Not all fractals are self-similar. A fractal is an infinitely complex system that will continue to be complex despite the depth of zoom. (like a coastline)
I was gonna make that exact comment. I'm so happy to know that someone else knew that the most common definition is one that Benoit didn't want. Benoit wanted the definition of the fractal to be much broader.
Debiller 777 hahaha! The funny thing is nobody knows what you’re talking about. Dummies!!! [Correction - I don’t know what you’re talking about... I’m the dummy]
ali709aliali I experienced the fractal pattern in our thoughts on a VERY deep level on a 200ug trip. And the fractals in nature especially stood out everywhere I looked. Some crazy shit man. At that moment I knew it’s the code to the universe and everything as we know it
In mathematics, a fractal is a subset of a Euclidean space for which the Hausdorff dimension strictly exceeds the topological dimension. Fractals are encountered ubiquitously in nature due to their tendency to appear nearly the same at different levels, as is illustrated here in the successively small magnifications of the Mandelbrot set. Fractals exhibit similar patterns at increasingly small scales, also known as expanding symmetry or unfolding symmetry; If this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self-similar. One way that fractals are different from finite geometric figures is the way in which they scale. Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the dimension of the space the polygon resides in). Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere resides in). However, if a fractal's one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power that is not necessarily an integer. This power is called the fractal dimension of the fractal, and it usually exceeds the fractal's topological dimension.
All the "interesting" fractals do not equal their topological dimension, but it was a mistake to exclude all the "normal" dimensions, just as it would have been a mistake for the early researchers into "just what are non-algebraic numbers" and "What is an irrational?" to exclude considering whole numbers as part of the entire real number system. Our usual dimensions are simply "dull fractals", which puts the number of fractal dimensions on a one to one, onto basis with the entire real number system. (people often forget the definition of logarithms does NOT exclude negative values.) Before you get all excited about the impossibility of negative dimensions, whenever turbulent flow goes to laminar flow, its fractal dimension decreases, a subtraction has taken place. History note: Ordinary people people knew for generations that if you spent a shekel a day for 10 days, -10 days times -1 shekel, a negative times a negative, you were a positive 10 shekels richer 10 days ago. Meanwhile, in academia, educated people argued about the meaning of zero, why have a zero symbol, and what could be meant by a negative number. Don't worry about what is meant by a negative dimension. Just know real world machinist deal with them, and mathematically they are not just useful, they become necessary. Now for the mind blowing part: Now that you are including whole number fractal dimensions, Do more than arithmetic with fractals. Do some algebra. And think about how many real world phenomena NEED complex numbers to describe it accurately, If you don't know of such needs, contact someone skilled in electric theory. Then ask yourself the Big Question , if you created a fractal shape, most of whose points were imaginary numbers, only certain ones were 100% real, what would it look like in our world? Would we even know they were connected? Or if we observed connections, how would it be interpreted? Spooky action at a distance?
Fran Tabor Unconventional 20th century mathematician Benoit Mandelbrot created the term fractal from the Latin word fractus (meaning irregular or fragmented) in 1975. These irregular and fragmented shapes are all around us. At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple and gets progressively more complex. One of the earliest applications of fractals came about well before the term was even used. Lewis Fry Richardson was an English mathematician in the early 20th century studying the length of the English coastline. He reasoned that the length of a coastline depends on the length of the measurement tool. Measure with a yardstick, you get one number, but measure with a more detailed foot-long ruler, which takes into account more of the coastline's irregularity, and you get a larger number, and so on. Carry this to its logical conclusion and you end up with an infinitely long coastline containing a finite space, the same paradox put forward by Helge von Koch in the Koch Snowflake. This fractal involves taking a triangle and turning the central third of each segment into a triangular bump in a way that makes the fractal symmetric. Each bump is, of course, longer than the original segment, yet still contains the finite space within. Weird, but rather than converging on a particular number, the perimeter moves towards infinity. Mandelbrot saw this and used this example to explore the concept of fractal dimension, along the way proving that measuring a coastline is an exercise in approximation [source: NOVA]. Think of it this way We think of mountains and other objects in the real world as having three dimensions. In Euclidean geometry we assign values to an object's length, height and width, and we calculate attributes like area, volume and circumference based on those values. But most objects are not uniform; mountains, for example, have jagged edges. Fractal geometry enables us to more accurately define and measure the complexity of a shape by quantifying how rough its surface is. The jagged edges of that mountain can be expressed mathematically: Enter the fractal dimension, which by definition is larger than or equal to an object's Euclidean (or topological) dimension (D => DT). A relatively simple way for measuring this is called the box-counting (or Minkowski-Bouligand Dimension) method. To try it, place a fractal on a piece of grid paper. The larger the fractal and more detailed the grid paper, the more accurate the dimension calculation will be.
