"Mandelbulb," a 3D Mandlebrot Construct, Discovered

symbolset writes "Many know the beauty and complexity of the Mandelbrot set. For some years now a few enterprising mathematicians / rendering fiends have been seeking a true 3D Mandelbrot set. A month ago a solution was found, and it is awesome to behold."

Comments

Actually, the Mandelbrot set is already 4D

[maxwell demon]

While the Mandelbrot set as usually defined is 2D, each point has an associated Julia set, where instead of the additive constant, the starting point is varied (the original Mandelbrot set always uses zero as starting point). Together, they give a 4-dimensional set, where two dimensions are given by the starting point (zr, zi), and the other two by the additive constant (cr, ci). The original Mandelbrot set is a cut through this 4D set at the plane zr=zi=0, while the Julia sets are cuts orthogonal to theat, at planes with constant cr and ci.

Re:Actually, the Mandelbrot set is already 4D

[jhesse]

This.

You can find a picture of a "4-D" Mandlebrot set in a mid/late 80's issue of Scientific American.
I was generating pictures of this on a 286 pc. (with EGA graphics) 15 years ago, and the pictures
in TFA of z^2 look *nothing* like that did.

Re:Actually, the Mandelbrot set is already 4D

[Eudial]

While not a pure mandelbrot, but a buddhabrot rendering: For the curious, here's a nice 2D projection of such a (rotating) 4D fractal I whipped up a while back.

Re:Actually, the Mandelbrot set is already 4D

[Forty Two Tenfold]

I want a stereogram. Please.

Re:Actually, the Mandelbrot set is already 4D

[caramelcarrot]

Also, trying to extend the Mandelbrot set to 3D is ill-defined as there is no good 3D algebra equivalent to the complex numbers (two, 1 and i) or quarternions (four, 1 and i, j, k) - hence you can't express the iteration formula in 3D.

Re:Actually, the Mandelbrot set is already 4D

[Anonymous Coward]

Well you could take a slice of the quaternion Mandelbrot and call it a day. What they came up with is not an algebra and it gives better results than the quaternion Mandelbrot which is just a solid of revolution, so I don't know where you're getting at.

Re:Actually, the Mandelbrot set is already 4D

[Garble Snarky]

I was following the fractalforums thread for a while, and IIRC that is what a lot of the discussion focused on - "how can we define the squaring operation in 3D such that the Mandelbrot iterative equation gives us something like our vague notion of what we want the Mandelbulb to look like?"

Site is down, but I got an email notification from fractalforums a few days ago, and they had some incredible results. The pursuit is at least as much aesthetic as it is mathematical, and in that respect they've succeeded marvelously.

Re:Actually, the Mandelbrot set is already 4D

[Anonymous Coward]

Can you make this a screensaver?

Re:Actually, the Mandelbrot set is already 4D

[SoVeryTired]

They defined a way of multiplying points in 2-space equivalent to the "stretch and rotate" interpretation of complex multiplication. The formula for (x,y,z)^2 is given at the top of this page.

It doesn't have the same mathematical structure as the complex plane, but as the article suggested, it may be the case that the "stretch and rotate" property is all you need.

Re:Actually, the Mandelbrot set is already 4D

[SoVeryTired]

Ugh, I meant 3-space, sorry.

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

I had missed a lot of interesting aspects of the 4D Julia/Mandelbrot combo when it was discovered, since computers were so much slower. I wrote my first Mandelbrot program on a Kaypro in high school. Used to run it over night just to get a 100x100 or so image, with low iterations.

The Mandelbrot set has those hairlike strands coming off of it, particularly at high resolution near pi radians. Nearby Julia set fragments, so to speak, all connect through those strands. Since the strand is between 1 and 2 dimensional in the Mandelbrot plane (having infinite arc length within a finite area, the strand within the 4-D coordinates is less than 4-D. So you could almost see something interesting in 3-D there. (Projected to 2-D of course. People who say they see 3-D crack me up, since the back of the eye is a 2-D surface.)

By the way, I particularly like the logarithmic spirals.

Re:Actually, the Mandelbrot set is already 4D

[Demena]

It is not the retina that sees but the visual cortex. So I wouldn't laugh too hard.

Re:Actually, the Mandelbrot set is already 4D

[maxwell demon]

{0,0,1}^2 doesn't seem to be well-defined.
Not only isn't the formula well defined at that point (division by zero), it cannot even be continuously extended to that point, because
lim_{e->0} {e,0,1}^2 = {-1,0,0}
while
lim_{e->0} {0,e,1}^2 = {1,0,0}
and even
lim_{e->0} {e,e,1}^2 = {0,-1,0}

Re:Actually, the Mandelbrot set is already 4D

[maxwell demon]

People who say they see 3-D crack me up, since the back of the eye is a 2-D surface.

But most people have two eyes, and the parallax between them gives the third dimension.

Re:Actually, the Mandelbrot set is already 4D

[fractoid]

This post needs more +insightful. What a lot of people are missing by getting wound up in the maths is that it is an artistic endeavour. Their definition of "a mandelbrot" (and yes, this broken terminology bugs the pedant in me beyond belief) is nothing to do with z^2+c, and everything to do with "a pretty looking blobby thing that maintains an aesthetically pleasing and visually interesting level of surface detail at all magnifications".

Re:Actually, the Mandelbrot set is already 4D

[odourpreventer]

> trying to extend the Mandelbrot set to 3D is ill-defined

Depends what you want to achieve. This could be said for all 4D objects that you want to project in a 3D space. Most fractal programs (that support quaternions) solve this by projecting three variables and varying the fourth through time.

Re:Actually, the Mandelbrot set is already 4D

[SoVeryTired]

Good point. Hamilton was working on multiplying triples when he discovered the quaternions. Perhaps it can't be done in a sensible way.

Re:Actually, the Mandelbrot set is already 4D

[Acer500]

Hehe, me too... that must blow your head off :)

Re:Actually, the Mandelbrot set is already 4D

[ObsessiveMathsFreak]

You don't even need a second eye, or at least, you don't need a parallax between them. Simply focusing on an object gives a good idea of its distance. To bring an object at a certain distance into focus, the eye muscles must contract "just so", allowing an estimation of that distance.

An then of course there is our brains, which interpret what we see. This is the reason why we can still have the illusion of 3D when looking at a truly two dimensional picture or TV screen. Of course, we can also be fooled, for example by cartoons or diagrams, into seeing 3D where none truely exists.

Our eyes really are designed to see in 3D. The grandparent appears to be suffering from chronic smartalecitis.

Re:Actually, the Mandelbrot set is already 4D

[Pedrito]

[i]People who say they see 3-D crack me up, since the back of the eye is a 2-D surface.[/i]

Really? A sphere is 2D? How are you enjoying things in flat world?

Re:Actually, the Mandelbrot set is already 4D

[tsalmark]

Well, that's beautiful. Thanks for sharing.

Re:Actually, the Mandelbrot set is already 4D

[Anonymous Coward]

Not really. There isn't enough degree separation between the eyes at any meaningful distance that gives depth perception. Our perception of depth comes from visual cues, not "binocular vision".

Re:Actually, the Mandelbrot set is already 4D

[Khelder]

Yeah, the stereoscopic effect of two eyes provides depth info, although only to about 20 feet.

Fortuantely, there are other cues, too. I don't think I remember them all, but a few are: parallax (different apparent relative motion of objects at different depth as the viewer moves), occlusion, and accomodation (like a camera, your eye focuses differently for different depths).

So yes, each retina is 2D, but even statically you can build a 3D model from that, and over time you get even more cues. (It is useful to remember, though, that the 3D model in your head is just a a model and may not correspond exactly to what's out there.)

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

No matter how many eyes you have, or where they are placed, you still see only surfaces. That's two dimensions, even though the two dimensions are embedded in three dimensions. I should have made that point without being dismissive of other people's use of the term 3-D.

A person's spatial sense approximates three dimensions, and having two eyes, and especially movement of the head, gives an awareness of where things seem to be in that space. The actual visual content is still two dimensional though.

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

The surface of a sphere, which is what would see even if you could see all sides at once, is two dimensional. Of course the sphere itself, which is inferred from the surface, is three dimensional But you do not attempt to form a mental image of anything except the surface.

Of course I am blowing off the separate question of how fundamental our 3-D model of space is, since it is also is a projection or simplification of something more subtle.

I should have been clearer about what I meant in the first place.

Re:Actually, the Mandelbrot set is already 4D

[Twinbee]

Strictly speaking, it gives 2 x 2D vision. If you could really see in 3D, you'd be able to see through stuff, and all at once. It'd be a very different sensation with masses more information being received by the brain/eyes.

Re:Actually, the Mandelbrot set is already 4D

[mapkinase]

1. http://www.google.com/search?q=smartalecitis&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a
2. ???
3. Profit

Re:Actually, the Mandelbrot set is already 4D

[maxwell demon]

Ever tried the "Magic Eye" pictures? There's exactly zero visual cues. Unless you manage to look at the image so that the left-eye and right-eye see it with a certain displacement (so different parts of the picture now match), you see not a single trace of the 3D figure hidden in it). The only depth information that is there is the displacement.

