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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 (4, Interesting)

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 (5, Interesting)

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

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 (0)

Anonymous Coward | more than 4 years ago | (#30111190)

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 (5, Insightful)

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.

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 [bugman123.com] 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.

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*

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:

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 (5, Funny)

Anonymous Coward | more than 4 years ago | (#30110736)

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.

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?

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? (0)

Anonymous Coward | more than 4 years ago | (#30111394)

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 (2, Insightful)

Anonymous Coward | more than 4 years ago | (#30110804)

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.

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.

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.

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.

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 [imachination.net] ?

Re:Looks like a big sea slug. (0)

Anonymous Coward | more than 4 years ago | (#30110744)

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

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.

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.

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.

*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.

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.

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.

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.

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.

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?

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 [uchc.edu] 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.

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.

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.

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. (1, Interesting)

Anonymous Coward | more than 4 years ago | (#30111542)

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.

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 (1, Funny)

Anonymous Coward | more than 4 years ago | (#30110970)

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

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

Mandelbrot says... (0)

Anonymous Coward | more than 4 years ago | (#30110660)

ITS GO TIME!

gee, guys (0)

Anonymous Coward | more than 4 years ago | (#30110670)

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?

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.

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.

Slashdotted (0)

Anonymous Coward | more than 4 years ago | (#30110710)

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

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 [deviantart.com] (it's buried deep in the thread, and fractalforums is creeking a bit)

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' [fractalforums.com] "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.

...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.

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.....

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

Yes... (2, Funny)

Anonymous Coward | more than 4 years ago | (#30111116)

A very nice open source app, available through the Ubuntu/Debian repositories. The author's page [mimec.org] 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 [mimec.org] doesn't seem all that populated..

WOW! (0)

Anonymous Coward | more than 4 years ago | (#30111642)

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

That's... (0)

Anonymous Coward | more than 4 years ago | (#30111730)

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 [spoonybardgames.com] and see for yourself.

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

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 [povray.org] .
It took my computer two week of computation to render 80 seconds of
animated 3D slices of a the quaternion [sugarlabs.org] .
Check out the scene source [sugarlabs.org] .

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

## frost piss! (-1, Troll)

## Anonymous Coward | more than 4 years ago | (#30110476)

foist foi9st!

## Actually, the Mandelbrot set is already 4D (5, Informative)

## maxwell demon (590494) | more than 4 years ago | (#30110486)

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 (4, Interesting)

## jhesse (138516) | more than 4 years ago | (#30110704)

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 (5, Interesting)

## Eudial (590661) | more than 4 years ago | (#30110740)

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

## Re:Actually, the Mandelbrot set is already 4D (1)

## Forty Two Tenfold (1134125) | more than 4 years ago | (#30110768)

I want a stereogram. Please.

## Re:Actually, the Mandelbrot set is already 4D (0)

## Anonymous Coward | more than 4 years ago | (#30111918)

Can you make this a screensaver?

## Re:Actually, the Mandelbrot set is already 4D (4, Insightful)

## caramelcarrot (778148) | more than 4 years ago | (#30111038)

## Re:Actually, the Mandelbrot set is already 4D (0)

## Anonymous Coward | more than 4 years ago | (#30111190)

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 (5, Insightful)

## Garble Snarky (715674) | more than 4 years ago | (#30111574)

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 (1)

## SoVeryTired (967875) | more than 4 years ago | (#30112194)

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 [bugman123.com] 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 (1)

## SoVeryTired (967875) | more than 4 years ago | (#30112204)

Ugh, I meant 3-space, sorry.

## Now do 4d and animate it! (2, Interesting)

## Anonymous Coward | more than 4 years ago | (#30110488)

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

## Re:Now do 4d and animate it! (4, Funny)

## JoshuaZ (1134087) | more than 4 years ago | (#30110878)

## Not a "true" 3D Mandelbrot (4, Informative)

## HEbGb (6544) | more than 4 years ago | (#30110496)

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 [skytopia.com]

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 (5, Funny)

## Anonymous Coward | more than 4 years ago | (#30110736)

## Re:Not a "true" 3D Mandelbrot (3, Informative)

## symbolset (646467) | more than 4 years ago | (#30110844)

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.

## always looked 3d 2 me:-) (1)

## airdrummer (547536) | more than 4 years ago | (#30111494)

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;-)

## "Not a 'true' 3D Mandelbrot" misses the point... (1)

## KonoWatakushi (910213) | more than 4 years ago | (#30111786)

While you may have

apoint, it is similar to complaining about Ampere's Law, before Maxwell's correction. Sure, it wasn'texactlyright, 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.

## Re:Not a "true" 3D Mandelbrot (4, Funny)

## Tumbleweed (3706) | more than 4 years ago | (#30112044)

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.

## Elder feuds reignited? (3, Funny)

## Mathinker (909784) | more than 4 years ago | (#30112368)

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? (3, Funny)

## Tumbleweed (3706) | more than 4 years ago | (#30112514)

UID 3706 replies to UID 6544:I am not a number, you young punk! And get off my damned lawn!