Interesting information about fractals however this is not a quantum circuit. Micro circuitry would be more appropriate. It still requires a copper backing and uses carbon molecules and electrons which are within the atomic size range. Quantum means sub-atomic. This is amazing but I wish scientists would stop exaggerating and making false claims. We are nowhere near being able to make quantum computers. Better circuits perhaps but not quantum. How would you utilize protons or quarks?
@@leaffen9616 how is that so shitty? Psychedelics have a different purpose than other drugs!! I've had philosophical realizations on LSD that to this day stand relevant
"Fractal" is a contraction of "Fractional dimension" or rather "Fraction dimensional". Rather than have say, 3 dimensions, you have say, 1.4 dimensions. But yes, it is quite a cool name. :)
Fractal Gates and Fractal Universe are already known metal bands so unless you're going for a different genre, I'd stay away from the whole fractal thing :D
@@leaffen9616 Personally I think this is a very interesting topic and I would like to have more info on it. The people that dedicated their time and energy to make this video could provide some links from the source of their research. If you have any issues please come at me with evidence, research papers and data. That would be educational for both of us. Not some meaningless comment coming from the safety of your anonymity.
@@TheLummen. I share your fascination with this topic. I just came across this. Watching it now. Hope it's good. "Fractals in Neurosciences by Dr. Antonio Di Ieva"- ua-cam.com/video/6dFVA7jfMNI/v-deo.html Let me know what you think.
@@TheLummen. He spends the first twenty minutes giving us a decent overview of fractals, although it is good to have a healthy understanding of fractals going in. After that he talks about using fractal analysis on the brains blood vessels on both the micro and macro scales. The fractal analysts uses parameters such as circumference, density, branching, et al, from sources like brain slices and MRI images to determine if cancer is present and how far along the progression is. He, then, spends a few minutes discussing a couple of other related topics. It was a fascinating talk. It helped to have a good understanding of neuroscientific vocabulary. If you like to geek out on fractals or neuroscience, or both you will enjoy the video more than once. Robert Sapolsky also touches on this subject in his Human Behavioral Biology course of lectures available on UA-cam. Also a fascinating binge watch. Fractals are discussed in lectures "21. Chaos and Reductionism" and "22. Emergence and Complexity."
Loved the video, but I would like to make some observations: - The dimension in fractals is different from the usual dimension; - Fractals are not always self-similar. I would recommend looking at "Fractals are typically not self-similar" to understand this concept better.
Im a material scientist, yet i struggle to understand some concepts in this videos like 1.58 dimensions (what that even means) and how fractals can improve electronic device? I understand structures give different properties in different atomic config... and each of them come with specific electron configuration, and i know we can arrange atoms, but, arrange electrons really?? Totally din't get how the triangle fractals config could improve efficiency of electronics. I think it's too brief info for common folks anyway, even for me.. interesting info, but leave me have way too much questions unanswered.. i just can't relate to it well yet to quantum mechanics principles i already know.. But thanks Seeker for putting down the journals so i can read more of the publications! Help me being a better scientist really to present these topics in attractive ways, otherwise i might have just skipped it when i read journals! I do get to know now we can arrange electrons (but im still confused abt the whole electron behaviour as a whole, aren't they supposed to be moving all the time) Anyway, Good Job!
