The Plastic Fractal Magnet

If my calculations are correct... by Anonymous Coward · 2003-01-03 22:06 · Score: 5, Funny

This new fractal magnet will allow my flux-capacitor to send this message BACK IN TIME... to get first post! .....

Great Scott!

Practical Applications? by kavachameleon · 2003-01-03 22:11 · Score: 5, Interesting

Is there any news on actual practical applications of these new magnets we've been hearing about? BTW... Discover Magazine had an article on Carbon magnets, quite interesting, because carbon is not *supposed* to be magnetic. Link here. Just my comments...

Re:Practical Applications? by Alsee · 2003-01-04 00:10 · Score: 5, Funny

Practical Applications?

Finally! A fractal magnet that will stick to my fractal refrigerator! The normal magnets always fell off because it doesn't have a flat surface.

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Fractal poetry by Toasty16 · 2003-01-03 22:14 · Score: 2

Fractal song

Kill me.

Less than one dimension is problematic... by dagg · 2003-01-03 22:26 · Score: 5, Interesting

Controlling nanoscale magnetic fields that exist in less than one dimension may prove problematic...

Am I the only one having problems understanding that article? I'm not a physicist, but I didn't think anything could exist in less than one dimension. Freaky.

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Re:Less than one dimension is problematic... by Jace+of+Fuse! · 2003-01-03 22:41 · Score: 3, Funny

Controlling nanoscale magnetic fields that exist in less than one dimension may prove problematic...

I didn't think anything could exist in less than one dimension. Freaky.

I would say if it can't exist in less than one dimention then controlling a nanoscale magnetic field that doesn't exist would prove QUITE problematic. If they can find a way to get around the whole "not existing" part, this could open up whole new areas of science.

--

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Re:Less than one dimension is problematic... by BattleWolf · 2003-01-03 22:42 · Score: 5, Interesting

Elsewhere in the article it states:
"A fractal is an object whose volume is not a simple product of its dimensions," Epstein told NewsFactor. Where "the volume of a rectangular box is its length times its width times its height, the volume of a snowflake is a fractal," Epstein explained. Fractal dimensions are fractional -- instead of 3-D or 2-D, they might be 1/2-D or 0.8-D.
I guess Fractals are freaky... they look kinda cool though... :)
Re:Less than one dimension is problematic... by f97tosc · 2003-01-03 23:21 · Score: 2

"Controlling nanoscale magnetic fields that exist in less than one dimension may prove problematic..."

Am I the only one having problems understanding that article? I'm not a physicist, but I didn't think anything could exist in less than one dimension. Freaky.

Anything that can be represented as a (or a finite number of) point could be considered to have a dimension of zero.

But in this case it was something more complicated than a point, it was a fractal object with a dimension greater than 0 but smaller than 1.

One way to understand this is to imagine that you want to draw the field on a piece of paper. Unfortunately you can't draw a line to represent this field; it has a dimension that is less than 1. Then you might figure that you could plot one or several small dots to represent the field. Well, bad news again. The field has a dimension that is greater than 0, so it would take an infinite number of points to draw the field.

Tor
Re:Less than one dimension is problematic... by civilizedINTENSITY · 2003-01-03 23:28 · Score: 4, Informative

Carbon nanotubes are used to transport single electrons. The wavelength of said electrons are such that the dimensions of the conduit result in what can best be modeled as a one dimensional potential well (as taught in senior-level Intro Quantum classes via ODEs, as a way to avoid the math of 3D potential wells and PDEs). So perhaps it could be said that 1D does exist for very very small, bound objects.
Re:Less than one dimension is problematic... by kasperd · 2003-01-04 00:06 · Score: 5, Interesting

Anything that can be represented as a (or a finite number of) point could be considered to have a dimension of zero.

That is true, but in fact you can even have an infinite number of points and still have a dimension of zero.

There are different kinds of infinity. The set of integers is what we call a countable infinity, while the set of real numbers is what we call an uncountable infinity. There are even uncountable infinites that are infinitely larger than the real numbers. In fact it is a suprprise once you realize how large infinities can become compared to the quite small infinity of the integers. In fact the inifinity of the integers is the smallest infinity you can find.

A set of countable infinity has dimension zero, anything with dimention larger than zero is an uncountable infinity same size as the real numbers. Wether the dimension is 0.1 or 3.0 the number of points will be exactly the same. And that is the case for any finite number of dimensions. And AFAIK no fractal can be of higher dimension than the space in which it exists, so we can never create fractals with inifinite dimension.

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Re:Less than one dimension is problematic... by paganizer · 2003-01-04 00:09 · Score: 2

Ahh, for a Mod +2 freaking hilarious........

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Re:Less than one dimension is problematic... by Henry+V+.009 · 2003-01-04 06:50 · Score: 3, Informative

You use the one-dimensional potential well because you don't need to take angular momentum into account (which would require the 3-D Schrodinger equation). Think about modeling a baseball in freshman physics. You could do that in 3 dimensions--but you could also beat yourself over the head with a club because it's so much fun when you stop. You model the baseball in 2 dimensions, because that is mathematically equivalent. That doesn't mean that ballistic motion is 2-dimensional.

