Mandelbrot to Mandelbulb - 3D Infinity

Recently, the now famous Mandelbrot Set was accurately rendered in 3D, and the results are astonishing. Discovered in 1980 by Benoit Mandelbrot, the fractal image has blown the minds of many given that the 2-dimensional design is in fact infinite. The underlying algorithm of the Mandelbrot allows for endless exploration of its intricate boundary - no matter how far you zoom in, rather than encountering simpler patterns, you instead find beauty in its increasing complexity.

The 3D Mandelbrot pattern, the 'Mandelbulb,' is unique and equally complex. Newly discovered algorithms by Daniel White and Paul Nylander gradually allowed the new form to take shape, and eventually the equivalent of an entire universe was found and rendered explorable. The fractal alien landscape is immense and is unlike anything ever seen before with caves, mountains, valleys, and never-ending repeating patterns resembling both microscopic objects and planetary surfaces.

The official site for the research is The Unravelling of the Real 3D Mandelbulb and many of the images below were created by either Daniel White or Paul Nylander. I've altered or cropped some images in order that they fit the thread better, however I've also linked to the larger variant of the original image.

[atsimg]http://files.abovetopsecret.com/images/member/62b9de5d7657.jpg[/atsimg] Mandelbrot Set history and explanation
Related ATS thread: A View of the Entire Universe- The Mandelbrot Set


Below are a few recent 2D views of the Mandelbrot Set which took the form to new creative levels, however even these pale in comparison to flying through the 3D realm of the Mandelbulb.

[atsimg]http://files.abovetopsecret.com/images/member/48d0840a5c6e.jpg[/atsimg]
[atsimg]http://files.abovetopsecret.com/images/member/7ddda575abfb.jpg[/atsimg]
[atsimg]http://files.abovetopsecret.com/images/member/a238be98089b.jpg[/atsimg]

Rather than being a simple 3D version of the 2D pattern (like below), White and Nylander were able to flesh out a final object that some might see resembling a bacterial spore or virus.

[atsimg]http://files.abovetopsecret.com/images/member/81ab0ac6caf0.jpg[/atsimg]

The Mandelbulb is a 3-Dimensional representation of the boundary only - it is the surface of the object that is infinite. You don't explore it by entering it, you simply 'poke' around the complex folds that make up the outer barrier. The more you poke around, the more stuff you find. That being said, Daniel White’s rendering of the object allowed for penetration of the structure revealing cross-sections of the bulb allowing us to look inside as well.

[atsimg]http://files.abovetopsecret.com/images/member/aa86d500a788.jpg[/atsimg]

Here are a few comparisons of similar regions in both the conventional 2D Mandelbrot and the new 3D Mandelbulb.

Spiral[atsimg]http://files.abovetopsecret.com/images/member/35eb7362ef65.jpg[/atsimg]

Stalk[atsimg]http://files.abovetopsecret.com/images/member/2bd3f015f1d2.jpg[/atsimg]

Also, here's a short video I threw together showing both 2D and 3D patterns - included are a zoom into the original pattern, still images from the new Mandelbulb, and a few fly-throughs created by Daniel White and other 3D artists:

Mandelbrot to Mandelbulb - 3D Infinity


Below are a series of 3D renders of various portions of the Mandelbulb.

These images below are my variants of some of the original Mandelbulb renders - some have been rotated, cropped, and color-tweaked to fit the ATS thread template, and I have provided links to the hi-res originals.

'Mandelbrot Crust'[atsimg]http://files.abovetopsecret.com/images/member/0e50629ae391.jpg[/atsimg] Larger variant image


'Outer Rim'[atsimg]http://files.abovetopsecret.com/images/member/fe9ebe789ca0.jpg[/atsimg]


'Fractal Hive'[atsimg]http://files.abovetopsecret.com/images/member/ee1a53b7c5a5.jpg[/atsimg] Larger variant image


'Mandel NightShade'[atsimg]http://files.abovetopsecret.com/images/member/8c1e8c5444e6.jpg[/atsimg] Larger variant image


'Cave of Lost Secrets'[atsimg]http://files.abovetopsecret.com/images/member/1d0b2a728bd0.jpg[/atsimg] Larger variant image


'Mandelbulb Garden'[atsimg]http://files.abovetopsecret.com/images/member/a833cb54825a.jpg[/atsimg] Larger variant image


'Ice Cream From Neptune'
[atsimg]http://files.abovetopsecret.com/images/member/439c96a75b6b.jpg[/atsimg] larger version