I'm a chemist, so I'll presume you have an understanding of material chemistry. I think how I would best use an analogy to help understand it. Is if you think of 1D as a line, and 2D as a sheet, the "in between" dimension is like a sheet with holes in it. You can't fully explore the 2D surface as it has constraints. Perhaps another way to think about this is if we take that 1D line and join it together into say a circle. It's now arguably a 2D surface, but if movement is still restricted to staying on that line then the shape isn't true 2D nor true 1D. It's somewhere in between. Fractals have these sorts of constraints but much more complex. Calculating it to be 1.58 is the level of "constraint" from 2D or the level of "freedom" from 1D. For the electron example given, the electrons can only move along the lines the fractal dictates. And we can improve electronics by understanding how to utalise those lines. I hope that makes sense and helps you visualise it? For further reading around the electronics I would recommend "Electronic band structure" and in particular "Valence and conduction bands"
For understanding that concept and many other in maths try watching the yt channel called 3 blue 1 brown. He has a vídeo on fractals too. Belive, it is way better than this one.
This is an attempt at creating micro circuitry which is compelling but calling it quantum is a bit of a stretch. If you are dependent upon a copper backing and the use of electrons for energy articulation than several key components are still within the atomic size range. For something to be truly quantum all its components and energy would need to be sub-atomic. I love the idea of using fractal patterns for creating micro circuitry but I hate when people make exaggerated claims about quantum computing.
Aditya Pradipta yay! The first post where someone doesn’t just comment on how much they are understanding the video; or how they took acid and just “see” this already and actually address the implications and the math and physics without trying to seem smarter than every other commenter! Thumbs up
@@fleecemaster Thanks for your explanation! however i still have few questions. im already familiar with how electron conducts electricity (valence, bands, etc), and in quantum dot material it's restricted to travel in only one dimension. in quantum wire it can only travel in both axis, due to de broglie wave restriction. so from what i understand, as long as a material have not reached a certain volume or length, it will not be conductive because the electron travel path is restricted; it cant travel if the size/dimension of the material is below it's de broglie wave length (different for each material); so maybe 1.58 dimension is a very small or restricted quantum wire? i still dont get why electrons being structured in a fractal could improve electronics? does it have to do with conductivity? less loss to restriction or something else? thanks man for spending time here
The Fibonacci sequence. Nature's beautiful impression of Phi, the Golden Ratio. Life is a fractal banging another fractal and creating a fractal of baby fractals.
Neurons are fractal? That might explain why I keep having nightmares of being able to enter a building but never able to find my way back out again. Thank you for the terminal prognosis! On a related note, if the wrinkles on a brain were fractal, would that make someone infinitely smart, or just trap them in infinite indecision?
I appreciate your seeking curiosity and so I will answer you as a friend would. Imagine if you will, the wrinkles of your brain as one long worm. A masterpiece of topological data which purpose is to send neurons through and around the loops at electrically charged speeds in order to give you a continual stream of conscious analysis through the connected senses of your nervous system. Now, the formation of the thoughts that occur to you are demonstrated to you through the reflection and refraction of various crystalline structures of the elements and molecules you introduce to your body, as the obstacles to your neurons firing through the loops. There's a college lecture available in the UA-cam catalog titled something along the lines of "the geometry of the dmt experience" or something like that. You might take a particular interest. Have a nice day.
there's a guy i know from high school who sells illicit substances at local dive bars who is a coke snowflake. is... is he a fractal? am i doing this right?
The way fractal dimensions work is based on scale; if you increase the size of a 1d object, its area increases by the same amount, if you increase the size of a 2d object, its area increases by that amount to the power of 2, if you increase the size of a 3d object, its volume increases by that amount to the power of 3; so in the case of the Koch snowflake, if you increase its size, its area increase by that amount to the power of 1.26... The measurement of area (or volume) is done by using unit squares, or lines, or cubes or whatever, you count how many squares (or whatever) the object is touching at various sizes and you calculate the proportion of that number to how much you changed the size of the object; and the bigger you make the object the more accurately you can calculate the dimensionality of the object.