Re:Actually, the Mandelbrot set is already 4D

[Hal_Porter]

Can you put a soundtrack on that? Like some 80s hair metal or something?

Re:Actually, the Mandelbrot set is already 4D

[Eudial]

Archive.org offers the full .avi file for download (the AVI version is about 4000 times more awesome than the flash version), and it's in public domain, so you are perfectly within your rights to go do it yourself.

Re:Actually, the Mandelbrot set is already 4D

[kryptKnight]

But most people have two eyes, and the parallax between them gives the third dimension.

That's almost completely wrong, the grandparent poster knows what he's talking about. Binocular vision is only useful for depth perception within about a foot or two of your face, beyond that and the difference between what your eyes see is too small to matter. Depth perception is almost entirely unconscious mental processing that's informed by cues like relative position, relative size, clarity and so on.

The reason you have two eyes is because of bilateral symmetry and a wide field of vision is useful. Think about rabbits, their eyes have almost no overlapping field of vision, but they manage just fine in 3d space.

Re:Actually, the Mandelbrot set is already 4D

[noidentity]

Please help me understand what a paragraph containing just the word "This" means. I keep seeing people write that and I still can't figure out what it means. Note that it's not a link to anything, just normal text. Thanks.

Re:Actually, the Mandelbrot set is already 4D

[noidentity]

Even closing one eye, you can accurately determine the distance to an object, because even a 2D surface illuminated by anything other than a pinhole lense is picking up views of the subject from more than one position. With a single eye, you can sift through the multiple views by adjusting its focus.

Re:Actually, the Mandelbrot set is already 4D

[not flu]

The 2D model in your head is just as much of a model and about as easy to manipulate with well known visual effects, too - so don't look down on the 3D model in our heads just because it can be slightly off.

Re:Actually, the Mandelbrot set is already 4D

[maxwell demon]

Thinking more about it, if we restrict ourselves to the unit circle, squaring a complex number is a continuous map from the circle on itself, which maps two opposite points of the circle to the same point. Now topologically, the pairs of opposing points of the n-sphere are equivalent to the n-dimensional projective space. The 1-dimensional projective space is topologically equivalent to the circle, so the continuous map is no problem. However, the two-dimensional projective space is not equivalent to a sphere. You can map it to a sphere if you map a whole straight line (i.e. for the original ball, a whole great circle, e.g. the equator) to a single point. To make that map, you can put a half-diameter sphere onto the equatorial plane of the original one, and then most diameters starting at a point on the original sphere cut the smaller sphere twice: once in the south pole (which is in the center of the original sphere) and then once more, which gives the image point. The diameters for the equatorial point pairs however only touch the south pole of the smaller sphere; all those pairs are then mapped to this single point. The result is continuous, but not any more 2 to 1 (since all the infinitely many points of the equator are mapped to the south pole). After that you can "blow up" the smaller sphere to the original size. Note that this map is continuous (the preimage of an open set is open; if the open set contains the south pole, the preimage contains the whole equator), however its "reverse" isn't (images of open sets don't need to be open; if the set contains part of the equator, the south pole is in the image, but is at the border of the image set).

I now think you can't make a map of a sphere onto itself which is both strictly 2 to 1 and continuous. I'm not completely sure, but I think whenever you have a 2-to-1 map of the sphere onto itself, it should be possible to apply a continuous bijection that moves those points to the opposite places of the sphere, so we end up in the situation described above, where it doesn't seem to work.

Of course a true mathematical proof (or disproof if I'm wrong) would be nice.

Re:Actually, the Mandelbrot set is already 4D

[Anonymous Coward]

It's been proven that there is no normed division algebra over R (real numbers) which has dimension 3 (over R). More specifically, the only normed division algebras over R are R itself, complex numbers, quaternions, and octonions. So, in that meaning of sensible it can't be done.

Re:Actually, the Mandelbrot set is already 4D

[DrVomact]

You can find a picture of a "4-D" Mandlebrot set in a mid/late 80's issue of Scientific American. I was generating pictures of this on a 286 pc. (with EGA graphics) 15 years ago, and the pictures in TFA of z^2 look *nothing* like that did.

Hah, I can beat that! I used a Compaq portable with an 8088 processor, 256 K of RAM and 2 floppies! I wrote a C program based on that original Scientific American article, and then had a Basic program read the results and display it. I think the C program took a week to run.

The joke, of course, is that the Compaq didn't have a color screen—it had a small grayscale monitor built in. But I still thought it was really cool.

Re:Actually, the Mandelbrot set is already 4D

[Anonymous Coward]

It's a "Me too!", but for Slashdot. It means "I wanted to say exactly the same, but someone else was first. Rather than saying nothing, I will clutter up the discussion".

The GP (grandparent) did add a bit of his / her own, so it wasn't as bad in this case.

Re:Actually, the Mandelbrot set is already 4D

[DrVomact]

No matter how many eyes you have, or where they are placed, you still see only surfaces.

That's interesting. As I think about it, I wander over to my aquarium and stare pensively. The water looks clean, the guppies seem as happy as guppies get. The seaweed is wafting gently back and forth. But wait, do I really see my aquarium? Or am I only staring at its surface?

Suddenly seized by philosophical doubts, I hold my hand in front of my face. Can I see my hand? —or only my palm?

Your remark is similar to one made by the British philospher G.E. Moore, in a paper published some time in the 1940s (I think). Can't remember the title at the moment...might have been "A Defence of Common Sense".

Re:Actually, the Mandelbrot set is already 4D

[49152]

"That's almost completely wrong"

No, that is only slightly wrong. The parallax helps our brain create an illusion of three dimensions.

"Binocular vision is only useful for depth perception within about a foot or two of your face, beyond that and the difference between what your eyes see is too small to matter."

Yes, depth perception due to binocular vision is limited. But the useful limit is far greater than a foot or two. It is more like 10-20 foot, which makes it plenty useful for lots of everyday human actions.

Re:Actually, the Mandelbrot set is already 4D

[Twinbee]

I've argued the same thing for ages - you're completely right of course. Glad I'm not the only one...

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

Of course the hand is really there, even though this is only inferred from seeing the palm. What other kinds of things are real that we can infer with some reliability but can not see directly?

It seems most of us naturally and habitually think of the world we experience as being the real world, rather than an internally generated cartoon model of it. As you point out, recognizing the cartoon as a cartoon can be unsettling at first. Notice that we experience sounds as having locations, rather than as volumes of waves in the air, but our method of assigning location to a possible point of origin is problematic. It seems to me that most of us experience our thoughts as being in our heads mostly because our heads are midway between our ears, and only coincidentally because our brains are also in our heads.

But the upside of recognizing the model as a model, is then you have a better chance of recognizing other things about the world that haven't been in your sense model. For example I'm pretty sure that our 3-D model isn't the only way to think about space, even though its a natural and very good first order approximation, and the one that we all consciously use for the most part.

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

I first realized it when thinking about 4 dimensions, and realizing how limited my everyday experience of 3 was.

I think it can seem like a big deal when you first experience some of the implications, but its not relevant to most people.

It seems a part of my mind, mostly subconscious, works in a space different from the somewhat kludged 3-D spatial model that I navigate around in. On rare occasions I've seen a glimmer, a slice from an unfamiliar angle that shows relationships that I don't normally notice.

Re:Actually, the Mandelbrot set is already 4D

[B00KER]

Yes.

Re:Actually, the Mandelbrot set is already 4D

[Impy the Impiuos Imp]

So "This" was missing either an up arrow to point to the parent post, or a colon, to point to itself?

Re:Actually, the Mandelbrot set is already 4D

[Impy the Impiuos Imp]

Is that a 2D projection of a 4D rotating object, or a 2D film of a 3D projection of a 4D rotating object?

It sounds funny, but it's not.

Re:Actually, the Mandelbrot set is already 4D

[DrVomact]

Of course the hand is really there, even though this is only inferred from seeing the palm. What other kinds of things are real that we can infer with some reliability but can not see directly?

Your mistake is to think these things are simple, or in any way obvious or easy. Leaving aside the question what "really there" might mean, you do realize that inferences can be mistaken, right? So there's room for doubt that you are looking at your own hand. If you find this disturbing, you should take some philosophy classes. You might then attain a state of honest confusion about these issues. If not...well, never mind. Moore also had some remarks about the difference between "seeing directly" and seeing...well...not so directly, I guess. Wrote a dissertation about that remark, I did.

Re:Actually, the Mandelbrot set is already 4D

[Iron Chef Unix]

This.

Re:Actually, the Mandelbrot set is already 4D

[severoon]

I can see thru stuff, all at once. Like air, water, fog. Does that count?

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

Your mistake is to think these things are simple, or in any way obvious or easy. Leaving aside the question what "really there" might mean, you do realize that inferences can be mistaken, right?....If you find this disturbing, you should take some philosophy classes.

I gave an example in the same post of how an inference can be mistaken, in relation to sound, so yes, of course I realize that.

Ironically, your inference about my understanding based on my brief and perhaps poorly chosen words seems to have missed the mark also.