Personally, I think the word dimension should be banned from from all discussions of popular science. But hell, there are enough Ph.D.'s out there that shoot thier mouths off like they are unclear on the concept.
Re:Less than one dimension is problematic... by merlin_jim · 2003-01-06 07:00 · Score: 2

Fractal dimension is not spatial dimensionality (axes) as normally taught in physics classes.

Technically, this is known as the Hilbert dimension and is a representation of how complicated and self-referential a particular form is.

It has to do with boundaries and with derivatives. How folded is a boundary? Let's say you have a 2-d fractal shape of some sort. The outside edge has some non-intuitive length because of its complexity. Imagine an outside edge that is so incredibly complex that by virtue of its complexity, it is somewhere in between being a length and an area. It is so twisty and convoluted that it cannot be described simply by a measurement in centimeters, but centimeters squared is a little too much for it.

This is a fractional dimension. No real life (matter) objects exhibit fractional dimensions; only hypothetical objects can exhibit them. This is because atoms have sizes and crystal structure, and cannot occupy the same place at the same time, which provides concrete limits on the amount of complexity in an object. Fractional dimensionality can only come from a complexity that is infinite in scope... the object must be convoluted at any scale at which you wish to measure it. Things made of tiny balls aren't like that.

Note: I may have gotten the name "Hilbert" wrong. It's been 6 years since I had any formal schooling or use for Chaos Theory.

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Great by FS1 · 2003-01-03 22:28 · Score: 3, Funny

Something else that i don't understand that will change my life forever.

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Re:Great by Crusty+Oldman · 2003-01-04 06:17 · Score: 3, Funny

Something else that i don't understand that will change my life forever.
Just wait 'till you discover women!

I have a question... by rgoer · 2003-01-03 22:31 · Score: 5, Interesting

The article, in its initial description of fratal geometry, cited this comparison: where a rectangluar prism has volume of length times width times height , a snowflake has a volume that is fractal in nature. The article went on to say that while the rectangular prism's volume is three-dimensional, the volume of the snowflake, being fractal, was fractionally dimensional (i.e. 1/2d or 0.8d or something, instead of 3d).

My question: if you were to find a huge snowflake, and melt it down, and measure that water in a graduate, wouldn't you find its volume? And wouldn't that volume be 3d? How does its volume, assuming it remains constant, change from being 1/2d or whatever to 3d? Sorry if I sound ignorant, but fractal mathematics is a little beyond me.

Re:I have a question... by jazir1979 · 2003-01-03 22:47 · Score: 5, Informative

I'm by no means qualified to answer this, but heck i'm a-gonna do it anyway!

Yes, the volume of the water would be 3D. The volume changes from 1/2D to 3D because you are changing the geometry of the object! Honestly, I think the answer *is* as simple as that..

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Re:I have a question... by f97tosc · 2003-01-03 22:57 · Score: 5, Informative

The snowflake would have a true 3D volume because it is not perfectly thin; it is a physical approximation of a mathematical concept.

The analogy of the snowflake refers to the edge of the snowflake. Imagine that you took a thread and tried to put it along the edge of the snowflake. Assuming that the thread was very thin it would take an infinitely long thread to cover the entire edge, because of the way it is folded. Thus the 'edge' can be said to have a dimension higher than 1 (it does not fit into one dimension). Using mathematical techniques one can also demonstrate that the the infinite thread takes zero space in 2D, thus the dimension is somewhere between 1 and 2; it is a fractal.

Tor
Re:I have a question... by civilizedINTENSITY · 2003-01-03 23:03 · Score: 3, Informative

Fractal implies a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry. While there is a finite volume associated with a snowflake, you are right (I think) in attributing the "fractional" dimensionality of the snowflake to its geometry. Obviously the fractal nature is lost as soon as the flake melts. Consider the question: how doe we determine the volume of the snowflake without destroying its fractal nature? That is to say, what linear measurements of length can be used to calculate its volume? Note: weighing the fractal and using density also avoids the question of a geometric calculation of volume and would be cheating.
Re:I have a question... by boomgopher · 2003-01-03 23:19 · Score: 3, Informative

I'm a jackass, forgot it was html formatted.

The dimension D of an object made of N exact copies of itself, each shrunk by a factor of S is:

log(N)
------
log(1/S)

So, a fractal is an object with a non-integer D.

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Re:I have a question... by gilroy · 2003-01-03 23:35 · Score: 3, Informative

Blockquoth the poster:

That is, you've got one three-dimensional liter of water versus one fractionally- dimensional liter of water?

No, the volume is changed both qualitatively and quantitatively. Even with classical geometry, the volume isn't conserved. Melting an ice cube changes its volume. Why shouldn't melting a snowflake? As has been mentioned, the alteration of the configuration does indeed affect volume.