Thank you, Maren Hansenberger. Your narration and handling of this subject was both delightful and enlighting. The camera loves you; and your MIT association is admirable. I've only had the occasion to visit MIT, would love to have attended, but lacked the credentials. You; on the other hand, you clearly made the grade. Well done:-) Also; I must say, I admire people like Yuliya, who get to do undergraduate work in the field of fractal research, and at MIT no less. Well done again:-)
WarioGiant ...She said that natural fractals aren't totally self similar" all the way", but mathematical ones are, or can be, because they are designed to be, like the Mandelbrot Series. In Theory you can do a lot, with mathematical precision, in practise, nature goes so far as it needs, and doesn 't then, get bogged down in Rules , - it makes the rules . Maybe this is why we find things like quantum mechanics so enigmatic! .
Why are fractals in nature? Why are the same patterns in your ear in the same patterns on a snails shell? Why do you see fractals when you take dmt or shrooms? Life is a mystery we need to solve
Life's structure comes from DNA, if DNA give a recursive instruction then you'll see a fractal. There's a video about Fibonacci spirals that talks about why plants all seem to spiral the same way. But if your outcome depends on your last two outcomes, you'll probably see some sort of Fibonacci pattern.
Because fractals are structures that can be described with much less information then they appear to(because of their self symmetric nature). Structures in nature all arise from a simpler set of laws so complexity can either arise from those laws creating chaos( giving uninteresting noise or turbulence) or by recursion, creating fractals.
2:50: "It's weird I had literally no idea it was possible" But that's the definition of a fractal. Fractal means fractional dimension, that's why it's called FRACTal.
I made a model MIPS more than a decade ago to see if I could figure out how to conceptually capture how lighting works based on how I see light interactions on a macroscopic scale. While I can't see molecules, I know how they impact the world because I used to basically see Cherenkov radiation pretty much everywhere. This got me interested in lightning specifically (after I learned about radiations influence on matter). I noticed this effect much more strongly around stormy weather. Some days I could see working electronics through otherwise opaque matter even several feet away. I always assumed my skin had something to do with this sensory perception and perhaps my hydrophobic skin layers played a role in this when the nano structures were more tightly grouped together (when I was smaller/younger)? Hydrophobic materials suspend liquids by not breaking their surface tension. This is possible because of micro-optic or sub-optical structures sometimes comprised of single atom thick splines organized in specific patterns typically aligned in a single orientation like those found on the leaves of lotus plants. I posted a video about how my skin suspends water droplets and how water can move almost frictionlessly after my skin is exposed to water. After being struck by lightning I studied ways to interfere with its formation and I can say that I'm very sure about how this can effectively be disrupted, but I'll leave it at that. I believe that I'm not the only or first human with this ability (though most who I think had this ability are now dead). I assume most other humans who had this ability helped make massive strides in making electricity useful for the rest of civilization. So it's not all bad. I do think the ability fades over time as the skin grows and those nanoscale splines spread farther apart from eachother. I have never seen people's skin repel water nor have I heard about this or any medical conditions associated with this (see here: ua-cam.com/video/rUuM5yqLwSA/v-deo.html wow, just noticed this video was private since upload, that's how weird I think this is). I likely have a few tissue disorders plus a known benign congenital bone/limb deformity too... So it's not all good either.
I hate my brain sometimes. I understood that fractals appear in the body but I didn't think of extrapolating that over to the brain. I'm totally glad you mentioned that. Thanks. I'm definitely gonna try to apply that to my very own style of artificial neural network. (It could just be that I'm up late but I don't know if that's true right now since I've "sleeping around the clock" for the past week and a half (that's what I call pushing my bed time later and later almost every other day.) I might fall asleep at 10am or noon. idk)
It would be nice if seeker sought out a little research before dropping a video about maths. I dunno, maybe know what Mandelbrot *actually* said about fractals before sh*tting out another half-assed pop-science video full of errors.