If I sounded condescending in my reply that wasn't my intent. I didn't mean to dismiss the hand example as simple. What I meant was to affirm that there is something of an objective reality, sort of, even though the senses can be fooled and our models are inadequate. Some people throw the idea of objectivity out entirely as soon as they realize their senses are limited, and imagine that everything they experience is an arbitrary reflection of personal will. I assumed your thoughts on this were considerably deeper than that, and I meant to express agreement.

I tried taking a philosophy course once. The text was a complete collection of Plato's dialogues, which I had already read carefully and in its entirety a few weeks earlier. The professor wouldn't let me take the course unless I took an introductory course in logic, nothwithstanding my several years of experience writing computer programs and mathematical proofs.

This sort of characterizes my experience of Philosophy as a field. I respect the knowledge that people gain by its study, and the intelligence that inspires it. But I'm disappointed by the condenscending ignorance that attempts to measure a person's mind by what hoops they have jumped through, what formally recognized position they hold, what vocabulary they use, and what recognized works they make reference to. Language is important, and so is rigor, and history, but not to the point where it begins to squeeze out insight. More could be learned, and shared, but pride gets in the way.

I'm not trying to hang any of that on you by the way. I'm just saying it would be a mistake to make assumptions about what I do and do not know when you haven't seen of more than a sliver of my thought on the subject.

Re:Actually, the Mandelbrot set is already 4D

[DrVomact]

I didn't interpret your remarks as condescending, nor was my intention to diminish you—I was trying to tell you that you are touching on questions that have been asked for literally thousands of years. You are saying some of the things I used to say, questions that gripped me so tightly that I spent four years studying something completely impractical (in the sense of "will not put money in my bank account").

The reason I replied to you was that though you were saying stuff many intelligent people without philosophical training say, your phraseology struck me as remarkably like that of one of my favorite philosophers—George Edward Moore. The paper I was thinking of was, indeed, "A Defence of Common Sense". You might be able to find it in a used book somewhere. I think you'd probably agree with Moore. However, if you read some of the commentaries on the paper, you'll find that there are other philosophers who don't think that what Moore said was all that obvious.

I took one Philosophy course as an undergraduate (pre-Socratic philosophy), and swore I'd never touch the stuff again. That was, of course, before I learned that what you get out of a course is proportional to the effort you put into it.

So you let a single academic jerk discourage you? Jeez. Back in my day, we had gumption; we were creative; we lied. Of course it's easy today for a prof to verify what courses you've taken—he probably has access to your academic records. In the good old paleolithic days when I was a student, it was a lot of trouble for a prof to verify what courses you had actually taken...so they didn't usually bother, and believed what I told them. Heh.

Had you taken the course from a competent teacher, the first thing you would have learned is that you didn't really understand Plato as well as you thought. How do I know this? I know it because if you read all of Plato's dialogues in a matter of a few weeks, then you didn't stop when you came across some of the truly strange and outlandish things he wrote, and study those passages. It's easy to misunderstand Plato if you forget that he is not a contemporary; many of his ideas sound superficially familiar, but are actually quite alien to our normal ways of thinking. What, for example, is a "good man", according to Plato?

Re:Actually, the Mandelbrot set is already 4D

[maxwell demon]

The surface of a sphere, which is what would see even if you could see all sides at once, is two dimensional.

Given that the sphere is, by definition, the surface of a ball, I wonder what the surface of a sphere is meant to be? It may be the border of the sphere according to the topology of the 3D space it is embedded in, in which case it's the sphere itself again. Or it may be the border of the sphere in its own topology, in which case it's the empty set because a sphere simply has no border (you cannot fall off the border of the world).

Re:Actually, the Mandelbrot set is already 4D

[maxwell demon]

The actual visual content is discrete: It consists of a finite number of neurons firing a certain sequence of pulses. While the information comes indeed from 2D images in the eyes, that's not the visual content. The visual content is the activity of the neurons.

Re:Actually, the Mandelbrot set is already 4D

[billbaggins]

Technically true, but look beyond the formulae for a brief moment and look at what they're *doing* and you'll see the way out: his mechanism for computing [x,y,z]^n is to convert it to spherical coordinates [r,theta,phi], then do something similar to complex exponentiation - [r^n,theta*n,phi*n] - then convert that back to rectangular coordinates. So rectangular [0,0,1] becomes polar [1,0,0], which squares to polar [1,0,0].

Makes sense as long as you think about it a little, but not too much.

Re:Actually, the Mandelbrot set is already 4D

[Anonymous Coward]

Here's an animation of the complex "4D Mandelbrot" mentioned - generally referred to as a Julibrot:

Julibrot Animation

Just to add that:

A Mandelbrot Set is a view of what happens to the iterated orbits of many different functions with a fixed starting value. (note here that's Mandelbrot Set generally and *the* Mandelbrot Set specifically which is a view of what happens to the orbits of z^2+c where z and c are complex)

A Julia Set is a view of what happens to the iterated orbits of a single function given many different starting values (again that's Julia Set generally and *the* Julia Set specifically - the other way of viewing z^2+c where z and c are complex).

So if you consider the Julibrot itself then even considered as a 4D object it can't be described as a true general Mandelbrot (or Julia) because it is a view of iterated orbits using both different functions and different starting points.

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

Fair enough.

I meant the academic anecdote as an example of a larger and pervasive pattern of experience. Of course everything is a mixed bag, there is much good in the study of Philosophy, and its nice that other people are doing it. I could have gotten through all the suffocating pedantry and gotten a Philosophy PhD had I wanted one bad enough, but it wasn't worth it for me personally.

I didn't mean that it only took me a few weeks to study Plato. I said that I had finished a few weeks previously, meaning that it wasn't something I'd done a decade earlier and forgotten. Having said that, I'm sure its true that I don't understand Plato in the same way that academics do however, and also that there is real depth there that I have missed.

On the flip side, many, many times I have read something that I found deep and personally useful, then was taught what it supposedly meant to the person who wrote it, and found that version to be presumptuous and not half as valuable. For example, everyone treats the story of four legged androgenous humans getting chopped in half by an angry god as a joke. And no doubt it was a lighthearted story. But there's a significant truth in the metaphor also, a very valuable one to me. What was Plato's understanding? Knowing that would have some utility of course, but in the final analysis, I don't really care. If he understood something that he can teach me, fine. If he was more like a 'poet' in being a pipe that insight flows through without understanding it in every sense that another person can understand it, that's OK too.

I'm 40, not as old as you, apparently, but old enough to see something of how much the world has changed. So I hear something of what you are saying. As it happens, I have devoted my life to philosophical knowledge, I've just done it in a way that fits my quirks, strengths, and weaknesses better than formal study would have.

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

I said that I had finished a few weeks previously, meaning that it wasn't something I'd done a decade earlier and forgotten.

Whoops, I see that's not what I said. Your point remains valid in either case.

Re:Actually, the Mandelbrot set is already 4D

[DrVomact]

As it happens, I have devoted my life to philosophical knowledge, I've just done it in a way that fits my quirks, strengths, and weaknesses better than formal study would have.

One can certainly study outside of academia—these days, it's probably easier. I was lucky enough to encounter some good teachers. The most interesting person I know doesn't have a B.A. For me, it was important to go the academic route, because I needed to learn discipline. I doubt whether I would have fit in well, had I ever got that tenure track appointment that I thought was my dream. I think academia has become largely a huge waste of time and resources. Very few people would benefit from studying philosophy in an academic setting. Yet, I also think it's very, very difficult to study it alone. One needs an intellectual community.

Re:Actually, the Mandelbrot set is already 4D

[shadowofwind]

One needs an intellectual community.

This is true. Though there's a tendency for communities to try to control the minds of their members, and a person will often prefer to work alone than yield to that.

Any person who seriously seeks knowledge soon acquires the tools to be a sociopath, and there's a lot of subtle ways to go off the tracks with that. I think its a self correcting problem in the sense that a person's failings tend to produce conditions that prevent them from acquiring more knowledge. But it does contribute to social fragmentation. Also, the idea areas that are natural for different people to explore aren't always compatible.

Math graduate school helped me with rigor, and the abstraction changed the kinds of thoughts I was capable of. Actually just seeing those changes was of value in itself. I still tend to leap to extreme conclusions from very limited data, but consider this to be an asset as well as a failing.

I will check out your reading suggestion when I get a chance.

Now do 4d and animate it!

[Anonymous Coward]

Or would that open up a Lovecraftian dimension better left to slumber?

Re:Now do 4d and animate it!

[JoshuaZ]

No, Bob Howard at the Laundry already confirmed this one was ok. However, this is perilously close to the Turing-Lovecraft theorem which the public isn't supposed to know ab n34pnt!@!$ *NO CARRIER*

Not a "true" 3D Mandelbrot

[HEbGb]

It's definitely nifty, the pictures are beautiful, and the creator deserves praise, but the author himself says it's probably not a "true" 3D Mandelbrot:

http://www.skytopia.com/project/fractal/2mandelbulb.html#epilogue

As exquisite as the detail is in our discovery, there's good reason to believe that it isn't the real McCoy. ... ...
Evidence it's not the holy grail? Well, the most obvious is that the standard quadratic version isn't anything special. Only higher powers (around after 3-5) seem to capture the detail that one might expect. The original 2D Mandelbrot has organic detail even in the standard power/order 2 version. Even power 8 in the 3D Mandelbulb has smeared 'whipped cream' sections, which are nice in a way as they provide contrast to the more detailed parts, but again, they wouldn't compare to the variety one might expect from a 3D version of Seahorse valley.

