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News Science

The Plastic Fractal Magnet 161

Posted by michael from the attractive-ideas dept.
bedessen writes "An article at NewsFactor summarizes the developments in new plastics that exhibit magnetic fields of fractal dimensions. 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. As these fields become increasingly interlocked, they exhibit a unique kind of order. This intensely ordered structure might one day be key to storing information with a very high density. The researchers behind this are Arthur Epstein, director of the Center for Materials Research at Ohio State University, and Joel Miller, a professor of chemistry at the University of Utah. There's also this PDF overview of the subject, which is quite technical but still readable."
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The Plastic Fractal Magnet More

The Plastic Fractal Magnet

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  • If my calculations are correct... (Score:5, Funny)

    by Anonymous Coward on Saturday January 04, 2003 @06:06AM (#5013500)
    This new fractal magnet will allow my flux-capacitor to send this message BACK IN TIME... to get first post! .....

    Great Scott!

  • Practical Applications? (Score:5, Interesting)

    by kavachameleon ( 637997 ) on Saturday January 04, 2003 @06:11AM (#5013511)
    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 [discover.com]. Just my comments...
  • Fractal song [bgu.ac.il]

    Kill me.

  • Less than one dimension is problematic... (Score:5, Interesting)

    by dagg ( 153577 ) on Saturday January 04, 2003 @06:26AM (#5013536) Journal
    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.

    • 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.

    • Re:Less than one dimension is problematic... (Score:5, Interesting)

      by BattleWolf ( 637645 ) on Saturday January 04, 2003 @06:42AM (#5013564)
      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... :)

      • Fractal dimension... (Score:5, Informative)

        by wirelessbuzzers ( 552513 ) on Saturday January 04, 2003 @12:31PM (#5014195)
        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."
    • "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... (Score:5, Interesting)

        by kasperd ( 592156 ) on Saturday January 04, 2003 @08:06AM (#5013680) Homepage Journal
        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.
    • 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.

  • Great (Score:3, Funny)

    by FS1 ( 636716 ) on Saturday January 04, 2003 @06:28AM (#5013537)
    Something else that i don't understand that will change my life forever.

  • I have a question... (Score:5, Interesting)

    by rgoer ( 521471 ) on Saturday January 04, 2003 @06:31AM (#5013544)

    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... (Score:5, Informative)

      by jazir1979 ( 637570 ) on Saturday January 04, 2003 @06:47AM (#5013571)
      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..
      • So the volume doesn't change quantitatively, just qualitatively? That is, you've got one three-dimensional liter of water versus one fractionally-dimensional liter of water? Ok, I guess that makes sense... in an ooh-my-head-hurts-folding-space kind of way ;^)
        • Yeah I guess so. Anybody else?

          I kinda assumed that the mathematical definition of volume is consistent, regardless of the dimensional propreties of the object in question. If not, I think our heads could start hurting even more ;)

          (In fact, I wonder if the whole reason that fractional dimensions are useful is that they allow us to maintain a consistent definition of volume across such geometric transformations??)

        • Re:I have a question... (Score:3, Informative)

          by gilroy ( 155262 )
          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.
          • I don't see what the fact that water expands when frozen has to do with the question. What if the snowflake were made out of some compound that neither expanded nor contracted when melted? Would that change the answer? I don't think it should.
            • 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.
            • Better thought question: what's the volume that you get if you melt the snowflake and freeze it into a cube?
      • 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.
        • 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.

        • Note: weighing the fractal and using density also avoids the question of a geometric calculation of volume and would be cheating.

          And you would have to answer the question of whether or not you have the density right, since you can't verify it...

        • 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...

    • Re:I have a question... (Score:5, Informative)

      by f97tosc ( 578893 ) on Saturday January 04, 2003 @06:57AM (#5013588)
      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
      • 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?

        • Re:I have a question... (Score:5, Informative)

          by f97tosc ( 578893 ) on Saturday January 04, 2003 @07:40AM (#5013651)
          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
          • 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? Can't you say a fractal is limited by a tiny epsilon? (epsilon being the minimum measure you can take)

            I thought a fractal's characteristic property was its self-repeating structure through scale changes. The scale changes should be theoretically unlimited, but practically you do have a limit.

            • 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.

              • 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.

            • 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.

          • Fractals can be said to be infinite just the way as pi is infinite. While pi has infinite digits, it never goes beyond - say - 3.15. But all of pi isn't just a finite number.

            A true fractal is just a mathematical definition, like pi. You add a little to it, less and less every time, you don't reduce the time as you do it. So a true fractal CAN be said to be infinite, but never exceeds a certain boundary.

            But, anyway, infinity is not the interesting point about fractals, but the scale invariance. That is, it remains the same no matter how close you are. Or, in the case of non-strict fractals, has the same degree of roughness, no matter which scale you use. Of course, no natural ocject is a true fractal, instead they can be said to hold for a certain number of magnitudes. If an object is a fractal over just two magnitudes, defining it as fractal really doesn't help much. But objects that remain self-similar over, say, eight magnitudes clearly show a fractal nature, and fractal geometry can help us understand them.

            and, of course, no natural object is really infinite.
        • 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.
      • 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... (Score:4, Informative)

          by f97tosc ( 578893 ) on Saturday January 04, 2003 @07:47AM (#5013658)
          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
    • Think of it like this, a line is infinitely-thin, and has length in one dimension. A snowflake's edge is also a line, but so 'crinkled' that it tends to fill space in two dimensions. 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 I'm tired now, goodnight.
      • 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.
    • 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.