@@TheHellogs4444 yes but it grows the more you zoom in and decreases the more you zoom out. I know there is an agreed way to measure them but nonetheless the paradox exists.
I work as a currency trader and fractals appear in an almost ever repeating pattern. As you zoom into the volume /price data, the same fractals appear inside fractals until you zoom into the smallest measurement of price, a tick. By using this geometry, traders are able to anticipate price movements. What's curious to me is why the fractals occur in the first place. These patterns are everywhere, what's weird is they don't just show up in stock prices, you can pick any data from the weather to school attendance figures and the same fractals exist. From a fundamental perspective, the price of an asset is influenced by human behaviour. However, the presence of these fractals allows us to build machine learning algorithms to trade the markets.
The woman presenting this is so cute! (Yeah, I kinda followed the science, and was interested, but I am concerned about interfacing electronics with the human brain.)
starts off with non factual definition of a fractal... it doesn't have to be self similar by means of smaller versions within itself... I don't know how this got left in but it really should be corrected, teaching wrong is worse than not teaching
To explain the infinite perimeter and finite area, think of this: There are two kinds of infinities: The small infinity 1,2,3,4,5,6,7,8....... And the large infinity 1. 1.0000000000......1 1.0000000000......2 1.0000000000......3 ............ 1.9999999999......9 2. It would take an infinite amount of time to reach the number two in this example. Fractals have the larger infinity for its perimeter, which is why it would take forever to measure as it keeps getting smaller and smaller to an infinite amount of decimals (as a number).
I love I found this video. People seem to be afraid of my image like its some kind of satanic symbol. I took this shop class, when I was young, and our instructor assigned us a special project. He had us make these small bridges out of paper. We all came up with our shapes. I don't even remember what my shape was. After we were done we put the strength of the bridges to the test by stacking weight on them. The weights were textbooks. Most of our bridges collapsed from one book. Then, there was this student who made the structure of triangles holding the bridge up. We kept stacking books on it and it finally give at around five books. Imagine this microscopic shape building up to a macroscale bridge support.
@@madscientistshusta , with the Koch snowflake as its perimeter increases its area does too, but its area approaches the limit of a circle. If you add 1/2 + 1/4 + 1/8 + 1/16 ... it always gets bigger but approaches 1, never quite reaching it. The *Menger sponge* is like a 3D Sierpinski triangle. It starts with a cube, and exponentially smaller cubes are removed ad infinitum. It has infinite surface area, occupies a volume, yet has zero volume.
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
Infinite perimeter, finite area.
1.58 dimensions.
Every day of my life, the world has become slightly less comprehensible.
3Blue1Brown made a pretty comprehensible video on this, you should check it out some time.
ua-cam.com/video/gB9n2gHsHN4/v-deo.html
Yh, I was like wtf? 🤯
It just means it has a donate amount of space taken, but has an infinate distance around it
@@thelaw3536 You are misusing the word "donate". And - I KNOW what it means. I just don't understand how it can be so, and you don't either.
@@TheMrCiwan Wow that video explains a lot! Thanks for sharing!
Not all fractals are self-similar. A fractal is an infinitely complex system that will continue to be complex despite the depth of zoom. (like a coastline)
Thank you
Yeah, the Mandelbrot isn't really self-similar either.
Further viewing
"Fractals are typically not self-similar." by 3blue1brown
I like the coastline analogy.
@@Shkunk1 The analogy that really helped me understand fractal dimensions was the surface of an ocean.
The girl: A fractal is a self similar shape
Benoit B. Mandelbrot: Am I a joke to you?
dont get it
Incel: lets push anti girl naratives cause will never get laid anyway
I was gonna make that exact comment. I'm so happy to know that someone else knew that the most common definition is one that Benoit didn't want. Benoit wanted the definition of the fractal to be much broader.