'Deep-blue zoom'
[atsimg]http://files.abovetopsecret.com/images/member/a96d6e41340a.jpg[/atsimg] larger variant image


'Mandelbulb Spine'[atsimg]http://files.abovetopsecret.com/images/member/33823c9e61c4.jpg[/atsimg] Larger variant image


'Honeycomb Heaven'[atsimg]http://files.abovetopsecret.com/images/member/7d0086f4af22.jpg[/atsimg] Larger variant image


'A Slice of Mandelbrot Gateau'[atsimg]http://files.abovetopsecret.com/images/member/672478fd7390.jpg[/atsimg] Larger variant image


'Caramelized Hazelnut Swirl'[atsimg]http://files.abovetopsecret.com/images/member/9c322647b8a2.jpg[/atsimg] Larger image


All the above was found by typing an equation into a 3D graphics renderer and letting the PC crunch away to render the visuals. If by chance you have infinite time and processing capability, the fractal Mandelbulb universe can be explored forever.

Amazing.

The Unravelling of the Real 3D Mandelbulb

So why are fractals relevant? Besides giving one a modest glimpse into infinity, some propose that fractals (which are basically patterns that build upon themselves by repeating those same patterns to achieve higher complexity) are actually the best way to describe reality. There are those that believe the physical 3D Universe, Time, Multidimensionality, and Consciousness can all be defined, or at least accurately described, by applying ‘fractal geometry.’ This idea, for the most part, is touched upon in Fractal Cosmology.

So how exactly are these things fractal? One factor is that of scale. The other is that of an observational and discerning perspective which infers the varying physical scales relatively to one another. Our consciousness provides that perspective.

The physical universe, from the microcosm to the macrocosm, could be described as one pattern repeated on a wide-ranging scale. Given what we’ve been able to observe of our surroundings, both here on Earth and beyond, what we’ve learned so far points to the repetition of matter and energy along with an accompanying transfer of complexity from one state to another. The sub-atomic realms lead to atomic structure, then to the molecules and chemicals which make physical matter. That in turn comprises planets, stars, galaxies, galactic clusters, the entire physical universe, multiverse, and then whatever lies beyond.

Similar to the 3D universe, time can also be looked upon as a fractal, that is, layer upon layer of cycles of duration. The factors of scale and observation are likewise crucial in defining these cycles as fractal. The motion of objects at varying physical scales gives rise to individual timescales, and then each level can be experienced accordingly by whatever consciousness resides there. We experience localized individual consciousnesses and are only beginning to comprehend what a group, and higher still, a planetary consciousness might experience. So perhaps each fractal level of space-scale has its own time-scale. Civilizations on the brink of achieving global consciousness would also be on the verge of a new time.

Then there is the higher dimensionality aspect, which I believe is fractal as well, though that obviously remains to be ascertained. M-Theory, which unifies previous string theories and supposedly defines the entire multidimensional nature of the universe is based on 11 dimensions. For the universe, multiverse, or existence to be dimensionally fractal, there would have to be endless dimensional realms, endless parallel worlds, and perhaps even infinite timelines.

Intimately linked to all the above is consciousness (the observant state of being or data-pool housing information and intent). Without consciousness, the varying levels of the fractal would serve no purpose, and there would be no driving force continually seeking out complexity in the dying universe. Consciousness seems to defy the second law of thermodynamics in that the path to entropy is reversed where there is in fact a gathering of information which itself is approaching infinity as opposed to the physical universe cooling and dispersing towards absolute zero. Perhaps consciousness is not an isolated system, but an all-purveying system, therefore it cannot even be compared to the physical universe. Whatever the case, consciousness must also exist at varying levels which are all built up from the previous – see the graphic below:

[atsimg]http://files.abovetopsecret.com/images/member/8a35d2a933fe.jpg[/atsimg]

When the space, time, all dimensions, and consciousness are combined, you then more than likely get an undefinable macro-fractal structure (in something not unlike the Mandelbulb). Either this continues forever in both directions of scale to the unimaginably big the incomprehendably small, or perhaps it ‘loops around’ meaning, once you reach the top of the size scale you find yourself peeping back into the deep sub-atomic realms (like travelling around the world to only end up where you started). So instead of being limited to the physical realm, perhaps this looping happens in space, time, parallel dimensions, and consciousness.

