The Plastic Fractal Magnet

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Posted by michael on Friday January 3, 2003 @10:03PM 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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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...
1. 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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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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1. 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... :)
2. 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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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.
1. 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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2. 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
3. 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
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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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?
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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Limekiller
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.
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."

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