
Scientists discover fractal patterns in a quantum material - jonbaer
https://phys.org/news/2019-10-scientists-fractal-patterns-quantum-material.html
======
blix
Magnetic 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
Thanks for the link. I knew I'd read about this before some time ago.

------
gjm11
Copied (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)

------
pen2l
DNA 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/fract...](http://blogs.discovermagazine.com/notrocketscience/tag/fractal-
globule/)

------
emsign
Makes 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.

------
pixelpoet
As 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.

~~~
toxicFork
I 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
> 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.

~~~
smallnamespace
I would like a word that means 'exhibits self-similar structure at different
scales '. This is a useful definition because people outside of math can
notice this pattern in our world.

If not _fractal_ , then what word?

~~~
TeMPOraL
> _If not fractal, then what word?_

 _self-similar_?

~~~
partyboat1586
Sorry to polute your pure and precise word but outside of mathematics people
will continue using fractal to mean self similar. As with many mathematical
words the colloquial meaning is different.

------
cgrealy
As 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 :)

------
alexfromapex
My favorite thought experiment: if you think you’ve found the smallest thing
in the universe, then what is it made out of?

~~~
kromem
Considering 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"?

------
ars
Wait, they can focus x-rays?? Wouldn't that be amazing for lithography for
making chips?

------
HugoDaniel
Im going to spend the day matching demos just because of this. pouet.net here
i go...

------
pixelpoet
Getting some deja vu here:
[https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly](https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly)

~~~
vardump
"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
The whole universe is fractal. Like a hologram. You do the math.

~~~
nixpulvis
Here's some: [https://en.wikipedia.org/wiki/Space-
filling_curve](https://en.wikipedia.org/wiki/Space-filling_curve)

------
soulofmischief
Sounds like a potential avenue for developing critical memory systems which
can survive an EMP. Hope that pans out.

------
buyingarmor
Everything is a fractal, even socially

~~~
coldtea
Well, a sine wave is not a fractal, for one...

~~~
Scene_Cast2
Random 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
Here 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.