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The Mongrel Dogs Who Teach
Re:I have a question... by civilizedINTENSITY · 2003-01-03 23:36 · Score: 2

I agree that the snowflake analogy breaks down. I think I'd paraphrase your statement that its about how we'd have to sum the edges to generate the surface. But doesn't the analogy breakdown because the pattern can't truelly repeat scaling down forever? That is, there will have to come a level at which the resolution of the molecules destroy the ever repeating pattern, like grain in a photograph. I didn't think fractals required a 2D object.
Re:I have a question... by f97tosc · 2003-01-03 23:40 · Score: 5, Informative

Imagine that you took a thread and tried to put it along the edge of the snowflake. Assuming that the thread was very thin it would take an infinitely long thread to cover the entire edge, because of the way it is folded

Isn't this comparable to the Paradox of Achilles and the turtle [openetwork.com]? Meaning that the thread does not have to be infinitely long? Well this is a valid but unfortunately rather complicated discussion. When you add an infinite number of objects with size zero (or approaching zero), the sum can turn out to be finite or infinite depending on exactly in what way the objects approach zero size (and sometimes, if I remember correctly, it even depends on the order in which you add them).

In the case of this 'paradox', you add an infinite number of objects (stretches of time) that approach zero so quickly that the total is actually finite. This is what some of the Greek thinkers did not realize.

For fractals, on the other hand, when you add the infinite number of small (approaching zero size) objects they end up taking infinite amount of space. This is a necessary condition; if you add them all and the total is finite then it is not a fractal.

Tor
Re:I have a question... by f97tosc · 2003-01-03 23:47 · Score: 4, Informative

But doesn't the analogy breakdown because the pattern can't truelly repeat scaling down forever? That is, there will have to come a level at which the resolution of the molecules destroy the ever repeating pattern, like grain in a photograph

Yes, this is true for all fractals with a physical manifestation. There is always some lower and upper scale where the fractal properties break down. The lower scale is often, as you suggest, on an atomic level.

A mathematical fractal is an abstraction that has infinite resolution. Such abstractions can be useful to study the properties of physical fractals, even though we know that these are only approximations.

Tor
Re:I have a question... by jericho4.0 · 2003-01-03 23:56 · Score: 3, Informative

IANAP, but here goes;
Everthing you can see or interact with, from snowflakes to magnetic fields, exists in a 3d universe. Such things as electrons, quarks, superstrings etc might not, but I've never seen one.
The snowflake exibits a fractal dimension over a wide range of scales. If you took a microscope you could magnify it many times over and keep finding the same level of detail being revealed. So we say it has a fractal dimension. Without knowing the fractalness of a paticular snowflake, the dimensions of the snowflake wouldn't be enough to tell you how much water was in it with much accuracy.
A coastline has the same property on a human scale. As the size of your measuring stick decreses, the length of the coastline increases.

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"A language that doesn't affect the way you think about programming, is not worth knowing" - Alan Perlis
Re:I have a question... by bedessen · 2003-01-03 23:57 · Score: 3, Informative

A 2D object's area (or "volume" if you will, since there are only two dimensions) changes as x^2 as you scale the object. A 3D object's volume changes as x^3 as you scale the object. An object with fractal dimension has a volume that scales as some non-integer power as you scale the object.

(additional story link where Epstein confirms this)
Re:I have a question... by kasperd · 2003-01-04 00:13 · Score: 2

Fractal implies a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry.

And this is exactly where the snowflake breaks down. You might find the same patterns in a snowflake at many different scales, but when you go to smaller and smaller scales, eventually you will reach the molocular scale at which the pattern changes.

A snowflake is not a perfect fractal. If we could really create fractal physical objects, I have ideas for applications in computers. You wouldn't imagine the processing power of a fractal CPU.

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Re:I have a question... by gilroy · 2003-01-04 03:04 · Score: 2

Blockquoth the poster:

What if the snowflake were made out of some compound that neither expanded nor contracted when melted?

Firstly, there can be no such material. But leaving that aside: The original post asked how a snowflake could have a fractal volume, if when melted the resulting water has a good old 3D volume. I was merely pointing out that deducing anything about the snowflake's volume from the behavior of a different phase is invalid. It's like proving that the volume of a sphere can't be (4pi)/3 r^3, because if I take an iceball of radius r and melt it in a cylindrical container, the volume turns out to be pi r^2 h. The two facts are independently true but have no necessary relation.

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The Mongrel Dogs Who Teach
Re:I have a question... by ryanvm · 2003-01-04 05:06 · Score: 2

You are correct.

As a practical matter the snowflake does have a 3D volume. It does not exhibit true fractal geometry in that it doesn't fold upon itself infinitely. Nothing can (or at least certainly not a snowflake).

Posters below saying that melting it ruins it's infinite fractal geometry are just being silly. The snowflake ALWAYS has a 3D volume (and geometry), we just don't have a good way of measuring it's proportions so it seems fractal. It's not.

Occam's razor, folks.
Re:I have a question... by Com2Kid · 2003-01-04 06:24 · Score: 2
- But eventually you'll reach the limits of physical matter: atoms, neutrons, protons, electrons, quarks; or the limits of whatever you're using to represent the fractal ... What does it happen when you reach that limit?
Well then you say screw it, your mathmatical model just hit real world limits.

As a posted above stated, snowflakes are not *perfect* fractals. Perfect fractals do not exist in nature for exactly the reasons you stated.

Then again for those very same reasons, perfect spherse, squares, triangles, or perfect versions of any other mathmatical construct also do not exist.

