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Scientists discover fractal patterns in a quantum material
- gjm11 7y agoCopied (with permission, but so far as I can tell without a link) from MIT's press release at http://news.mit.edu/2019/fractal-patterns-quantum-1016 http://news.mit.edu/2019/fractal-patterns-quantum-1016 Actual article in Nature Communications: https://www.nature.com/articles/s41467-019-12502-0 https://www.nature.com/articles/s41467-019-12502-0 PDF version of article: https://www.nature.com/articles/s41467-019-12502-0.pdf https://www.nature.com/articles/s41467-019-12502-0.pdf
- buyingarmor 7y agoEverything is a fractal, even socially
- coldtea 7y agoWell, a sine wave is not a fractal, for one...
- nickthemagicman 7y agoOn a quantum enough level it may be. (I have no idea what that means)
- Scene_Cast2 7y agoRandom interesting (to me) tangent - couldn't you find a recursive function that, at its limit, was a sine? Could any function be generated this way? And throw some variant of Kolmogorov complexity metric on this class of function-generating fractals and this becomes a neat mathematical area.
- excessive 7y agoHere is one in Python. Uncomment the if statement if you want it to terminate. def sin(x): def recur(x, n, s, p, f): #if n > 9: return s; return recur(x, n + 2, s + p/f, -p*x*x, f*(n + 1)*(n + 2)) return recur(x, 1, 0, x, 1) Of course maybe it's cheating from your intent because it's really just implementing the Taylor series, and it has too many arguments. I believe any analytic function could be defined this way if you can figure out the pattern for its derivatives.
- perl4ever 7y agoFunction sine(x As Double, Optional term, Optional p = 1#) As Double If IsMissing(term) Then term = x End If If term <> 0 Then sine = term + sine(x, -term * x / (p + 1) * x / (p + 2), p + 2) End If End Function Edit: This is my interpretation of the Taylor series approximation, but it's probably a bad idea to use this for anything that matters. One reason is that it doesn't reduce large angles, and another is that people who know what they're doing prefer to use some other formula, from a cursory Googling...though I'm not sure why.
- pbhjpbhj 7y agoDefine fractal?
- drdeca 7y agoSomething with non-integer fractal dimension? Actually, idk if that is exactly the right definition, because I think some fractals have integer dimension? Idk
- golergka 7y agoWe live in a society.
- nickthemagicman 7y agoOr does society live in US?
- knolax 7y agoBOTTOM TEXT
- soulofmischief 7y agoSounds like a potential avenue for developing critical memory systems which can survive an EMP. Hope that pans out.
- pixelpoet 7y agoAs someone who's studied fractals, written commercial fractal art software, given talks about fractals, etc... it amazes me how the topic is such a magnet for pseudoscientific types, the sort who would get a high score on the Baez crackpot index. They come to you after the talk etc and excitedly say that whatever was in your talk proves their theory that, say, "time is a fractal", or "life is a fractal", ... of course never with any rigorous quantitative justification.
- DenisM 7y agoThat would make for a nice article methinks.
- phs318u 7y agoThanks for the pointer to the Baez crackpot index. Had never heard of it before, but it’s truly wonderful. For those wondering: http://www.math.ucr.edu/home/baez/crackpot.html http://www.math.ucr.edu/home/baez/crackpot.html
- toxicFork 7y agoI am not the OP but I like the challenge so I will entertain the thought. I guess in some ways, socially, you can see a person embodying certain behaviors and values. And this can spread out in a fractal-like pattern. Let's say this person is violent and sometimes shouts swear words at other people. Then we look at a family whose members say bad things about another family. Then we look at a village and see it having graffiti on its walls, bad words about another village. Same thing with sports fans. Same thing with countries, having a sort of trade war with each other. Let's now go the other way, perhaps the micro organisms in your body are having a conflict right now, spurting out this liquid and that gas and so on. In some ways we can consider this to be a fractal.