So, Slashdot, I know this is asking a lot, but can you PLEASE at least read the article before posting? Thanks.

Re:Not a "true" 3D Mandelbrot

[Anonymous Coward]

You must be new here.

Re:Not a "true" 3D Mandelbrot

[symbolset]

There is a subtle difference between "a solution" and "the solution".

But yeah, I was selling it a bit because the pictures are so lovely.

Re:Not a "true" 3D Mandelbrot

[Tumbleweed]

So, Slashdot, I know this is asking a lot, but can you PLEASE at least read the article before posting?

No! I hate everything you stand for.

Re:Not a "true" 3D Mandelbrot

[fractoid]

OK, I stood up for these guys and their 'artistic' definitions of things before, and it's hurting my soul, so to balance it out here I'm going to grump at you for your use of the term 'Mandelbrot'. It's a surname, not a mathematical object. Benoit Mandelbrot is a mathematician who was a pioneer in the field of fractal geometry. The object is known as the Mandelbrot set.

My pedantic nature is appeased. As you were, gentlemen.

Re:Not a "true" 3D Mandelbrot

[Sebilrazen]

Looking at their UID I'd say they were here when here was new.

Re:Not a "true" 3D Mandelbrot

[Anonymous Coward]

that's why it's funny.

(shakes head...sometimes the best thing a mod can do is not to mod at all)

Re:Not a "true" 3D Mandelbrot

[John Whitley]

Erk. I now know how Star Trek characters feel upon finding themselves in one of those episodes that makes them into old codgers/crones for the next 45 minutes.

Re:Not a "true" 3D Mandelbrot

[tehcyder]

Looking at their UID I'd say they were here when here was new.

They were also probably here when the first *whoosh* of a joke flying over someone's head occurred.

Re:Not a "true" 3D Mandelbrot

[HEbGb]

Yeah, I've been asking Slashdot to do this for a looooong time... :) Someday!

Ice Cream From Uranus?

[Anonymous Coward]

That ruined it for me.

Re:Ice Cream From Uranus?

[Anonymous Coward]

"Ice Cream From Uranus?"

If that bugged you I'd avoid the movie by the same title.

Re:Ice Cream From Uranus?

[SeNtM]

Professor: "I'm sorry, Fry, but astronomers renamed Uranus in 2620 to end that stupid joke once and for all."
Fry: "Oh. What's it called now?"
Professor: "Urrectum. Here, let me locate it for you."

Re:Ice Cream From Uranus?

[Anonymous Coward]

Two girls, one ... oh never mind.

Re:Ice Cream From Uranus?

[inio]

I came here to say that. Seriously great work until the 2G1C reference.

Re:Ice Cream From Uranus?

[EdIII]

Ice Cream From Uranus? In accordance with that very popular rule of the Internet... there is another picture for that... a more illustrative one too.

Tub Girl. Google It. You're Welcome... bwahahahahahhahahahahhhahah!

Re:Ice Cream From Uranus?

[Anonymous Coward]

Ice Cream From Uranus? In accordance with that very popular rule of the Internet... there is another picture for that... a more illustrative one too.

Tub Girl. Google It. You're Welcome... bwahahahahahhahahahahhhahah!

Man, you must be a hit at parties.

Re:Ice Cream From Uranus?

[fractoid]

Here was I thinking of the scene from Evolution.

[Harry has just had an alien removed rectally]
Dr. Allison Reed: It's over, it's over. You did great! Do you need anything? Can we get you anything?
Harry Block: Ice cream... I'd like an ice cream please.
Dr. Allison Reed: Okay, what flavor?
Harry Block: It doesn't matter. It's for my ass.

Re:Ice Cream From Uranus?

[Snarf You]

When I first looked at the site a few hours ago, I saw Uranus. It has since been renamed to "Ice Cream From Neptune".

That thing looks like all of my nightmares.

[Anonymous Coward]

You could put it in a horror movie and make it pulsate.

Re:That thing looks like all of my nightmares.

[Anonymous Coward]

"And if I could, I'd film my dreams and show you what's inside. We'd watch them on the silver screen and you would run and hide" Alu - Circus Cosmos

Re:That thing looks like all of my nightmares.

[Anonymous Coward]

There's a few things I'd like to put inside of you and make pulsate :O

Re:That thing looks like all of my nightmares.

[XDirtypunkX]

Yes, in so many ways yes.

Re:That thing looks like all of my nightmares.

[Anonymous Coward]

really? you have nightmares about broccoli too?

Poorly-defined problem

[Brian Gordon]

What are they trying to do, make up some 3D fractal that just looks like the mandelbrot? This mandelbulb seems pretty arbitrary, and the whole point of the story seems to be that they've found a good one, not that they've found any kind of "true" solution.

Re:Poorly-defined problem

[Anonymous Coward]

They're trying to make a particular kind of 3d fractal, ie: has no simple edges. I'm sure these images look neat to the old and computer illiterate, but if publishable math has become "wow check out my graph!" then it's a sad day indeed.

Re:Poorly-defined problem

[XSpud]

It's not the particular mathemetical formulae that are important but the fact that very complex structures can be created from very simple formulae. Our understanding of computer-generated fractals in the last 20 years or so has given science an insight into how common fractals are in nature. It's not coincidental that fractal images such as these often remind us of structures we see in nature.

Re:Poorly-defined problem

[jowilkin]

Who says this is publishable? Seems like some people having fun on a fractal forum. Interesting to look at, but probably not publishable in an academic sense.

Re:Poorly-defined problem

[XDirtypunkX]

These particular fractals remind me of things I hope never to see in nature.

Looks like a big sea slug.

[Ethanol-fueled]

I wonder if we'll ever reach the point where we will be able to define, with equations and rules, a sea slug using the principles of cellular automata?

Re:Looks like a big sea slug.

[Anonymous Coward]

Please mod parent up! Unless that link takes you somewhere like goatse, it's entirely on-topic.

Re:Looks like a big sea slug.

[wizardforce]

I wouldn't doubt it a bit. A sea slug is already defined by known rules and equations, it's just a matter of doing the math. Their genomes aren't terribly extensive compared to other organisms so it should be quite possible to simulate one quite accurately with a few simple equations and basic rules of chemistry and physics.

Re:Looks like a big sea slug.

[brusk]

Except we don't know those rules well enough yet to do that. We don't understand protein folding. Heck, we don't fully understand water. The equations might prove not to be that simple.

Re:Looks like a big sea slug.

[lawpoop]

A sea slug is already defined by known rules and equations, it's just a matter of doing the math.

Really? What are they?

Re:Looks like a big sea slug.

[wizardforce]

*assignment of codons to specific amino acids (conversion of the genetic code into polypeptides)
*energy minimization of protein structure (protein folding and interactions)
*capacitor electronics (nervous system)
It's all chemistry, physics and math.

Re:Looks like a big sea slug.

[wizardforce]

Not quite. We do know the rules of chemistry well enough to model proteins, the problem is that the amount of sheer number crunching is enormous. As for water, that's also not quite true. We have the equations for interactions between molecules worked out it's just a matter of doing the math which is a lot... It took weeks to simulate proton jumping using similar equations in superacids for a time period of less than a microsecond. There's a lot of math involved but it's math that we know how to do.

Re:Looks like a big sea slug.

[Antique Geekmeister]

And this is, of course, worse than saying that a computer is just a pile of transistors. The environment in which the object grows, its diet, the concentrations of salt and oxygen and the temperature of its environment all affect the most basic of its functions. Worse, it ignores the mitochondria and the environment of the egg in which it was hatched.

It may all be chemistry, physics, and math, but a lot of the most critical functions are completely unsoluble and intractable if you treat them this way. And the math make very clear that it is useless to attempt many of such models.

Re:Looks like a big sea slug.

[Wonko the Sane]

Really? What are they?

The basic quantum physics formulas that cover the interactions of protons, neutrons and electrons.

Given sufficient RAM and processing capability we could simulate practically anything via a brute force approach. I doubt that the worldwide total of either one is enough to fully simulate a sea slug down to the subatomic particle level, but we already know algorithms that could do it.

Re:Looks like a big sea slug.

[Tomfrh]

It's all chemistry, physics and math.

That's just handwaving.

No one fully understands the complete physics and chemistry of the simplest forms of life, let alone a sea slug.

Re:Looks like a big sea slug.

[wizardforce]

Not really. Our computors are advancing rapidly and from what I've seen in the field, there's significant room for efficiency improvements in the way we do the calculations. Protein folding for one may benefit from some newer algorithms being developed in the field. The mitochrondria are very simple by comparison to the rest of the organism. That doesn't pose much in the way of being an obstacle. Then there's the part where you aren't forced to model every single molecule in the cell at once. Just the atoms in each protein to determine their interactions and properties and fit all of it together like lego blocks to form the whole organism.