## Ice Cream From Uranus? (5, Funny)

## Anonymous Coward | more than 4 years ago | (#30110518)

That ruined it for me.

## Re:Ice Cream From Uranus? (0)

## Anonymous Coward | more than 4 years ago | (#30110692)

"Ice Cream From Uranus?"

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

## Re:Ice Cream From Uranus? (5, Funny)

## SeNtM (965176) | more than 4 years ago | (#30110814)

Fry: "Oh. What's it called now?"

Professor: "Urrectum. Here, let me locate it for you."

## Re:Ice Cream From Uranus? (0)

## Anonymous Coward | more than 4 years ago | (#30111394)

Two girls, one ... oh never mind.

## Re:Ice Cream From Uranus? (1)

## inio (26835) | more than 4 years ago | (#30111622)

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

## Re:Ice Cream From Uranus? (1)

## EdIII (1114411) | more than 4 years ago | (#30112034)

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!

## That thing looks like all of my nightmares. (5, Funny)

## Anonymous Coward | more than 4 years ago | (#30110520)

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

## Re:That thing looks like all of my nightmares. (1, Funny)

## Anonymous Coward | more than 4 years ago | (#30110612)

## Re:That thing looks like all of my nightmares. (1, Funny)

## Anonymous Coward | more than 4 years ago | (#30111242)

## Poorly-defined problem (4, Insightful)

## Brian Gordon (987471) | more than 4 years ago | (#30110558)

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 (2, Insightful)

## Anonymous Coward | more than 4 years ago | (#30110804)

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.

## A sad day indeed... (5, Insightful)

## symbolset (646467) | more than 4 years ago | (#30110882)

## Re:Poorly-defined problem (1)

## XSpud (801834) | more than 4 years ago | (#30111566)

## Re:Poorly-defined problem (1)

## jowilkin (1453165) | more than 4 years ago | (#30112156)

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.

## Looks like a big sea slug. (5, Interesting)

## Ethanol-fueled (1125189) | more than 4 years ago | (#30110560)

## Re:Looks like a big sea slug. (0)

## Anonymous Coward | more than 4 years ago | (#30110744)

## Re:Looks like a big sea slug. (2, Interesting)

## wizardforce (1005805) | more than 4 years ago | (#30110850)

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. (1)

## brusk (135896) | more than 4 years ago | (#30110990)

## Re:Looks like a big sea slug. (1)

## wizardforce (1005805) | more than 4 years ago | (#30111112)

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. (1)

## lawpoop (604919) | more than 4 years ago | (#30111018)

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. (1)

## wizardforce (1005805) | more than 4 years ago | (#30111094)

*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. (1)

## Antique Geekmeister (740220) | more than 4 years ago | (#30111148)

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. (1)

## wizardforce (1005805) | more than 4 years ago | (#30111192)

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. (1)

## Magic5Ball (188725) | more than 4 years ago | (#30111852)

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.

## Simulating a sea slug (1)

## AlpineR (32307) | more than 4 years ago | (#30111616)

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.

## Re:Looks like a big sea slug. (1)

## Tomfrh (719891) | more than 4 years ago | (#30111182)

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. (1)

## lawpoop (604919) | more than 4 years ago | (#30111416)

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. (3, Informative)

## scheme (19778) | more than 4 years ago | (#30111654)

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 [uchc.edu] 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. (4, Insightful)

## Artifakt (700173) | more than 4 years ago | (#30112500)

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

allof them will definitely work makes about as much sense as claimingallcomputer based aircraft models can safely skip the wind tunnel test stage of development.## Re:Looks like a big sea slug. (1)

## Wonko the Sane (25252) | more than 4 years ago | (#30111178)

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. (1)

## lawpoop (604919) | more than 4 years ago | (#30111516)

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. (1, Interesting)

## Anonymous Coward | more than 4 years ago | (#30111542)

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.

## Flashback (4, Funny)

## Tx (96709) | more than 4 years ago | (#30110580)

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 (1, Funny)

## Anonymous Coward | more than 4 years ago | (#30110970)

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

## Re:Flashback (1)

## Tablizer (95088) | more than 4 years ago | (#30111344)

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

## Re:Flashback (1)

## Progman3K (515744) | more than 4 years ago | (#30111844)

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

## Movie possibility? (1)

## martinX (672498) | more than 4 years ago | (#30110618)

## Or something like... (2, Funny)

## denzacar (181829) | more than 4 years ago | (#30110778)

Langoliers remake.

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

## All I see is a big white rectangle (2, Funny)

## Anonymous Coward | more than 4 years ago | (#30110648)

## Re:All I see is a big white rectangle (5, Funny)

## MobileTatsu-NJG (946591) | more than 4 years ago | (#30110904)

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 (1)

## TheVelvetFlamebait (986083) | more than 4 years ago | (#30111782)

Yeah. Nothing changed. :-(

## Re:All I see is a big white rectangle (4, Funny)

## The Dark (159909) | more than 4 years ago | (#30111860)

Did you try zooming in?