A rotating Toroidal Structure could provide this infinite 'looping' making the scale seem endless:

[atsimg]http://files.abovetopsecret.com/images/member/e6dac5c9fa1a.jpg[/atsimg] *edited post to add this image above and video clip below*

Toroidal Structure in motion

Check out this image of a mice brain compared with a 3D render of the universe:

[atsimg]http://files.abovetopsecret.com/images/member/016c28958aab.jpg[/atsimg] larger version

By comparing ‘fractal layers’ on very different scales we’re able to see similarities we never dreamed possible.

Lastly here’s a video I put together over a year ago entitled Journey Through the Universe, Hyperspace, and Beyond, and I’m sure some of you have already viewed it in some of my previous posts. It’s basically a view of the universe beginning with the familiar, traversing into the imagination across varying scales and fractal boundaries, into consciousness, and then back down to a parallel reality all the way back down to the infinitely small. The vision here is a tiny glimpse of the immensity I’m attempting to convey. Hopefully at least some aspect of this thread will in some way blow your mind or at least open the door to another way of looking at the universe, and what may lie beyond it as well as deep within.



More reading on Mandelbrots, Mandelbulbs, fractals, and fractal cosmology:

Fractal Cosmology

The Mandelbulb: first 'true' 3D image of famous fractal

Is the universe a fractal?

Fractal Universe (New scientist: March 10, 2007)

Galaxy map hints at fractal universe

Fractal Universe

Why the Universe is a Fractal

The Universe as a Multi-Dimensional Fractal

The Electro-Fractal Universe

Nassim Haramein's 'The Resonance Project'

[edit on 9/2/10 by Evasius]

Wow... this was and is probably one of my favorite threads now on ATS.

Amazing 3D images of everyone favorite fractal! Breath taking; I can't wait to see the 4D version of a fractal animated.

What I also like about the 3D fractals are the textures which are self-similar to living organisms and coral in the reef.

Although I do believed reality as a whole is based on fractal self-similar processes; it is a fractal that is steered by consciousness.

A fractal Universe makes sense if we also look at the possibility that reality is actually a virtual reality simulation like some other emerging theories present.

The brain is a very fast acting quantum supercomputer and the digital nature of how it renders perception into reality may be self-similar to how the universe itself is structured from an information system.

reply to post by Evasius
Very interesting thread and your enthusiasm is evident. Many of the images look familiar and I couldn't put my finger on it. Some are reminiscent of H.R. Geiger's paintings and work on the Alien movies.

Without consciousness, the varying levels of the fractal would serve no purpose, and there would be no driving force continually seeking out complexity in the dying universe. Consciousness seems to defy the second law of thermodynamics in that the path to entropy is reversed where there is in fact a gathering of information which itself is approaching infinity as opposed to the physical universe cooling and dispersing towards absolute zero. Perhaps consciousness is not an isolated system, but an all-purveying system, therefore it cannot even be compared to the physical universe.

Not sure I wholly agree with this passage, but it's the part I found most interesting in the thread. If I get a chance, I'll likely be thinking about these points today. Not a lot of threads survive in my consciousness when the browser closes, so thanks.

You should read the link in my sig...guess what it's about? Yup, entropy and human consciousness spread across infinity...Given the above...I suspect you'll find it fascinating

S&F

reply to post by Evasius

Very beautiful and evocative images. A flag from me.

In the view of the universe as a giant fractal, is there room for quantum effects? Is there anything to explain how fractal spacetime manifests matter and energy in theories of quantum gravity? Is that process also fractal? And is there any evidence supporting such ideas, or just aesthetics and a sense of 'rightness'?

I can imagine how a person, seeing these images, may become convinced that they are somehow 'real'. The proliferation of detail with increasingly close examination is very real-seeming, especially after the photoshop kids at Fractal Forums have done their work. But verisimilitude does not imply verity.

You just made my day. What an excellent presentation and passion on one of my all time favourite subjects. S+F for sure, thanks a dozen! Now, back to reading this mind-blowing, psychoactive material.

Wow.

Those images are stunning. I've always had a thing for fractals, such beauty and complexity. Thanks for the thread, but now you've given me a small problem. Which one do i use as a background for my work PC?!!

From the first time i learned about the Mandelbrot set and julia sets from a documentary with Arther c clark, i was immediately stunned and blown away by the implication that it presented.

people always say they cant fathom infinity, well look no further. the 2d sets were fantastic in themselves but the 3d sets are even more fantastic. sometimes i wish the future would get here faster. we need more break throughs like this daily.


imagine what a 4D version of this might look like??