Re:Looks like a big sea slug.

[lawpoop]

It's all chemistry, physics and math.

Has anyone actually done this? With even a ''simple'' organism ( yes, those are air-quotes ), like a paramecium? It sounds easy in theory, but I bet when we actually get down to it, there'll be a few speedbumps and unexpected obstacles in the way.

Once we get the sea slug calculation going, anyway, how do we test it? You know, to see that these formulas actually create a phenomena that mimics a sea slug, beyond just looking like one, cellularly? The environment that a sea slug lives in is probably orders of magnitude more complex than the sea slug. So what kind of program do we test it in? It might look like a sea slug, but would it act like one?

Re:Looks like a big sea slug.

[lawpoop]

The basic quantum physics formulas that cover the interactions of protons, neutrons and electrons.

Well, I think you're over-simplyfying it. We do know the physics and equations for those, but just plugging them into a computer won't give us sea slugs. ( I think the domain of possibility of DNA life is infinite). We need to actually specify the 'sea slug' program -- as another poster pointed out, the DNA that specifically is a sea slug.

Re:Looks like a big sea slug.

[Anonymous Coward]

No. read this (quite interesting):

http://en.wikipedia.org/wiki/Digital_physics#Pancomputationalism_or_the_Computational_universe_theory

and go from there. The fact that we know the equations doesn't mean we can simulate anything.

For example : say a slug was a spherical shape. Just to represent pi, and therefore its volume would require infinite precision. There is a massive difference between knowing the ideal equations and simulating an organism.

Re:Looks like a big sea slug.

[scheme]

It's all chemistry, physics and math.

Has anyone actually done this? With even a ''simple'' organism ( yes, those are air-quotes ), like a paramecium? It sounds easy in theory, but I bet when we actually get down to it, there'll be a few speedbumps and unexpected obstacles in the way.

Things are not even close. Look at vcell to see what's close to the state of the art in cell simulation. Right now, it's a matter of trying to get a few reactions and cell compartments working correctly. I don't think anyone has even come close to modeling any type of complete cell.

Re:Looks like a big sea slug.

[Magic5Ball]

The useful computability of your simplification to parts, and its neglect of emergent properties, assumes a solution to at least one of Clay Millennium Prize Problems, which is not currently in evidence.

Re:Looks like a big sea slug.

[Artifakt]

Remember the film, Jurassic Park? They applied some simple math to make flocking behavior in their dino models look realistic. It works - just about everybody says the dinosaur flocking looks just like real flocking. Of course real biologists who have been trying to find the math behind real flocking have tested those equations the film makers used, and found some trivial little problem like you need to have faster than light telepathic communication between animal brains if you don't want the animals to get into a ridiculous gridlock once you add in some real environment modeling, but it sure looks like it's real flocking.
      And I'm sure we'll get paramecium models or mitochondrion models, or whatever, which 'look just like' the real thing, but turn out to be built on math that has fundamental problems with the rest of reality and uses some cheap hack like omitting surface roughness or gravity to gloss over that part, many times before anyone gets an actual model. We'll see 'accurate' models of atomic nuclei that build all 13 stable elements (or all 1047). 'Accurate' models of natural selection that show only plants should evolve eyes will follow. Eventually, your sea slug will act just like a real one does when the liquid it swims in is molten Sodium, (but not, unfortunately, in water).
      People will probably work some or most of these out. Accurate computer modeling of some events has happened, and many more will probably happen with advances in technology. Claiming that all of them will definitely work makes about as much sense as claiming all computer based aircraft models can safely skip the wind tunnel test stage of development.

Re:Looks like a big sea slug.

[Anonymous Coward]

You don't need to model all of the parts in a sea slug (like proteins) to model the organism itself. It depends on what level of behavior your model is trying to describe. For example, if you want to model the spatial organization of cells in a sea slug, you can use the law of large numbers to ignore many variables (like protein folding) and only focus on variables that aren't averaged out probabilistically. This is why we can relate pressure, volume, and temperature in gases (PV=nRT), it is why we can describe chemical equations by rate constants. It is why the laws of physics work.

To say that we can't model sea slug body plans because we can't predict protein folding is missing the point. In modeling, you select the important variables and ignore the unimportant variables. If you don't think you can model complex behaviors by simple rules, there are some interesting examples to the contrary. For example, Mark Krasnow's lab at Stanford has identified very simple rules that almost completely describe the branching patterns in mouse lung development. A picture of a mouse lung is extraordinarily complex and to think that lung development is governed by these simple rules is quite amazing. Extending this to the sea slug, I wouldn't say it is too farfetched to try and model it with a simple system of rules.

To try and model it with a single equation (like a fractal) does seem a little crazy though. :)

Re:Looks like a big sea slug.

[Plunky]

Not quite. We do know the rules of chemistry well enough to model proteins, the problem is that the amount of sheer number crunching is enormous. As for water, that's also not quite true. We have the equations for interactions between molecules worked out it's just a matter of doing the math which is a lot... It took weeks to simulate proton jumping using similar equations in superacids for a time period of less than a microsecond. There's a lot of math involved but it's math that we know how to do.

If only you had a bunch of rocks, and plenty of time..

Re:Looks like a big sea slug.

[dkf]

I wonder if we'll ever reach the point where we will be able to define, with equations and rules, a sea slug using the principles of cellular automata?

"Ever"? Could well happen. But soon? Even with Moore's Law, not likely. (I'm assuming you're talking about doing the behavior and physiology, not just something that looks like one.) The issue is simply one of scaling up; a sea slug has a heck of a lot of elementary particles in it and just being able to cope with that many interactions is really tough. Of course, since there's not actually that many orders of magnitude of difference between a sea slug and a person, we'll be able to simulate people shortly after sea slugs, and humanity (at current population levels) not long after that.

Re:Looks like a big sea slug.

[SharpFang]

I still believe a cell is performing a small set of relatively simple processes that affect the rest of the organism, except in a very complicated manner - they need to maintain, repair and power self primarily, on top of affecting others.

It would mean that we should be able to approximate a cell quite accurately with relatively simple model that is nothing like a cell internally but performs the same functions. Treat the cell as a black box, and replace it with a black box that behaves the same, but differs internally.

Still, to do that adequately, we need a 100% working (internally) model of a cell, which we can then begin to simplify in a way that doesn't affect the I/O.

Re:Looks like a big sea slug.

[Legion303]

"Eventually, your sea slug will act just like a real one does when the liquid it swims in is molten Sodium"

Well shit, I can model that right now. Probably in about 10 lines of code. And I'm not even a programmer! Wait, here it is in one (8086 assembly):

NOP

Re:Looks like a big sea slug.

[Rosy At Random]

In a Platonic fashion, I tend to think that these ideal models do represent reality -- in that they are the limits of what reality is tending to. What reality is doing is complicated, but can be expressed elegantly and meaningfully as echoes of the process it is ghosting.

A fern leaf may not be a true fractal, but up to a point reality is behaving fractally. It is pretty difficult to describe it in any other way.

Re:Looks like a big sea slug.

[ConceptJunkie]

It might look like a sea slug, but would it act like one?

Stick it in a room with a couple hundred others. See if it tries to pass a health care reform bill so complicated no one could ever understand it. If it does: close enough.

Re:Looks like a big sea slug.

[I(rispee_I(reme]

Progress is being made towards just such a scenario; however, due to the computational expense, the only such definition (so far, to my knowledge) is a tobacco mosaic virus in a drop of water.

This was simulated on the atomic level, and according to the article ~50 million atoms were virtualized. Again due to computational expense, the emulation ran for only 50 nanoseconds.

It raises the old conundrum of how accurate a model can be before it ceases to be useful or becomes a copy.

Re:Looks like a big sea slug.

[Godeke]

Assume a Spherical Cow

Re:Looks like a big sea slug.

[Lunzo]

I don't think using mathematical models from a film for real science is a good idea. The point of the film is to appear realistic, not actually be the same as nature. Another example would be lighting equations used in computer graphics. The aim is to give the illusion of realistic lighting, not actually reproduce reality. It turns out that the actual equations for light fall-off from the physical world don't look as realistic as the ones that are used.

Re:Looks like a big sea slug.

[EnglishTim]

http://en.wikipedia.org/wiki/Boids

Re:Looks like a big sea slug.

[Wonko the Sane]

For example : say a slug was a spherical shape. Just to represent pi, and therefore its volume would require infinite precision. There is a massive difference between knowing the ideal equations and simulating an organism.

Not infinite precision. Assigning enough bits in your coordinate system such that one bit equals the planck length should be enough.

It's simply a matter of having enough* RAM and processor cycles.

*Yes, I understand how ridiculously large "enough" is.

Re:Looks like a big sea slug.

[Anonymous Coward]

Already done; it's call a sea slug.

Re:Looks like a big sea slug.

[Cybrr]

If a computer can do it, so can this Turing Machine implemented in Conway's Game of Life. It's just a little slow.

