Scientists discover fractal patterns in a quantum material | Hacker News Reader

Scientists discover fractal patterns in a quantum material

phys.org

172 pointsjonbaer49 comments

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

Thanks for the link. I knew I'd read about this before some time ago.

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

Actual article in Nature Communications: https://www.nature.com/articles/s41467-019-12502-0

PDF version of article: https://www.nature.com/articles/s41467-019-12502-0.pdf

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...

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.

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.

Thanks 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

Hi Thomas! Chaotica is amazing! Glad to see the project still lives. As a long-time Apophysis user I just want to say you're making a killer product. I've made some incredible things with Chaotica.

Seems you've been experimenting with n-body simulations, that's cool, pretty much what I've been doing in my free time lately. Doing research into physics-based cellular automata and self-correcting systems. Anyway good luck, can't wait for the official release of Chaotica 2!

Soulofmischef, I've been experimenting with n body sims too. Have you seen PPS?

https://youtu.be/I6bHpJ2GV0Y I made a few videos, and have some more coming soon. Loads of fun.

What a cool system, thanks for sharing! That crystalline structure formation was very interesting. The fact that matter naturally tends to fall into a self-sustaining low-energy state when entropy is added to a system governed by at least one force (a.k.a. you shake a bottle of sand up and down and gravity pulls the denser particles to the bottom to achieve pressure equillibrium) really is the key to making this all work, huh? I'd be interested to see a version of this experiment [0] with a rapidly alternating magnetic field instead of a static one.

I am exploring the physical implications of a philosophical concept I have been working on for a while which I refer to as Zodeasim, specifically I am trying to couple consciousness with the concept of system which is able to expend energy in order to exert a mind-to-world fit in the interest of the system's continued growth and stability. This is similar and complimentary to Friston's free energy principle [0].

That is, I am a conscious being precisely because at any time, I can use the energy within my system to act against the natural lowest energy state in which I exist. I can jump up, against gravity, or I can push against strong winds, or lift heavy objects. The very act of using energy in order to act against external forces is what separates me from the air I breathe and the ground upon which I stand, because it implies some kind of physical calculation which results in a particular orchestrated motion carried out by every atom in my body. The complexity of these physical calculations, and the senses which define the way in which these calculations take place, create an emergent layer which we perceive as consciousness.

The ability to perceive emotions is a powerful apparatus which greatly extends the capability of a system to perceive itself as a single entity which has certain needs which need to be met, so even if a bug also constantly consumes and expends energy in order to remain in a higher energy state, our perception of the world and of ourselves is radically different. This makes it difficult for us to agree upon what a "conscious experience" is, and if all forms of life are even "conscious". The Panpsychists believe that even a rock contains "consciousness", however my assertion is that only periodic systems with the ability to consume and expend energy in a directed fashion have any sort of "experience".

So naturally, I propose a higher order layer of consciousness, one that we cannot quite perceive since we are constituents of the layer from which it arises. I define any motion in the universe which is a result of a system changing energy states as a result of a physical computation to be a "kin". Any other kind of motion, like a rock falling from my hand to the ground, is just regular, abiotic motion. As an independent organism, my system is a culmination of a great deal many different kinds of kins, which can usually be broken down into simple rules, such as the activation potential of a neuron in my brain being a straight-forward non-linear response to the amount of voltage it is receiving from other neurons, as well as non-kins, such as a protein "walking" across a cell, a.k.a continuously "falling" into the lowest energy state. Thus I do not gain any conscious perception from such proteins, but I do gain it from the total network effect of all my brain's neuronal structures making simple calculations based on sensory input.

Thus the namesake of Zodeasim: Zoo = alive, idea = idea. I posit the existence of a form of "life" in the sense of a self-sustaining system capable of expelling energy in self-interest, which lasts far beyond the average human lifespan. We are able to encode into the universe "ideas" which have the capability to sustain themselves and, over time, either strengthen, evolve, or die out. Whereas we use our neurons to do our computations, an idea is able to carry out its computations across the entire noosphere [1] and it is within that system that the idea exists. An idea is able to gather intel from the senses of many different creatures, and make changes to its form which are suitable. An idea can travel through any medium. I can speak something to you and the idea can travel through the sound waves. I can write to you and let it travel through photons. But ultimately, it can use any channel available to communicate itself. Some ideas are so strong that, just by hearing them, they completely overtake your body for their purposes. I know it seems wonky but if you consider that we don't understand the nature of our own free will, such ideas don't necessarily have to be acting in their own "free will" in order to be conscious, so long as they are defined by their kins, which are able to change energy states in self-interest according to internal and external conditions.