Phaedrus Socrates how did you get “anti girl” from what he said lmfao
She said that and I SCREAMED
*No electrons were harmed during the making of this video...*
Underrated 😂👌🏻
The lava flying around in Star Wars (with the fight scene between Anakin and Obi-Wan) was constructed with fractals
Seeker: Fractals are self-similar
3b1b: Hold my beer
Debiller 777 hahaha! The funny thing is nobody knows what you’re talking about. Dummies!!!
[Correction - I don’t know what you’re talking about... I’m the dummy]
Oh I got it
*Fractals are typically not self-similar*
0:35
that just makes them more like real fractals
Yessssss another 3b1b fan
Now let's store memes in fractals so they would live forever
this is an idea worth exploring lol
If there was reddit gold on UA-cam.. 🥇
What if we kill the fractal
Memes the dna of soul
Isn't that what memes about memes are?
Fractal Geometry: *exists*
Me: “It’s some kind of Elvish, I can’t read it”
Evariste Galois haha shiiiiitt 😂
it's called the triforce, silly.
😂😂
We all know it fractals were built by the dmt elves
There are few who can. The language is that of Theoretical Physicists, which I will not utter here.
Triforce gone scientific.
And failed miserably.
Tons of damage!
I See fractal niples everywhere.
@@xerejuneseve6333 *nipples
Woman's always woman's
You can't just put a triforce in the thumbnail and "wild" in the title and *not* expect these kinds of responses.
actually, it’s one of these: en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle
Seeker: 0:48
me, an intellectual: ua-cam.com/video/gB9n2gHsHN4/v-deo.html&vl=en&t=60s
I already knew the brain was fractal from a 350mcg acid trip. Lol.
ali709aliali really
The key to the universe 👁
ali709aliali
I experienced the fractal pattern in our thoughts on a VERY deep level on a 200ug trip. And the fractals in nature especially stood out everywhere I looked. Some crazy shit man. At that moment I knew it’s the code to the universe and everything as we know it
350 mic? Damn. What else did you see
Try DMT
I thought that was the Tri-Force from Zelda for a second 😂
Same!
You're not the only one...
Same
Pretty sure the scientists knew what they were designing. They could have chosen many fractals but chose the Sierpenski triangle. They knew.
Who says it isn’t?
Jeez! Possibly one of the coolest titles I’ve seen for a video on UA-cam!
Nicely done Seeker. Nicely done. 🙌🏻
I read titles as titties is it okay?
Praveen Kumar lol same here
A cool title?? It's a clickbait title...
Nice to see you here! Keep up the wonderful work :)
Yeah I'd slap em up
In mathematics, a fractal is a subset of a Euclidean space for which the Hausdorff dimension strictly exceeds the topological dimension. Fractals are encountered ubiquitously in nature due to their tendency to appear nearly the same at different levels, as is illustrated here in the successively small magnifications of the Mandelbrot set. Fractals exhibit similar patterns at increasingly small scales, also known as expanding symmetry or unfolding symmetry; If this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self-similar.
One way that fractals are different from finite geometric figures is the way in which they scale. Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the dimension of the space the polygon resides in). Likewise, if the radius of a sphere is doubled, its volume scales by eight, which is two (the ratio of the new to the old radius) to the power of three (the dimension that the sphere resides in). However, if a fractal's one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power that is not necessarily an integer. This power is called the fractal dimension of the fractal, and it usually exceeds the fractal's topological dimension.
All the "interesting" fractals do not equal their topological dimension, but it was a mistake to exclude all the "normal" dimensions, just as it would have been a mistake for the early researchers into "just what are non-algebraic numbers" and "What is an irrational?" to exclude considering whole numbers as part of the entire real number system.
Our usual dimensions are simply "dull fractals", which puts the number of fractal dimensions on a one to one, onto basis with the entire real number system. (people often forget the definition of logarithms does NOT exclude negative values.)