Flashback

[Tx]

Weird, I definitely saw that thing after taking acid once, in fact I floated though it for quite a while. It may look all pretty on your screen, but that shit put me off drugs for life, man.

Re:Flashback

[Anonymous Coward]

I'd like to show you the inside of my Fleshlight sometime.

Re:Flashback

[Tablizer]

No, that's the Goatsebrot set you're thinking of.

Re:Flashback

[Progman3K]

A few of those things look like magnified pictures of pollen...

Re:Flashback

[Korbeau]

Weird, I definitely saw that thing after taking acid once, in fact I floated though it for quite a while. It may look all pretty on your screen, but that shit put me off drugs for life, man.

Modded informative?!?

What, is seeing the "mandelbulb" the mathematical incarnation of "this man" http://thisman.org/?

Re:Flashback

[Twinbee]

Hi I'm the author of the article. Curious, which image was it that created the flashback?

Re:Flashback

[Anonymous Coward]

Weird, I definitely saw that thing after taking acid once, in fact I floated though it for quite a while. It may look all pretty on your screen, but that shit put me off drugs for life, man.

Than you should see the resemblance to diatoms on the microscopic scale and the structure of the mapped known universe on a universal scale. Amazing stuff fractals.

Re:Flashback

[Tx]

'Scuse the slow reply, didn't expect any serious comments. The image captioned "Mandelbrot Crust" was the one that stood out. One would look at something with simple curved lines, like a pattern on a carpet, and it would spring into 3D, with seemingly infinite fractal detail the closer you looked, and sort of glowing in the "deep" parts, as if lit from below, with all the detail moving as if made from lots of little constantly rotating parts. "Mandelbrot Crust" sort of took on that kind of motion when I looked at it.

I should point out that the comment about that putting me of drugs for life was somewhat flippant, I did a pretty average share of experimentation at university (a good few years ago now), and I did not really enjoy psychedelics; it wasn't actually any particular experience that put me off, I just didn't like having my mind messed with like that.

Re:Flashback

[JDeane]

Seeing these makes me wonder if that perhaps Einstein would have been inspired. I know these are just graphical representations and that particle interactions and DNA and things like that are far more complex but it does make one wonder.

That with the correct formula a seed number (big bang) would lead to a universe where one could scale time out zoom in and see life evolve on some little spec of dust floating near a point of light.

Of course the amount of calculations would be fantastic and far beyond anything I can imagine.

Maybe some sort of time compressed computer using tachyon quantum gates so that the calculations could be carried out before you asked the question lol (too many Scifi movies for me sorry to all the physics majors out there collectively either laughing at me or looking for some rope to string me up from the closest tree by my toes)

Would have to be buried at the bottom of a black hole lol

I think I remember reading some where that to simulate the universe would require a computer with more matter in it then the universe actually contains. This made sense to me since emulation requires hardware more powerful then the original.

Re:Flashback

[repapetilto]

can you provide good pics for that

Re:Flashback

[dotar]

I tell you what, fractalling wasn't a particularly pleasant experience (to put it mildly), but I never really understood fractals until then.

Movie possibility?

[martinX]

Looks marvellous. I can see a sci-fi movie based on this, something like The Cube. Or Fantastic Voyage. Mmmmm Raquel Welch.

All I see is a big white rectangle

[Anonymous Coward]

With a message saying Page cannot be displayed. Not that impressive.

Re:All I see is a big white rectangle

[MobileTatsu-NJG]

With a message saying Page cannot be displayed. Not that impressive.

Did you try zooming in?

Re:All I see is a big white rectangle

[symbolset]

Try the mirror. (It needs sound and it takes a while to cache.)

Re:All I see is a big white rectangle

[TheVelvetFlamebait]

Yeah. Nothing changed. :-(

Re:All I see is a big white rectangle

[The Dark]

Did you try zooming in?

It's 404s all the way down.

Re:All I see is a big white rectangle

[six025]

With a message saying Page cannot be displayed. Not that impressive.

Did you try zooming in?

Yes, but the same message keeps repeating over and over and over ...

Re:All I see is a big white rectangle

[EdgeyEdgey]

40404040404040404040404040404040404040 etc.
"Your comment violated the "postercomment" compression filter. Try less whitespace and/or less repetition."
Damnit

Re:All I see is a big white rectangle

[Anonymous Coward]

With a message saying Page cannot be displayed. Not that impressive.

Did you try zooming in?

Yes, but the same message keeps repeating over and over and over ...

See, it's self-similar.

Mandelbrot says...

[Anonymous Coward]

ITS GO TIME!

Re:Mandelbrot says...

[Anonymous Coward]

Mandelbulb! Mandelbulb! Mandelbulb!

gee, guys

[Anonymous Coward]

why in the world can't slashdot mirror websites or at least the articles/pictures instead of just unleashing its entire audience on some poor shmuck's webspace? I can't count how many interesting things that slashdot has rendered nigh-inaccessible with the flood, it's getting ridiculous.

i mean obviously you're just externalizing the cost of the traffic, isn't that the first no-no of doing legitimate business on the web?

Video games need these now

[sayfawa]

Picture Half-life's Xen, Doom's Hell, or some Final Fantasy dimension rendered with these. Awesome.

Re:Video games need these now

[ArcadeNut]

You mean like this? http://en.wikipedia.org/wiki/Rescue_on_Fractalus!

Re:Video games need these now

[sayfawa]

Holy crap, it's even better than I imagined! :)

Katamari Mandelrot

[Riddler Sensei]

I imagine if they included Mandelbrot fractals as something you can roll up in Katamari, then there would no longer be ANY need to experiment with psychedelic drugs ever again.

Zooming

[Spy Hunter]

Here's a 7500x7500 (56 megapixel) image of the fractal: http://seadragon.com/view/fnr.

Re:Zooming

[Sir_Lewk]

I love how ontopic your signature is.

Re:Zooming

[hey]

Nifty but it seems to be a Microsoft thing so can't actually be good. :) Seems to work with javaScript and not Flash or Silverlight!

Re:Zooming

[WoodenTable]

I have to say, that looks like the sort of thing scientists might find deep, deep in the ocean. The sort of thing where its researchers start inexplicably disappearing, one by one.

Re:Zooming

[SanityInAnarchy]

Though they do say "for better performance, install Silverlight."

Re:Zooming

[Anonymous Coward]

Is that one word now? Is its associated quality or state "ontopy"?

Re:Zooming

[thisisntme]

Your post lacks ontopy.

Re:Zooming

[Anonymous Coward]

There is no sig anymore. What was it?

Slashdotted

[Anonymous Coward]

I think we crashed their server.
Waiting to see it >.>

Slashdotted

[Kaladis Nefarian]

Seems to be slashdotted, cached version: http://www.skytopia.com.nyud.net:8090/project/fractal/mandelbulb.html

Or something like...

[denzacar]

Langoliers remake.
Those things already look like they are made of teeth. Endless rows of teeth that devour the world.

A sad day indeed...

[symbolset]

If that's the case, it's been a sad day since at least 1984. These things teach us interesting things about numbers and are interesting in and of themselves. As a way of making math more visually beautiful they also serve to draw the interest of youth to a field ordinarily seen as dry and boring.

w00t

[lycium]

cool, nice to see my images linked on slashdot :) hopefully we'll have some gpu-accelerated results to show you all soon (and for those with opencl supporting cards, executables).

btw interested parties might like to check out my 3840x2400 resolution render of the 7th degree version here: http://lyc.deviantart.com/art/siebenfach-139038934 (it's buried deep in the thread, and fractalforums is creeking a bit)

Re:w00t

[gr8_phk]

Time to dig out my realtime raytracing library and do some voxel rendering :-)

Re:w00t

[lycium]

oh wow, paul kahler :) i remember you from the heady realtime ray tracing days, all those years ago now...

Re:w00t

[six11]

Thanks for this. It takes me back to 1991 or so when I discovered fractals and suddenly didn't detest math any more.

Re:w00t

[Per Wigren]

I rewatched the original Alien movie just yesterday and that image looks like it could be a pause picture from the base at the planetoid where they discover the aliens.

Re:w00t

[srmalloy]

I agree; that rendering is amazingly Gigeresque.

Re:w00t

[ConceptJunkie]

Yes, I definitely thought of how this might be done using POV-Ray. IANAM, I doubt you could make an isosurface version of the Mandelbulb, but POV-Ray is a full-blown programming language, so I'm sure something can be done.

Re:w00t

[gr8_phk]

Hey, don't be linking my real name, my hobby identity, and my slashdot trolling identity all together now ;-) Next thing you know Facebook will start making suggestions.

...and in other news

[Linker3000]

...and in other news: Shares in printer ink manufacturing companies rose significantly tonight, and a spokesperson for local schools' IT said they hoped this development would now give them something to finally replace that picture of the cartoon duck smashing the computer with a large mallet, provided the aged blue tack hadn't fused the original printout from 1998 permanently to the computer room walls.

What if the "true" set is more mundane?

