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The Plastic Fractal Magnet
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."
This new fractal magnet will allow my flux-capacitor to send this message BACK IN TIME... to get first post! .....
Great Scott!
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...
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.
Sex - Find It
Something else that i don't understand that will change my life forever.
A Fatal OE Exception has occurred, Sig will now reboot.
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.
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.
Be you Admins? nay, we are but lusers!
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.
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.
My
Limekiller
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?
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?
My
Limekiller
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
-- If at first you don't succeed, lie!
From the pdf link: 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):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.
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.
Doesnt this therefore introduce the need for a (quantum like) million bits error correction per one bit problem?
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....
They had enough fun with plain ol' obloidish magnetic field calculations. Can you imagine the math once we start throwing in fractals?
May we never see th
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.
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.
:-)
fractical
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!
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
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.
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
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
Your sig:
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...
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!--- Nothing clever here: move along now...