[edit on 9-2-2010 by TiM3LoRd]

sweet! inspirational too. this is what came to mind when i saw them (note i gave them my own titles)

'Pink Chantilly Lace'[atsimg]http://files.abovetopsecret.com/images/member/0e50629ae391.jpg[/atsimg] Larger variant image


'Baby's Blanket'[atsimg]http://files.abovetopsecret.com/images/member/fe9ebe789ca0.jpg[/atsimg]


'Lavendar Soap Dish'[atsimg]http://files.abovetopsecret.com/images/member/ee1a53b7c5a5.jpg[/atsimg] Larger variant image


'Tropical Island'[atsimg]http://files.abovetopsecret.com/images/member/8c1e8c5444e6.jpg[/atsimg] Larger variant image


'Spider's Nest'[atsimg]http://files.abovetopsecret.com/images/member/1d0b2a728bd0.jpg[/atsimg] Larger variant image


'Green Man's Sanctuary Temple'[atsimg]http://files.abovetopsecret.com/images/member/a833cb54825a.jpg[/atsimg] Larger variant image


'Desert Dragons'
[atsimg]http://files.abovetopsecret.com/images/member/439c96a75b6b.jpg[/atsimg] larger version


'Wormhole'
[atsimg]http://files.abovetopsecret.com/images/member/a96d6e41340a.jpg[/atsimg] larger variant image


'Rooms with a View'[atsimg]http://files.abovetopsecret.com/images/member/33823c9e61c4.jpg[/atsimg] Larger variant image


'Grandma's Pineapple Tablecloth'[atsimg]http://files.abovetopsecret.com/images/member/7d0086f4af22.jpg[/atsimg] Larger variant image


'Mint Frosting'[atsimg]http://files.abovetopsecret.com/images/member/672478fd7390.jpg[/atsimg] Larger variant image


'Creation of Adam'[atsimg]http://files.abovetopsecret.com/images/member/9c322647b8a2.jpg[/atsimg] Larger image

There is a question in this story. But wow, this is absolutely amazing. When I was in 11th grade I took a computer science class and the teacher had a graphic novel of sorts, but relating to physics and for some reason once I was able to visualize what the numbers were, physics in relation to space, time and dimensions clicked. I was his teachers assistant in 12th grade but had my grade based on his physics class. Since by school standards I didn't have the necessary completed math courses I was unable to take physics and this was the only way. I never continued the schooling unfortunately. But the question is this. When looking at the diagram of the 4th dimension, it looks like the space in between is a finite number of 3rd dimensions, making both infinite when going to the fifth and so on. So is there hypothetically an infinite number of 4th dimensions, with each finite 4th dimension being interlocked between a finite amount of 3rd dimensions allowing travel from one 3rd dimension to a possible other 3rd dimensions? But still going along with the theory of infinity because of each different 3rd dimensions relation another 4th dimension. I hope that makes sense.

It's not a matter whether the universe MAY be fractal but it IS. There's enough proof and data on this which is considered crackpot science for the sake of convenience and ignorance. The universe scales everything.This instantly renders the quest for elementary particles useless as there's no such thing. We can only study the patterns to understand the fractal, trying to find god particles and be as arrogant to state we understand the complete universe will be our own doom and shame.

You don't need highend renders to see how all works:

Romanesco (Vegetable):


Fern:


Cauliflower:


Aloe:


Tree:

What tickles my fancy in all this is watching for the new words that must be forged in our consciousness to describe the NOVEL inpressions these images provide.And we WANT to talk about them.Too cool for school!

[edit on 9-2-2010 by trueforger]

WOW

That is some seriously mind blowing crap you have presented right there...this is one of the best threads I've seen in a while...I'll have to come back later to read it, but looking at the pictures is enough for now!

It's truly astonishing what can be done with mathematics and fractals...I thought the Mandelbrot set was awesome...screw that! Mandelbulb all the way bro!!! Are you diggin' it? I know I am...

[edit on 9/2/10 by CHA0S]

Great thread! Star and flag for you!

Images are outstanding, nothing to add but my own glee!

reply to post by Evasius
hah, fractals, see one and you've seen 'em all

well, if reality is fractal, the base must be complex beyond comprehension

Fractals are cool to help understand higher awareness. They help expand the mind in such a way to actually see and sense proof of infinite, even if it is still a self-similar finite.

I wouldn't go so far to say the universe is a fractal, as I've seen/read even deeper concepts that go much into further expansion beyond fractals. Fractals do tend to be the one of the easier tools to use to scientifically communicate such concepts!

reply to post by dzonatas

I wouldn't go so far to say the universe is a fractal,

I would...it seems plainly obvious IMO...

as I've seen/read even deeper concepts that go much into further expansion beyond fractals.

Care to elaborate?