It is math, it has limits. :) But it IS a useful analogy, and fractals ARE darn cool and really pretty looking to boot. They actualy aren't all /that/ hard to get down once you read up on them enough. :)

(I had my intro to them a few years back in some other /. story. Hehe. ^_^)

The typical example used to explain fractals is that of a coast line.

Think of drawing a costal outline. Now think of adding more detail do it, the big rocks. Then the bumpss on the big rocks. Then the moss growing on the bumpss on those big rocks. Then the little hairy things on the moss growing on the bumpss of those big rocks. Then the bacteria living on the hairy things on the moss on the bumpss on those big rocks.

The point here is that you can keep on zooming in until you hit the real world limits of our universe, but it just so happens that modeling a fractal and treating certian intervals of that graph as your "coastal line" is a far easier way to go about and do it.

Now part of the definition of a fractal is that you can keep on zooming in forever and getting more and more detail. Obviously for the real world this will not work out, but within certian intervals the fractal is a pretty darn good approximation of reality. Just like almost any other graph or mathmatical construct, it has its constraints, but within those constraints, it is darn useful.
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Re:I have a question... by Webmonger · 2003-01-04 06:39 · Score: 2

Better thought question: what's the volume that you get if you melt the snowflake and freeze it into a cube?
Re:I have a question... by sjames · 2003-01-04 06:44 · Score: 2

limited by a tiny epsilon? (epsilon being the minimum measure you can take)

In the real world, there is an epsilon. It may be the size of a molecule,atom, pixel, or even a quantum of space/time itself.

In mathematics, epsilon is 0 unless it is applied mathematics.
Re:I have a question... by Hentai · 2003-01-04 12:09 · Score: 2

That sounds really confusing. Let me see if I can make it simpler.

A snowflake *IS* a three dimensional object, and therefore has a set three-dimensional volume, which can easily be determined by melting said snowflake. The snowflake itself isn't a fractal.

Likewise, an ice cube is a three-dimensional object, and therefore has a set three-dimensional volume, which can easily be determined by side^3. The ^3 means it's a measurement of dimension three.

Now. The snowflake has a surface area, right? This is a two-dimensional value. Each of its tiny little facets has a two-dimensional area, and by summing up all that area, you can determine exactly the total 'surface area' of the snowflake. This would take forever, considering our snowflake has an infinite number of surfaces, but we won't worry about that for now.

The ice cube, likewise, has a two-dimensional surface area - which we can very quickly compute by taking side^2, and multiplying by 6 (since a cube has 6 sides). The ^2 means it's of dimension two.

Now, comes the fun part. A cube has eight edges, each of equal length. Thus, 8 * side^1 equals the total length of all edges in the square. This is of dimension one (see the ^1?)

The snowflake also has edges. It has an infinite number of them, in fact, all of zero length. But something weird happens if you try to measure the length - it just never stops. It gets so twisty and curvy, that its edge length is infinite. This implies that at least ONE edge is fractal.

See, there's different types of solids... a sphere is the most... I'll use the term 'economical', because it has the least amount of surface area compared to volume. A cube is less economical, in this sense, because it uses more surface area to contain its volume. An incredibly thin string is even less economical, using even more volume. But all of these are still three-dimensional objects. Except that, with the string, you can eventually get a string so small that its volume and length are the same - its third dimension, its thickness, has just shrunk to 0.

This might be a hard concept to swallow, but imagine that this is a single point:

.

That is, even though I know it takes up a certain number of pixels on your screen, pretend it has no width, no height, no nothing. Now, there's an infinite number of points, exactly like that one, in this dash:

-

Bear with me, and pretend that that line segment has a thickness of exactly one point. Now, we'll call the number of points 'one zillion'. Thus, we now have a system of measurement. This would contain 'two zillion' points:

--

Now. Take one of those 'zillions' and make a square (again, bear with me, ASCII isn't the best drawing medium - pretend it's connected, and solid all the way through):

[]

Now, just like that line was made of a zillion points, all lined up next to each other, this square is made up of one zillion lines, all stacked up on top of each other. Thus, it contains one zillion lines, which each contain one zillion points. It has a perimeter, which is all the points that aren't completely surrounded on all four sides (left, right, up, down) - obviously, there's the one line on the very top, and the one line on the very bottom, so that's two zillion - plus a single point on the left and right of all the zillion other lines, which makes four zillion. Thus, the area of the square is 'one zillion squared', or one square zillion - while its perimeter is four zillions.

Now, take that square, and stack it out (towards you) a zillion times - you now have a cube. It's got one zillion CUBED points, and its 'surface area' - i.e., the measure of all the points not completely surrounded in all six directions (up, down, left, right, fore, back) - is pretty easy to figure out, since the first and last squares are both exposed, and there's a zillion edges on each of the other four sides - and we already know that a zillion edges each a zillion points wide make a one-zillion-square square.

Now, fractals are strange creatures, in that, while they obviously exist within one set of dimensionality (for example, a two-dimensional Koch snowflake clearly resides on a page, and therefore is a two dimensional object), their 'edges' are infinite in the next dimension down. I.e., the snowflake has a definitely measurable area (dimension two), but its PERIMETER isn't of dimension one! It's just got too many points exposed. So that implies that that edge, with all its twists and turns, is 'fractal'. Say we measure it out, and it turns out that it's got 3.6 zillion^1.6 points - that implies that that weird curve has a dimensionality of 1.6.