- dvt 7y ago> In some ways we can consider this to be a fractal. Except, of course, we can't. The term fractal is a well-defined mathematical object. There might be "self-similarity" there, but (just a fun fact) fractals are typically not self-similar, so it's not a very good litmus test.
- pixelpoet 7y agoGetting some deja vu here: https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly
- vardump 7y ago"In condensed matter physics, Hofstadter's butterfly describes the spectral properties of non-interacting two dimensional electrons in a magnetic field. The fractal, self-similar, nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter[1] and is one of the early examples of computer graphics. The name reflects the visual resemblance of the figure on the right to swarm of butterflies flying to infinity. It is one of the rare non-random fractal structures in physics, along with KAM tori.[citation needed] The Hofstadter butterfly plays an important role in the theory of the integer quantum Hall effect, and D.J. Thouless has been awarded the Nobel prize in physics in 2016 for the discovery[2] that the wings of the butterfly are characterized by Chern integers[3], the quantized Hall conductances discovered in 1980 by Klaus von Klitzing for which he has been awarded the Nobel prize in 1985. The colors in the diagram reflect the different Chern numbers." Thanks, that's pretty interesting, and somewhat relevant to the article.
- kd3 7y agoThe whole universe is fractal. Like a hologram. You do the math.
- blix 7y agoMagnetic domain transtitions are phase transitions, just like the solidifcation of a snowflake. It's not that surprising to me that magnetic domain structure could be fractal, many phase transitions can look fractal in the right conditions, of which water solidifcation into snowflakes is just one example. Despite the fact that several versions of this story claim this is the "first ever" observation or discovery of fractal domains, it seems to have been reported at least a decade earlier [1], in a similar but somewhat more complex ternary neodynium compound. [1] https://arxiv.org/abs/0901.3515 https://arxiv.org/abs/0901.3515
- soulofmischief 7y agoThanks for the link. I knew I'd read about this before some time ago.
- pen2l 7y agoDNA is packed in a fractal-like manner as well. That's actually one of the most important things we've learned about genome in recent time. Everyone knows that the content is important (ACGT, etc.), but what's also extremely important is the way it is packed. Particularly, it being a certain kind of fractal ensures that the parts of the densely packed DNA can go move around as needed efficiently. http://blogs.discovermagazine.com/notrocketscience/tag/fractal-globule/ http://blogs.discovermagazine.com/notrocketscience/tag/fract...
- cgrealy 7y agoAs someone with only a very passing knowledge of fractals and quantum mechanics... my first thought was that I'd be surprised if there weren't fractal patterns in quantum materials. It would be insufficiently weird :)
- ars 7y agoWait, they can focus x-rays?? Wouldn't that be amazing for lithography for making chips?
- alexfromapex 7y agoMy favorite thought experiment: if you think you’ve found the smallest thing in the universe, then what is it made out of?
- kragen 7y agoThe demiurge.
- nobrains 7y agoWaves
- caconym_ 7y agoItself
- mikekchar 7y agoTurtles
- kromem 7y agoConsidering the whole difference between classical and quantum is continuous vs discrete numbers, it's kind of like saying "how many whole pies are in a half of a pie"?
- krastanov 7y agoYou would have to be more careful with that statement. It is a bit of a misnomer that quantum mechanics is inherently discrete and classical is not. There are plenty of examples of continuous descriptions in quantum mechanics (e.g. an oscillator in the coherent state basis, which is an extremely commonly used model). And plenty of examples of discrete behavior in classical mechanics (modes of oscillation, standing waves, etc). In the case of light, most of the "discreteness" of the quantum description is already present in the classical case. More importantly, there is plenty of the continuous description left in the quantum model.
- sideshowb 7y agoSize itself is an emergent phenomenon, if you can reduce it to entanglement the question goes away
- emsign 7y agoMakes sense. Fractals are a cheap way to achieve complexity on a larger scale with relatively little code. The ancient alien timelords who are running our universe simulation had to be efficient.
- HugoDaniel 7y agoIm going to spend the day matching demos just because of this. pouet.net here i go...