    • 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 [eet.com])
    • You have a very valid point.

      While it may be fractal in nature, you can ultimately find volume via measuring it's displacement.

      Problem is, most methods of measuring the displacement value of a snowflake are very....destructive.

      The problem is not finding volume or mass, but finding said values without destroying the object ;)
    • Comment removed based on user account deletion
    • 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.
    • 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'?

  • Interesting (Score:3, Funny)

    by acehole ( 174372 ) on Saturday January 04, 2003 @06:31AM (#5013545) Homepage
    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.

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

    What kind of uses exist for superconductors at these temperatures? This seems like an overoptimistic article about a non-technology.
  • Plastics make it possible =)
  • as fragile as a dvd, as corruptable as a floppy disk, and as portable as a hard disk? Honestly, why would I want to use this? Will I be able to afford its super-high density? Hard disks haven't evolved in more than a decade for a reason!
    • Many new technologies start as being too difficult to be practical, or to push out on a large scale -- and of course many technologies never get off the ground because the difficulties can't be overcome.

      But that is no reason to stop researching stuff..! Even if it seems impractical at first, you really never do know..

  • Temperature Issues (Score:5, Interesting)

    by limekiller4 ( 451497 ) on Saturday January 04, 2003 @06:47AM (#5013569) Homepage
    From the article [newsfactor.com]
    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.
    • 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.

      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...
      • 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.

        • ...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.

          Yeah, I certainly wouldn't bet on ever seeing it in actual use, but that's more than can be said for a lot of university research. ;-)
    • I predict that it'll do wonders for the liquid nitrogen cooled wallet market.
    • it will fall on the floor and smash.

      Although I'd be too busy shivvering to notice

    • The CHART (Score:3, Insightful)

      by aphor ( 99965 )

      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!

      • 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.

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

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

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

  • Getting away from magnetic storage... (Score:5, Interesting)

    by silvaran ( 214334 ) on Saturday January 04, 2003 @06:51AM (#5013575)
    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?
    • 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? (Score:5, Funny)

    by limekiller4 ( 451497 ) on Saturday January 04, 2003 @06:53AM (#5013577) Homepage
    From the article [newsfactor.com]:
    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?
    • Me too (my girlfriend, not yours).

      I think I may finally have a use for that old chest freezer in the garage 8o)
    • 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.

  • Plastics, Fractal Magnetics & Optics.. (Score:4, Interesting)

    by jamesjw ( 213986 ) on Saturday January 04, 2003 @07:02AM (#5013592) Homepage

    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 :)

    • Re:Plastics, Fractal Magnetics & Optics.. (Score:5, Informative)

      by civilizedINTENSITY ( 45686 ) on Saturday January 04, 2003 @08:01AM (#5013674)
      "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 [slashdot.org], Highlight #7,Magnets open the gate to nanoscale logic [physicsweb.org] , 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.
  • Of the pdf file [216.239.53.100]

    (In typical google-htmlized pdf style)
  • I think science would be a more relevant topic for this one. Interesting, tho.
  • is november 2000... kinda old...?

  • Easy intro to fractal dimension (Score:4, Informative)

    by infolib ( 618234 ) on Saturday January 04, 2003 @08:10AM (#5013691)
    Is here [vanderbilt.edu]

    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.

  • A fractal harddrive? (Score:3, Interesting)

    by happyhippy ( 526970 ) on Saturday January 04, 2003 @08:30AM (#5013711)
    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.... (Score:4, Funny)

    by morganjharvey ( 638479 ) on Saturday January 04, 2003 @09:04AM (#5013748)
    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 (Score:4, Funny)

    by 0x0d0a ( 568518 ) on Saturday January 04, 2003 @09:05AM (#5013749) Journal
    They had enough fun with plain ol' obloidish magnetic field calculations. Can you imagine the math once we start throwing in fractals?
    • Actually, it should get a bit easier. Instead of doing a whole lot of complicated euclidian mathematics, which, by the way, never gives more than an estimate, and maybe iterating a VERY complex algorithm to get a closer approximation, you just get the fractal dimension, and the rest comes for free!

      Just imagine calculating the space of a snowflake. You begin with dividing the while lot into squares, triangles, circles, etc, calculate each one, and add together, or MELT IT and thereby destroying it. Or you could find the fractal dimension, which, by the way, tels you a WHOLE LOT more than it's mere volume and accept that its volume is infinite (it really isn't, but who's bothering to find THAT out, anyway?).
  • 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.

    • 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 [sourceforge.net]
      • 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.
  • But , here [geocities.com]'s a alternate pdf location.
  • I find it interesting that physicists use this term, which I personally only learned in Comp Sci...

    This leads to history dependent M(H) magnetic behavior (hysteresis)

    That is: Stateful.

  • Maxwell (Score:3, Funny)

    by MarkusQ ( 450076 ) on Saturday January 04, 2003 @10:56AM (#5013930) Journal

    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

    • 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.
  • I don't see how this could be used to store data. The article doesn't really describe this. I thought the structure of a fractal was sort of "predetermined" by only a few variables. Like the Mandelbrot set, for example. I suppose you could fiddle with those variables until you got a magnetic field that just "happens" to fit all your stored data, but that seems awfully inefficient. I guess I just don't understand.

  • Biological Fractals (Score:3, Informative)

    by Dollyknot ( 216765 ) on Saturday January 04, 2003 @12:45PM (#5014262) Homepage
    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
  • Funky fields.. mmmm Magic.
  • 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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