It's 404s all the way down.

## Re:All I see is a big white rectangle (1)

## six025 (714064) | more than 4 years ago | (#30112226)

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 (2, Funny)

## symbolset (646467) | more than 4 years ago | (#30111062)

## Mandelbrot says... (0)

## Anonymous Coward | more than 4 years ago | (#30110660)

ITS GO TIME!

## gee, guys (0)

## Anonymous Coward | more than 4 years ago | (#30110670)

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 (2, Interesting)

## sayfawa (1099071) | more than 4 years ago | (#30110698)

## Re:Video games need these now (1)

## ArcadeNut (85398) | more than 4 years ago | (#30111150)

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

## Re:Video games need these now (1)

## sayfawa (1099071) | more than 4 years ago | (#30111668)

## Katamari Mandelrot (3, Insightful)

## Riddler Sensei (979333) | more than 4 years ago | (#30110702)

## Zooming (4, Informative)

## Spy Hunter (317220) | more than 4 years ago | (#30110708)

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

## Re:Zooming (3, Insightful)

## Sir_Lewk (967686) | more than 4 years ago | (#30111024)

I love how ontopic your signature is.

## Re:Zooming (2, Funny)

## Anonymous Coward | more than 4 years ago | (#30112076)

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

## Re:Zooming (1)

## hey (83763) | more than 4 years ago | (#30111156)

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 (1)

## SanityInAnarchy (655584) | more than 4 years ago | (#30111628)

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

## Re:Zooming (1)

## WoodenTable (1434059) | more than 4 years ago | (#30111176)

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.

## Slashdotted (0)

## Anonymous Coward | more than 4 years ago | (#30110710)

I think we crashed their server.

Waiting to see it >.>

## Slashdotted (5, Informative)

## Kaladis Nefarian (655671) | more than 4 years ago | (#30110754)

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

## w00t (5, Informative)

## lycium (802086) | more than 4 years ago | (#30110884)

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 [deviantart.com] (it's buried deep in the thread, and fractalforums is creeking a bit)

## Sorry about crushing your server (1)

## symbolset (646467) | more than 4 years ago | (#30110976)

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' [fractalforums.com] "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.

## Re:w00t (1)

## gr8_phk (621180) | more than 4 years ago | (#30111180)

## Re:w00t (1)

## lycium (802086) | more than 4 years ago | (#30111196)

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

## Re:w00t (1)

## six11 (579) | more than 4 years ago | (#30111796)

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

## ...and in other news (1)

## Linker3000 (626634) | more than 4 years ago | (#30110916)

...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? (1)

## ChronoFish (948067) | more than 4 years ago | (#30110928)

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

## Broccoflower formula? (1)

## lawpoop (604919) | more than 4 years ago | (#30111030)

## Yes... (2, Funny)

## Anonymous Coward | more than 4 years ago | (#30111116)

Looks like a Yes album art generator...

## Oddly Familiar (1)

## Tablizer (95088) | more than 4 years ago | (#30111292)

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

## a great leap forward (5, Funny)

## circletimessquare (444983) | more than 4 years ago | (#30111374)

for scientific screensaverology

## Fraqtive (5, Informative)

## nephridium (928664) | more than 4 years ago | (#30111618)

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 [mimec.org] doesn't seem all that populated..

## WOW! (0)

## Anonymous Coward | more than 4 years ago | (#30111642)

Now, :-D

there'sa reason for an octacore and a few GPUs## That's... (0)

## Anonymous Coward | more than 4 years ago | (#30111730)

...one badass fucking fractal.

## Ow my sanity (1)

## jaxtherat (1165473) | more than 4 years ago | (#30111912)

Amazingly cool maths though!

## Re:Ow my sanity (1)

## Tomfrh (719891) | more than 4 years ago | (#30112422)

They are nightmarish images alright...

The whole creature looks very malicious.

## Nature imitates art (1)

## jms (11418) | more than 4 years ago | (#30111958)

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 [wikipedia.org]

http://en.wikipedia.org/wiki/File:Van_Allen_3.jpg [wikipedia.org]

http://www.harboearch.com/getProject.php?projname=sullivancenterc [harboearch.com]

## Other fractal options (1)

## Spykk (823586) | more than 4 years ago | (#30112068)

## broccoli (2, Interesting)

## oliphaunt (124016) | more than 4 years ago | (#30112188)

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

## Animated quaternion (4, Interesting)

## _bernie (170285) | more than 4 years ago | (#30112292)

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 whereZ0 = 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 [povray.org] . It took my computer two week of computation to render 80 seconds of animated 3D slices of a the quaternion [sugarlabs.org] . Check out the scene source [sugarlabs.org] .

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

## I smell profit! (1)

## AndroidCat (229562) | more than 4 years ago | (#30112464)