly, when I watched the videos of the 3D renders, I felt...a sense of euphoria, regardless of what song came on next. Has anyone else felt this?

Originally posted by [davinci]
Very interesting indeed, great job.

What got me is the Toroidal displays, particularly the top right most.

This is a very good (albeit simplistic) view of the discovered Epi-genome, a secondary DNA strand that encircles our main DNA. Very interesting as research is showing that the epi-genome provides virtually real time genetic change by manipulating gene expression in the main DNA strand (things you experience today will manifest in your grandkids).

This type of research lends credence to the thought that the eventual explanation for Life, the Universe and Everything will be an equation that can fit on the front of a T-shirt.

Sadly the answer is probably not 42.



[edit on 9-2-2010 by [davinci]]

perhaps another piece of the puzzle as to how the mind effects changes in the DNA?