[ChronoFish]

I found that hot chocolate (not too watered-down) in a white ceramic mug leaves a very rudimentary but easily discernible "Mandelbrot" set. At least the classic image (I have no way to zoom in to great detail on the side of my mug.). The set is left over from "chocolate bubbles".

Is it possible that the lines of the Mandelbrot set are simply outlines of colliding bubbles? The 3D version of this, while cool - would be significantly less impressive than the images from the article.....

-CF

Re:What if the "true" set is more mundane?

[imakemusic]

I have no way to zoom in to great detail on the side of my mug.

Have you tried moving your head closer?

Re:What if the "true" set is more mundane?

[Twinbee]

Hi can you possibly take a photo, and send it to me?

Sorry about crushing your server

[symbolset]

Reading through the thread on fractalforums was inspiring. You guys play off each other remarkably well. Some gorgeous work all through there.

You guys helped correct JosLeys' "error" where he had large bridges under the bulbs. I'm not sure that wasn't a mistake... his work was remarkable also and the peer norming there may be throwing out something interesting.

Broccoflower formula?

[lawpoop]

While we're on the subject, can someone point me to where I can find a formula for generating a broccoflower shape? I want to make one in 3d, but I'm not so good with teh maths.

Yes...

[Anonymous Coward]

Looks like a Yes album art generator...

Oddly Familiar

[Tablizer]

I swear I've seen the first 3 already when I accidentally ran over a toad.

a great leap forward

[circletimessquare]

for scientific screensaverology

always looked 3d 2 me:-)

[airdrummer]

i'll have to fire up the ti99 to find the coords, but doing a CLUT sweep made the area look 3d, like roots descending into the earth;-)

Simulating a sea slug

[AlpineR]

It's still just physics. You don't have to do any energy minimizations or understand how protein folds. Just solve it the way Nature does: brute force. Stick some atoms together and plot their movement over time. If you want to include the slug's environment and food, then expand the box to include those things too.

The only problem is that your computer isn't fast enough. You can't simulate a slug. You can't simulate a slug's heart. You can't simulate a single cell. You can't simulate a strand of DNA. The best you can do with current technology is to spend a week of processor time to simulate a few atoms moving around for a few nanoseconds. To scale that up to a slug (with interactions making the computational work scale much worse than linearly) would take more than all the computer power ever assembled by all of humanity.

My point is that our computers are pathetic compared to Nature's computers. If we could do a fraction of what Nature does with even a hundred atoms we'd be closer to simulating life. There's tremendous room for improvement.

Fraqtive

[nephridium]

A very nice open source app, available through the Ubuntu/Debian repositories. The author's page even got a windows version.

It supports multi-core CPUs, i.e. if you really want to tax each of your CPU's core to the limit, just use the app to browse through the mandelbrot set. It also supports a 3D extrapolation of the 2D set (OpenGL and software).

Strangely enough it doesn't seem all that popular, as the forum doesn't seem all that populated..

WOW!

[Anonymous Coward]

Now, there's a reason for an octacore and a few GPUs :-D

That's...

[Anonymous Coward]

...one badass fucking fractal.

"Not a 'true' 3D Mandelbrot" misses the point...

[KonoWatakushi]

While you may have a point, it is similar to complaining about Ampere's Law, before Maxwell's correction. Sure, it wasn't exactly right, but it more or less had the same properties.

This may not be the simplest function, but it retains the most fundamentally interesting properties of 2D fractals: infinite detail generated by a simple mathematical function. It is fascinating just the same, and is only a (very) minor modification of the original 2D function.

The Mandelbulb is awe-inspiring, and it is disappointing to see that story nitpicking outclasses your interest in this wonderful piece of work. If it were merely pretty pictures generated by iterative functions, I think you would be justified. It isn't though--this is an amazing structure generated by a pure and simple piece of math.

Ow my sanity

[jaxtherat]

Did anyone else get seriously freaked out looking at stills of the 3D fractals? Stuff of nightmares...

Amazingly cool maths though!

Re:Ow my sanity

[Tomfrh]

They are nightmarish images alright...

The whole creature looks very malicious.

Nature imitates art

[jms]

Compare the images to Louis Sullivan's late 19th and early 20th century ornamentation:

http://en.wikipedia.org/wiki/File:Van_Allen_Column_Capital.jpg
http://en.wikipedia.org/wiki/File:Van_Allen_3.jpg
http://www.harboearch.com/getProject.php?projname=sullivancenterc

Other fractal options

[Spykk]

As great as the mandelbrot set is, I personally feel that the burning ship set produces better imagery. Actually, some of the most interesting renders I have generated come from a set that is in between mandelbrot and burning ship. You can get a copy of the renderer that I wrote at Spoony Bard Games and see for yourself.

broccoli

[oliphaunt]

and here I thought I was coming to read a post about Romanesco Broccoli (link goes to gis for "romanesco"). Seriously, it's like eating math.

Animated quaternion

[_bernie]

The common Mandelbrot set is really a 2-dimensional slice of a 4-dimensional object identified by both the combination of the complex numbers Z0 and C in the canonical Zn+1 = Zn^2 + C. The mandelbrot set lives in the plane where Z0 = 0 + 0i, while the Julia sets live on infinitely-many-squared orthogonal planes in the remaining two dimensions, each one intersecting Mandelbrot's plane in a single point of complex coordinates C.

Visualizing this hyperspace monster was made easy by POV-Ray. It took my computer two week of computation to render 80 seconds of animated 3D slices of a the quaternion. Check out the scene source.

/me looks forward for a real-time Julia4D explorer.

Re:Animated quaternion

[Anonymous Coward]

He specifically says he did not use POV-Ray, and had to make his own rendering engine.

Re:Animated quaternion

[OeLeWaPpErKe]

Not to rain on your parade ... but the article's mandelbrot looks a hell of a lot more detailed.

Re:Animated quaternion

[_bernie]

Not to rain on your parade ... but the article's mandelbrot looks a hell of a lot more detailed.

We're comparing a power 8 version of the generlized Mandelbrot formula (Zn+1=Zn^k + C, with k=8) against a power-2 quaternion Julia.

In the epilogue, the author admits that there's less variety in the Mandelbulb-8 than even in the classic Mandelbrot.

Elder feuds reignited?

[Mathinker]

UID 3706 replies to UID 6544:

> No! I hate everything you stand for.

From my almost 7-digit standpoint, your feuding looks a lot like cyber-mythology! Is there a deeper story here? Were you both swallowed and subsequently regurgitated by a 3-digit UID?

Re:Elder feuds reignited?

[Tumbleweed]

UID 3706 replies to UID 6544:

I am not a number, you young punk! And get off my damned lawn!

Re:Elder feuds reignited?

[Anonymous Coward]

but do you even had computer in the 4 digit era? or was slashdot some sort of paper mail based discussion forum?

Re:Elder feuds reignited?

[Per Wigren]

I'm caught in between here :-(

Re:Elder feuds reignited?

[Tumbleweed]

but do you even had computer in the 4 digit era? or was slashdot some sort of paper mail based discussion forum?

Gawd, don't they teach you brats anything in school these days? It was all vacuum tubes back then. Of course, it's all ball bearings, now. We would've _killed_ for ball bearings back in the day!

Re:Elder feuds reignited?

[rsidd]

Once upon a time, Slashdot editors did read what they posted. I guess both 3706 and 6544 remember.

Re:Elder feuds reignited?

[Rubinstien]

Me too. Hmm. Newton's Method with UID's?

Re:Elder feuds reignited?

[bickerdyke]

"Grumpy old men" - Now on slashdot!

Re:Elder feuds reignited?

[Anonymous Coward]

I guess both 3706 and 6544 remember.

slashdot, Auschwitz style!

Re:Elder feuds reignited?

[Bill Currie]

*Burp*

And tasty they were, too.

Re:Elder feuds reignited?

[soybean]

Alright boys, calm down. No fighting here.

Re:Elder feuds reignited?

[cduffy]

Clearly, my memory is getting hazy in my old age.

Re:Elder feuds reignited?

[Nethead]

Both of you! To bed now!

Fsckin' kids.

Re:Elder feuds reignited?

[Tumbleweed]

Both of you! To bed now!

Same # of digits means sibling, not parent. You're not the boss of me!

I waited a long time before bothering to get a slashdot account, as there wasn't much benefit to it in the early days. Once the 'first post' morons came along en masse, though, it had a practical benefit, so I signed up. I've been around a lot longer than my 4-digit UID would indicate. :)

Re:Elder feuds reignited?

[Nethead]

Then you may remember my old Pent 133 box that I hosted images.slashdot.org on when Malda was getting started and his T-1 was slammed. I was working at an ISP in Seattle (wolfe.net) and we had the BIG pipe, a frickin T-3. (You can put a lot of modems on a T-3.)

Re:Elder feuds reignited?

[Rob Riggs]

All we need is The Glorious Meept!! to show up and we've got ourselves a party.

Re:Elder feuds reignited?

[Tumbleweed]

Then you may remember my old Pent 133 box that I hosted images.slashdot.org on when Malda was getting started and his T-1 was slammed. I was working at an ISP in Seattle (wolfe.net) and we had the BIG pipe, a frickin T-3. (You can put a lot of modems on a T-3.)