Make sense?

Now... what'll really cook your noodle: go back up through that whole 'zillion' bit, and replace the word 'zillion' with 'inch' or 'centimeter'.

Now do you understand, fundamentally, what we mean by 'distance', and what we mean when we say 'the number line is infinite'?

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-Hentai [in vita non pacem est]
Re:I have a question... by jafuser · 2003-01-07 04:04 · Score: 2

While pi has infinite digits, it never goes beyond - say - 3.15. Do you live in Indiana by any chance? =)
(I can't say much, I'm from there myself) =P

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Interesting by acehole · 2003-01-03 22:31 · Score: 3, Funny

I guess the applications for this are pretty big...

I mean you could have a harddrive that not only gets corrupt when you leave it in the sun (as you do..) but it can melt too.

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Yet Again.. by Metallic+Matty · 2003-01-03 22:38 · Score: 2, Funny

Plastics make it possible =)

Re:Too cold for practical applications... by hdparm · 2003-01-03 22:46 · Score: 3, Funny

What kind of uses exist for superconductors at these temperatures?

I don't know but if it's meant to be used for storing information in some kind of computer, that one for sure won't be using AMD processors.

Temperature Issues by limekiller4 · 2003-01-03 22:47 · Score: 5, Interesting

From the article
The plastic ultimately stabilized in 1.6 dimensions at a temperature of minus 269 degrees Celsius (minus 452 degrees Fahrenheit).

It would be nice if someone came up with a chart that plotted the correlation between the temperature necessary in the lab and the temperature necessary to bring the item to market for a significant number of products. Because I'm willing to bet that -249 C is pretty close to the Don't Hold Your Breath mark.

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Limekiller

Re:Temperature Issues by limekiller4 · 2003-01-03 23:31 · Score: 2

n0nsensical writes:
"Well obviously this version isn't practical for commercial applications, but the idea is the technology could be developed to that point in the future. The cathode ray tube needed to be developed before we could have television..."

I'm only semi-bitching because of comments like this in the article:

"...that could reinvent smart card technology and yield a dazzling new array of high-tech gadgets."
...to why my suggestion would be to append "...not anytime in the near future, you can expect to see this around the same time as flying cars." If they can't tell me when, maybe they could just hazard a guess as to when not.

You might argue that it is impossible to calculate such things but they're already going out on a bigger limb by assuming this can be brought to a consumer market (read; stabilized at room temperature) in the first place.

But I do see your point.

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My .02,
Limekiller

Getting away from magnetic storage... by silvaran · 2003-01-03 22:51 · Score: 5, Interesting

I'd like to get away from magnetic storage as a temporary removable storage device... The last time the floor waxer zamboni zipped past my locker I lost my college programming project... not to mention the number of VHS tapes that are useless now... am I alone in this?

Re:Getting away from magnetic storage... by pVoid · 2003-01-04 03:03 · Score: 2

Two things:
your lockers were probably not electrically grounded (if they were, then they would have been perfectly shielded by creating a Fermi Cage was it? - anyways).
Mini discs are magneto optical: a laser melts the substance in which magnets are bathing, and only then can you modify their state.
Magnetic is in dude. You just need proper care, that's all.

Help? by limekiller4 · 2003-01-03 22:53 · Score: 5, Funny

From the article:
The plastic ultimately stabilized in 1.6 dimensions at a temperature of minus 269 degrees Celsius (minus 452 degrees Fahrenheit).

I'd be happy if my girlfriend would stabilize in three dimensions at room temperature.

How long do you think it'll take for them to figure that one out?

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My .02,
Limekiller

Re:Help? by StikyPad · 2003-01-05 00:01 · Score: 2

I'd be happy if my girlfriend would stabilize in three dimensions at room temperature.

I've done a bit of research on this, but haven't been able to find a temperature which will cause pixels to stabilize as a three dimensional girlfriend. Please let me know if you have any success.

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Plastics, Fractal Magnetics & Optics.. by jamesjw · 2003-01-03 23:02 · Score: 4, Interesting

It raises an interesting possibility - with a new way of forming high density magnetic fields I wonder if we'll see a return to Megneto Optical media or weather the two will stay seperate..

It'd certainly be interesting to get more storage out of yer cd sized media if you could use the plastics as a storage medium as well as the optical layer..

Maybe its a crazy idea..

Somebody will probably take this idea and ger rich off it none the less :)

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-- If at first you don't succeed, lie!

Re:Plastics, Fractal Magnetics & Optics.. by civilizedINTENSITY · 2003-01-04 00:01 · Score: 5, Informative

"It'd certainly be interesting to get more storage out of yer cd sized media..."

Checkout the link in the previous story The Top Ten Physics Highlights of 2002, Highlight #7,Magnets open the gate to nanoscale logic , to see how nano-sized mangetic structures could be used. The hard part is going to be interfacing to this structures. These structures are *small*.
the ferromagnetic NOT gate is a "completely new class of device" that could be made even smaller. The researchers have also created a 13-bit shift register by linking the devices together, and believe it should be possible to make a full set of logic gates using their technique
Note: this is digital logic without transistors, but with nanoscale ferromagnetic wire.