This is what I am trying to experiment with n-body systems. The transfer of information between systems and the ability for systems to act in self-preservation in a more controlled and simplified environment. I hope I find some of the answers I seek.

[0] https://en.wikipedia.org/wiki/Free_energy_principle#Free_ene... https://en.wikipedia.org/wiki/Free_energy_principle#Perceptu...

[1] http://www.jetp.ac.ru/cgi-bin/dn/e_034_06_1257.pdf

[2] https://en.wikipedia.org/wiki/Noosphere

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.

> 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.

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?

> If not fractal, then what word?

self-similar?

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.

> 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.

Per the Wikipedia article, they are not well defined. Also, self-similarity of some kind is one of the requirements. Is it completely wrong, or is this a debated topic in mathematics?

How do you define a fractal? Unless you give me your definition I can make a definition match what I need.

Let's look at one paragraph from Wikipedia.

> Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.

Let's consider the context of behavior again.

A person is an object of elaborate and infinitely complicated boundary. You may look at one instance of behavior at one time and you may see a certain value, like you see at a fractal at a particular zoom and configuration. In a sense, particular details at this magnification. A family of several people has an elaborate and infinitely complicated boundary and has details of it's own, in addition to the people within it. A village... A city... A country... A planet... An organ...

Let's look at Merriam-Webster: > any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size.

Do you see how it fits?

If we consider shape more literally, it may be something like, a person has an arm to grasp things. Let's take one function, picking an object up and bringing it nearer to you. A community has an appointed person to deliver things. A country has a company to do so. A world has a certain country which is the most efficient for transport. A cell has a protein or a function of its membrane to interact with some molecules to bring them closer.

Your analogy doesn't work, because on one wall there is graffiti while on another there is nothing. One family is cold and the next is loving. What you're discussing is the systematic results of averaging out the individual actions of people. Not the same thing as a mathematical fractal, which has a fairly rigorous definition as defined by Mandelbrot, the guy who coined the term.

In a Mandelbrot fractal on one pixel you may see one value, on another you see another.

Let's say on the second wall, instead of graffiti of violence, you see a message of love. You look around the wall and you see there is a person in love, a family sharing love, a town with flowers, a peaceful city.

For a wall with nothing, it could be a value in the set that corresponds to a particular color that represents it did not meet the threshold.

Fractals don't have pixels.

Whatever you may consider to be an evaluation of it - for "looking at a fractal image" the pixel value is computed based on properties of the fractal at that particular magnification at that particular location.

Your analogy still doesn't make sense because people get murdered in front of beautiful murals all the time, and people walk past disheveled tenements without getting murdered all the time. This "fractal" nature you describe doesn't exist. You are confusing emergent properties of society with something entirely different.

I concede this argument, from your latter sentence, I am considering emergent properties at different scales to be fractal like indeed.

For the first sentence, my point was not to imply that a presence of one kind of behaviour leads to similar behaviour in related structures, but that at different scales, components of each structure may exhibit similar kinds of behaviour. E.g. a person can be considered to be violent or peaceful and so can a community. This could be from our nature of finding patterns in everything, though. Which I guess also leads to emergent properties anyway in some way, so I cannot add much more there.

Actually I am unsure if it fits the definition of emergence - "emergence occurs when an entity is observed to have properties its parts do not have on their own" - but it would be hypocritical for me to argue on that note :D

That would make for a nice article methinks.

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 :)

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

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"?

Size itself is an emergent phenomenon, if you can reduce it to entanglement the question goes away

Itself

The demiurge.

Æther

Turtles

Waves

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

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

Getting some deja vu here: https://en.wikipedia.org/wiki/Hofstadter%27s_butterfly

"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.

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

Here's some: https://en.wikipedia.org/wiki/Space-filling_curve

> You do the math.

Nice.

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

Everything is a fractal, even socially

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

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.

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.

    Function 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.

Define fractal?

Something with non-integer fractal dimension?

Actually, idk if that is exactly the right definition, because I think some fractals have integer dimension? Idk

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