Ahh, wolfe.net, my old ISP. I'm in the Seattle area. I was working for Spry ("Internet in a Box") at the time.

My first website in Seattle was www.wolfe.net/~tmblwd/

01d 5k001! :)

Re:Elder feuds reignited?

[Nethead]

Damn, I remember you on gonzo. I was joe@wolfe.net and my wife-to-be was tiff@wolfe.net. Irving Wolfe let me host /. images for no charge. I was the modem and T-1 guy there for about two years. I worked in the Westin for almost 7 years. Those were great days. Some friends and I talked Irving into starting wolfe.net when connected.com died, leaving Irving without his UUCP account.

Re:Elder feuds reignited?

[Tumbleweed]

Damn, I remember you on gonzo. I was joe@wolfe.net and my wife-to-be was tiff@wolfe.net. Irving Wolfe let me host /. images for no charge. I was the modem and T-1 guy there for about two years. I worked in the Westin for almost 7 years. Those were great days. Some friends and I talked Irving into starting wolfe.net when connected.com died, leaving Irving without his UUCP account.

I can't believe you remember me from that far back! Even the server name. That's really kind of scary. :)

Re:Elder feuds reignited?

[Defiler]

I don't remember that.

Re:Elder feuds reignited?

[HEbGb]

I have to say though, having a nice round UID number is almost as cool as having a nice 4-digit one.

Re:Elder feuds reignited?

[HEbGb]

So far you win for lowest UID, grandpa!

I smell profit!

[AndroidCat]

Time to buy stock in some select t-shirt companies!

In nature - I give you, Brassica oleracea!

[zooblethorpe]

These particular fractals remind me of things I hope never to see in nature.

Some of it, at least, has already happened: see this fine example of Brassica oleracea, for instance.

Then again, you might have been referring to some of the fractal images that call to mind the work of H. R. Giger... < shiver >.

Cheers,

Re:In nature - I give you, Brassica oleracea!

[KevinColyer]

Well, didn't think of Giger, but Gaudi sprung to mind at once.The Brassica is also impressive in real life.

Re:In nature - I give you, Brassica oleracea!

[tehcyder]

Some of it, at least, has already happened: see this fine example of Brassica oleracea [ubcbotanicalgarden.org], for instance.

I thought the most interesting point about fractals was that they do, in fact, occur in nature.

Re:In nature - I give you, Brassica oleracea!

[BevanFindlay]

Hmm, reminds me of a quote I read in a book once, basically God saying "I like fractals". :-) I'd have to agree...

Sea urchins and diatoms

[flyingfsck]

I think that the sea is full of 3D mandelbrot set creatures.

look

[Anonymous Coward]

at the bottom of this image: http://mandelbulb.s3.amazonaws.com/full/q50/Mandel3Dpersp-med.jpg

jesus in a toast!

he says to make more fractals nom nom nom

What about fractional powers?

[Anonymous Coward]

Like 7.5 or something like that. Of course it would slow rendering way down, but the gpu would make up for it.

Re:What about fractional powers?

[Twinbee]

I tried fractional powers. Not much difference really.

W00t, pretty pictures!

[Kickasso]

Thank you, my collection of backgrounds has just become one step closer to ultimate perfection.

Formations on Solaris

[jimboindeutchland]

The images remind me of how Stanislaw Lem described the formations created by Solaris. I better go and read it again.

I realise this is probably a stupid question

[boristhespider]

and doubtless the people who did this work have a very good reason not to do this, but why waste your time on a problem they've already accepted is ill-defined? Why not just make a 4D Mandelhyperbulb and then take slices through it? That way you could actually say that you *do* have a higher-dimensional Mandelbrot set, and still have 3D figures that you can render on a computer screen. This arbitrary "Let's make a 3D Mandelbulb by, err, fucking about a bit and not actually doing anything properly" is remarkably unsatisfactory -- and they seem to acknowledge that themselves.

Re:I realise this is probably a stupid question

[arethuza]

Just because it isn't academically rigourous doesn't mean it's cool and probably rather good fun to do.

Re:I realise this is probably a stupid question

[arethuza]

That should have been: "Just because it isn't academically rigourous doesn't mean it's NOT cool and probably rather good fun to do"

Re:I realise this is probably a stupid question

[Anonymous Coward]

The problem is that slices of quaternion mandelbrots look kinda boring. The result consists of lots of thin strings that fuse together rather than some sort of rough surface.

quat

[Anonymous Coward]

Remembers me of the quaternion generator:
http://www.physcip.uni-stuttgart.de/phy11733/index_e.html

Mandlebulbs dirty secret

[Anonymous Coward]

This shot from within the mandlebulb, gave me nightmares...

http://mandelbulb.s3.amazonaws.com/q85/IceCreamFromNeptune-small2.jpg

I've named it Death by a thousand penis'

steady hempin

[Anonymous Coward]

So it's a conicidence that all of those pictures look like enormous sticky buds? God does not play dice with the universe?

A 3D Mandelbrot needs 3d Julias...or something...

[swm]

Monkeying with the equation that generates the Mandelbrot set seems misguided.

The true definition of the Mandelbrot set is the set of points for which the corresponding Julia set is connected. This is the original motivation for the equation. If you want to get an interesting 3D object, start by searching for an interesting collection of sets that are parameterized by three coordinates.

Re:A 3D Mandelbrot needs 3d Julias...or something.

[Twinbee]

'True definition'?

I started out with a simpler geometrical/visual definition - rotate a point around, move away/towards from the center, and then translate by the initial vector. Keep doing this until it sinks to the centre, or moves away to infinity. You don't even need to use complex numbers for this, though it makes it simpler if you do.

Using that logic, I then tried to find a 3D equivalent, and think I did pretty well. Don't you at least find it curious that the buds are forever growing upon each other in a way that's never been seen before outside IFS systems? It really makes me think that the 'real McCoy' exists (see the end of the article).

Subject

[Legion303]

TFA says that they couldn't find a 3D program that rendered from formulas, but from what I remember, Maya will do just that (you need to use melscript). It's not exactly free, but hey...

Picky eater

[haapi]

I don't like broccoli.

real-time Julia4D explorer

[Anonymous Coward]

http://www.cs.caltech.edu/~keenan/project_qjulia.html
Have fun !

yes, but can they do this?

[Anonymous Coward]

http://students.ceid.upatras.gr/~sxanth/pyvm-2.0/logo.png

Turtles

[thinairart]

Looking at TFA's renders confirmed what I have always been told... Its turtles all the way down!

Aliasing

[Prune]

Most of the images on the site suffer from aliasing which is quite nasty in some areas and makes them lose some of the beauty. He needs to supersample the rendering and apply a decent filter.

Re:Aliasing

[Twinbee]

They're fairly low quality jpeg anyway because of bandwidth concerns.

Lets call it Beta

[zintli]

Seriously?
A 3D fractal and nobody mentions Defying Gravity??
So I really am the only person that watches that show.
*Sigh*

Cool.

[Anonymous Coward]

H.R. Geiger on prozac.

Looks familiar...Kindof like a

[Whomp-Ass]

Rotavirus or, surprisingly enough, the Novel H1N1 strain going around. Compare This particular iteration to the following: H1N1 or Rotavirus

and

[Anonymous Coward]

Mandelbutt - a 3D Mandelbrot Construct, Fondled

Mandelbra - a 3D Mandelbrot Support Mechanism for your 5-Dimensional Mistress, Tempest Vavoom

Mandelabra - a 3D Mandelbrot Lighting Device

Mandelburp - a 3D Mandelbrot Gaseous Utterance

Mandelhowie - a 3D Mandelbrot Comedian, or Canadian, nm, same thing

Mandrellbarb - a 3D Mandelbrot Comedian, or Country Singer, nm, same thing

It aint fightin' it is wrastling'

[Anomalyst]

Hows this for an soul-searing image?
3 and 4 digit UID holders in speedos a-wrastlin' in a kiddie pool of 0's and 1's.
Fair warning, the goggles they will do nothing.

Animated in 3d

[nycheetah]

Is it possible to see the 3d fractals rendered and animated?

So.. does it mean that math is beautiful?

[Hemi Rodner]

(n/t)

Balls, hollow balls, and spheres

[tepples]

Given that the sphere is, by definition, the surface of a ball, I wonder what the surface of a sphere is meant to be?

The inner surface or the outer surface?

In the world of things made of atoms, spheres don exits. Solid and hollow balls do. A solid ball has one surface, a topologic sphere, while a hollow ball is the volume between two concentric spheres, that is, a solid ball minus another solid ball. Just as an infinitely thin "curve" in a plane has a plot with thickness (an ultimately 3-dimensional deposit of ink on paper), a "sphere" in a 3-space has a plot with thickness, which I've called a hollow ball.

Re:Balls, hollow balls, and spheres

[maxwell demon]

Of course when getting into physics at atomar scale, then there simply is no well-defined surface, no matter which dimension, due to quantum mechanics.

A Better Name

[shambalagoon]

Mandelbroccoli