Re:FP? by civilizedINTENSITY · 2003-01-03 23:22 · Score: 3, Informative

Do they even need to get a current flow to generate their magnetism?

From the pdf link:

"The essential component of any magnetic material is the presence of an unpaired electron or more precisely, the spin associated with an unpaired electron. These spins, depicted in this article as arrows (a or b), and how they interact with each other determine the magnetic behavior of all magnets. Magnets are materials in which these spins are ordered."

Perhaps its all about the ordering (which could be due to the geometry of the molecular structure).

Note: the pdf file also states (towards the end):

"It is important to emphasize that magnetic ordering is not a property of an isolated molecule; it is a cooperative solid-state (bulk) materials property. Thus, to achieve bulk magnetic behavior for a molecular system, intermolecular interactions must be present in at least two, and preferably three, directions.

Its interesting that where we are looking at is (I think, perhaps) a non-bulk form of magnetism, and the statement is perhaps overstating a requirement.

Re:Too cold for practical applications... by civilizedINTENSITY · 2003-01-03 23:42 · Score: 2

I read "stabilize" to mean that the apparent dimensionality quiet increasing at that low a temperature. It started at .8, and went to 1.6 @ 269 C, but what temperature did it start at? Would it be enough to keep the temperature controlled in a more "comfortable" zone?

Google cache by infolib · 2003-01-04 00:03 · Score: 2

Of the pdf file

(In typical google-htmlized pdf style)

--
Any sufficiently advanced libertarian utopia is indistinguishable from government.

Re:Google cache by Boss,+Pointy+Haired · 2003-01-04 04:51 · Score: 2

you

mean

in

typical

google-htmlized

style

?

Easy intro to fractal dimension by infolib · 2003-01-04 00:10 · Score: 4, Informative

Is here

Among other results it is shown that Great Britain's coastline has a fractal dimension of 1.24, while that of South Africa is very nearly 1.

--
Any sufficiently advanced libertarian utopia is indistinguishable from government.

A fractal harddrive? by happyhippy · 2003-01-04 00:30 · Score: 3, Interesting

So doesnt that mean instead of just a single bit being corrupted affecting the one bit, in the fractal drive that bit could affect the rest of the drive?

Doesnt this therefore introduce the need for a (quantum like) million bits error correction per one bit problem?

So upsetting.... by morganjharvey · 2003-01-04 01:04 · Score: 4, Funny

I'm so used to coming home from the bars and getting very basic "here's an update to this" or "here's a new apache module" from slashdot.

But when I come home at 5 in the morning, not quite so sober, and you're talking about half dimensions? That's just not nice.... What the hell am I supposed to wrap my brain around? If it's only half dimensional, does that mean I only have to wrap just my left lobe around it? I'm sooooooo lost.... :)

Poor physics majors by 0x0d0a · 2003-01-04 01:05 · Score: 4, Funny

They had enough fun with plain ol' obloidish magnetic field calculations. Can you imagine the math once we start throwing in fractals?

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May we never see th

Re:Poor physics majors by 0x0d0a · 2003-01-04 10:29 · Score: 2

Ya know, your username has the wrong byte order.

Uh...okay, it's a profoundly ironic statement about the lack of standards in the world -- three EOL sequences, two byte orderings.

Good call. :-)

--
May we never see th
Re:Poor physics majors by 0x0d0a · 2003-01-04 10:31 · Score: 3, Interesting

Sorta. The volume's easier, but I was thinking of what happens if you're trying to figure out how two fields are interacting...

--
May we never see th

Re:Scandinavian Coast? by infolib · 2003-01-04 01:44 · Score: 3, Informative

Norway: Fractal dimension 1.52 (here and here, apparently from Feder.)
Google is your friend

I suspect the swedish coast has nearly as high a dimension, with Denmark a bit lower.

--
Any sufficiently advanced libertarian utopia is indistinguishable from government.

How do you measure 1.6 dimensions? by MickLinux · 2003-01-04 02:17 · Score: 2

Just a question from a guy who appreciates fractals for their artistry -- and can program a mandelbrot set -- but really doesn't understand the math.

How, exactly, do you calculate that something has 1.6 dimensions? Or is this something you measure?

I actually can visualize 2.9976 dimensions: just use as your spatial grid an interaction of very reactive particles that require 3 charges, and much less reactive particles that require 2 charges --

but I don't see how you'd calculate or measure this kind of thing in real life.

--
Correct Horse Battery Staple: 72 bits of entropy. Enter "Correct H" into google. When it generates the phrase, that's

Re:How do you measure 1.6 dimensions? by popmaker · 2003-01-04 02:40 · Score: 3, Insightful

You find out how the thing works, or evolves. Take a snowflake. You see how it comes to be, you begin with an ice particle, others start hitting it, sticking with it and form a crystal. This is obviously a process which we can set up mathematically. Like, for each iteration, this happens and that adds to the whole snowflake. By using mathematical rules we now use our knowledge of how a snowflake evolves to find its fractal dimension.

Now, fractals are said to be infinite, that is, they have infinite volume, and a self-similarity on all scales. Natural phenomena does, however, not. So no natural object is a TRUE fractal. But obviously, a snowflake IS self-similar, and it remains self-similar over a number of scales. To be a TRUE fractal it would have to be self-similar infinitely.

But anyhow, if a object is irregular, and behaves like a fractal, finding it's fractal dimension (or finding the dimension of the mathematical object representing it) is actually quite useful.

Just think of a fractal as a result of an iterated process. Trees grow leaves. Snowflakes grow, clouds grow, lightnings twist and turn, coastlines get beaten by oceans, etc. The idea of a fractal gives an insight into how such objects come to look like they do.

and check out my fractal program! :-) fractical
Re:How do you measure 1.6 dimensions? by MickLinux · 2003-01-04 05:44 · Score: 3, Interesting

Okay, here's an interesting project for you:

(1) Start with the Mandelbrot Set or the Julia Set, calculated to a resolution p (say, granularity of 0.0001.

(2) Calculate the curvature (curve-centered curvature, not x-axis-centered curvature) as a function of position along the line, down to a resolution of 2p.

(3) Take the fast-fourier transform of this data

(4) Use the FFT data to see if you can predict the FFT for lower levels.

My guess is that it won't be predictable -- but I don't know. It might be.

BTW... :

Snowflakes almost definitely aren't fractal. Rather, their development is probably going to be controlled by the semiconducting nature of the outer layer of ice as it freezes, and charges separating as widely as they can.

Nor are trees fractal. They have their rules, but those rules aren't within the definition of what fractal. Rather, fractals can help one generate convincing images of trees, but the similarity stops there.

--
Correct Horse Battery Staple: 72 bits of entropy. Enter "Correct H" into google. When it generates the phrase, that's

Nah it's Fine by Greyfox · 2003-01-04 02:44 · Score: 2

I predict that it'll do wonders for the liquid nitrogen cooled wallet market.

--

I'm trying to teach myself to set people on fire with my mind... Is it hot in here?

Maxwell by MarkusQ · 2003-01-04 02:56 · Score: 3, Funny

Whereas a simple bar magnet produces magnetic fields that go from the north pole to the south pole, the fields of the new hybrid plastic sprout like branches of a cactus lined with secondary fields that resemble needles

Shouldn't the headline have been "Maxwell's equations disproven!" or something else more fitting for such a revolutionary discovery?

Unless of course Maxwell's equations still stand, in which case the headline should have been something like "Hype replaces progress in science; film at 11:00"

-- MarkusQ

Re:Maxwell by Orne · 2003-01-04 08:34 · Score: 2

I don't believe this is a case of mono-poles; a field produced must still sink back into the object. A "traditional" bar magnet is a 3-dimensional cylender with a field emitter at one end and a sink at the other, while this substance has a non-uniform shape to it's magnetic field.

What they've done is discovered a magnetic material that, when cooled to a sufficiently low temperature, will re-organized its structure into a fractal pattern. Additionally, the (repeating) fractal nature creates tiny stable field "pockets" in organized patterns accross the material, at predictable locations once the pattern of the fractal is known.

It seems to me that what they're hoping is that they can exploit the pockets to hold a voltage charge, so that they can convert this material into a data storage device. The material would have a incredible number of stable pockets at extremely small spacing (thanks to the nature of fractals), which would make for more dense storage of information, leading to even more miniturization of electronics.

Comment removed by account_deleted · 2003-01-04 03:07 · Score: 2

Comment removed based on user account deletion

Fractal dimension... by wirelessbuzzers · 2003-01-04 04:31 · Score: 5, Informative

If the disjoint union of n disjoint copies of a fractal F makes a similar (in the geometric sense) one k times as big, then the fractal dimension of F is (log n)/(log k) = log base k of n.

This makes the fractal dimension of a square 2 because it takes four of them to make a square twice as big and log 4 / log 2 = 2. The fractal dimension of the Sierpinski Gasket is log 3 / log 2 because you can assemble 3 copies of it to get one twice as big.

The dimension of the Cantor set (that's the one where you start with the unit interval and remove the middle third of every line, or equivalently the numbers between 0 and 1, inclusive, whose base-3 expansion contains no 1s) is log 2 / log 3 which is less than 1.

The dimension of the rational points in a square is still 2, even though it has fewer points than the Cantor set. So, fractal dimensions are "freaky."

--
I hereby place the above post in the public domain.

Same for squares and cubes by A+nonymous+Coward · 2003-01-04 04:31 · Score: 2

A square may have sides of 1 cm but if you were to try to actually measure the perimeter with that thread, you would have bumps around the atoms and molecules, which not only would make it hard to define exactly where the boundary is, but they also vibrate, meaning you could only measure a static square at absolute zero.

--
Infuriate left and right

Biological Fractals by Dollyknot · 2003-01-04 04:45 · Score: 3, Informative

I first learned about chaos theory, from James Gleick's excellent book 'Chaos' about ten years ago. I've been hooked ever since.

The thing that stuck in my head was Fiegenbaum's number 4.669, which BTW is irrational. This ratio is everywhere and most profound of all, is visible in the architecture of our bodies. The main artery from the heart called the Aorta, is like the trunk of a tree, point being is, if you measure the distance between the heart and the first bifurcation, divide that distance by 4.669, it gives you the statistical length of the two branches from the first bifurcation. Now here is the kicker:- it is that ratio, all the way down to the smallest cappillary, to enable a blood supply for every cell in our bodies.

GM technology worries me, not because I'm scared of engineering. But because to my knowledge, we do not yet understand the mathematics of morphogenesis. DNA is a simple four bit code and yet somehow or other, nature manages to store a cellular doubling number in that four bit code.

We all start out as one cell, that doubles in a binary progression. Our body plan is formed by the x,y,z matrics of those doublings. The fractal like architecture of our bodies, gives us a hint to how, the miracle of storing our entire code base, in about four gig might be acomplished.

This new discovery excites me, who knows where it will lead, a new understanding of life maybe? New math? New electronics? The list is endless.

Cutting edge indeed.

Peter

--
It's called an elephant's trunk whereas it is in fact, an elephant's nose, a nose by any other name would smell as sweet

You have to use your discretion by DrSkwid · 2003-01-04 05:38 · Score: 2

Once you are at the scale of discrete particle then there is no edge to measure, only the distance between the particles.

While you are there you could measure the distance between applied mathematics and pure mathematics.

--
There are places where the networks are not touching,and there are places where they are-Boeing's Lori Gunter

If I don't hold my breath by DrSkwid · 2003-01-04 05:41 · Score: 2

it will fall on the floor and smash.

Although I'd be too busy shivvering to notice

--
There are places where the networks are not touching,and there are places where they are-Boeing's Lori Gunter

if in doubt - say it will do storage by DrSkwid · 2003-01-04 05:46 · Score: 2

1. Invent new thing
2. Say it will increase storage.
3. ??
4. Prophet

--
There are places where the networks are not touching,and there are places where they are-Boeing's Lori Gunter

Re:if in doubt - say it will do storage by borgboy · 2003-01-04 13:48 · Score: 2

Isn't that redundant? Prophecy in steps 2 and 4???

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meh.

Not repeated at every scale... by aphor · 2003-01-04 06:41 · Score: 2

Fractals have "similar" structures at different scales. There is no real pattern, because the structures are different everywhere in the fractal. There is only almost-repetition. It is critical to distinguish between self-identity and self-simlarity. No two parts of a fractal will ever match regardless of how you scale them. However, the self-similarity, and also the minute structural differences continue to express themselves within infinitessimal portions of the fractal, scaled to infinity (so we can see them), at least as far as we know...

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--- Nothing clever here: move along now...

The CHART by aphor · 2003-01-04 07:44 · Score: 3, Insightful

Your sig:

It's much easier to mod me down than to post an intelligent reply.

That's true only if the opportunities to mod or post are equal. That seems to be true only around 8:30 CST/CDT. Mod and post on the same discussion are prohibited. The opportunity to mod is a rare thing, and it gives the moderator more influence (although with the all-too-easy click-click convenience) than a poster (who can affect the visibility of the thread only at +2 when sufficient karma has been earned).

I believe the choice to moderate is an important one, and while I agree with your sentiment (I think...) that people who moderate without without knowing what they are doing should think harder about things, I don't think that differentiates moderation from posting replies.

Oh, which brings me to my point: it's easier to suggest that someone else make(or find) a chart instead of doing it yourself...

Note: the Slashdot "lameness filter" didn't like my ASCII art, but it apparently ignores journal entries...

<a ref="http://slashdot.org/~aphor/journal/20520">The chart</a>

is in my journal. Furthermore, Slashdot doesn't like hrefs from comments to a person's journal. The rules to this Slashdot game are neither simple nor obvious!

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--- Nothing clever here: move along now...

Re:The CHART by limekiller4 · 2003-01-04 08:57 · Score: 2

aphor writes:
"I believe the choice to moderate is an important one, and while I agree with your sentiment (I think...) that people who moderate without without knowing what they are doing should think harder about things, I don't think that differentiates moderation from posting replies. "

Moderation is both useful and necessary, but I'm far more concerned with learning something (by way of good, intelligent feedback) than racking up this nebulous karma. Who gives a shit about karma?

In other words, while it might look like I'm bemoaning the loss of karma, I really lamenting the loss of a good conversation. Very, very rarely do I get decent replies. And no, "decent" is not to be understood as "agreement." In fact, as soon as I saw that what you were replying to was my sig, I thought, "oh no, another AC troll" but was pleasantly surprised.

--
My .02,
Limekiller
Re:The CHART by aphor · 2003-01-04 10:50 · Score: 2

BUT WHAT DO YOU THINK OF MY CHART????

http://slashdot.org/~aphor/journal/20520

(it took me about 20 minutes straight...)

--
--- Nothing clever here: move along now...

Applications to superconductors? by A55M0NKEY · 2003-01-04 11:24 · Score: 2, Funny

Funky fields.. mmmm Magic.

--

Eat at Joe's.

yea... by Transcendent · 2003-01-04 13:45 · Score: 2

This intensely ordered structure might one day be key to storing information with a very high density.

Yea, who cares about this as helping us understand more and more about the quantum mechanics of our universe.... we get bigger hard drives for porn!

True, it is interesting that it could lead to bigger hard drives, but it annoys me when they post that as the "hot topic" of this new discovery.

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