Before you get all excited about the impossibility of negative dimensions, whenever turbulent flow goes to laminar flow, its fractal dimension decreases, a subtraction has taken place.
History note: Ordinary people people knew for generations that if you spent a shekel a day for 10 days, -10 days times -1 shekel, a negative times a negative, you were a positive 10 shekels richer 10 days ago. Meanwhile, in academia, educated people argued about the meaning of zero, why have a zero symbol, and what could be meant by a negative number.
Don't worry about what is meant by a negative dimension. Just know real world machinist deal with them, and mathematically they are not just useful, they become necessary.
Now for the mind blowing part: Now that you are including whole number fractal dimensions, Do more than arithmetic with fractals. Do some algebra. And think about how many real world phenomena NEED complex numbers to describe it accurately, If you don't know of such needs, contact someone skilled in electric theory. Then ask yourself the Big Question , if you created a fractal shape, most of whose points were imaginary numbers, only certain ones were 100% real, what would it look like in our world? Would we even know they were connected? Or if we observed connections, how would it be interpreted? Spooky action at a distance?
Fran Tabor Unconventional 20th century mathematician Benoit Mandelbrot created the term fractal from the Latin word fractus (meaning irregular or fragmented) in 1975. These irregular and fragmented shapes are all around us. At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple and gets progressively more complex. One of the earliest applications of fractals came about well before the term was even used. Lewis Fry Richardson was an English mathematician in the early 20th century studying the length of the English coastline. He reasoned that the length of a coastline depends on the length of the measurement tool. Measure with a yardstick, you get one number, but measure with a more detailed foot-long ruler, which takes into account more of the coastline's irregularity, and you get a larger number, and so on.
Carry this to its logical conclusion and you end up with an infinitely long coastline containing a finite space, the same paradox put forward by Helge von Koch in the Koch Snowflake. This fractal involves taking a triangle and turning the central third of each segment into a triangular bump in a way that makes the fractal symmetric. Each bump is, of course, longer than the original segment, yet still contains the finite space within. Weird, but rather than converging on a particular number, the perimeter moves towards infinity. Mandelbrot saw this and used this example to explore the concept of fractal dimension, along the way proving that measuring a coastline is an exercise in approximation [source: NOVA]. Think of it this way We think of mountains and other objects in the real world as having three dimensions. In Euclidean geometry we assign values to an object's length, height and width, and we calculate attributes like area, volume and circumference based on those values. But most objects are not uniform; mountains, for example, have jagged edges. Fractal geometry enables us to more accurately define and measure the complexity of a shape by quantifying how rough its surface is. The jagged edges of that mountain can be expressed mathematically: Enter the fractal dimension, which by definition is larger than or equal to an object's Euclidean (or topological) dimension (D => DT).
A relatively simple way for measuring this is called the box-counting (or Minkowski-Bouligand Dimension) method. To try it, place a fractal on a piece of grid paper. The larger the fractal and more detailed the grid paper, the more accurate the dimension calculation will be.
I didn't get a thing.
@@friendlyone2706 , that last paragraph blew my mind.
Interesting information about fractals however this is not a quantum circuit. Micro circuitry would be more appropriate. It still requires a copper backing and uses carbon molecules and electrons which are within the atomic size range. Quantum means sub-atomic. This is amazing but I wish scientists would stop exaggerating and making false claims. We are nowhere near being able to make quantum computers. Better circuits perhaps but not quantum. How would you utilize protons or quarks?
I've had this feeling that there are forms of math that we haven't discovered yet, and I think stuff like this brings us closer.
Electrons: *Becomes a Fractal.*
Me: Why does it look like a Triforce...?-
I see these patterns when I'm high on acid.
Same. Like the closer you look the more detailed it gets.
Me toooo 🍄🍄🍄
I see these on dmt
What a sad and shitty thing.
@@leaffen9616 how is that so shitty? Psychedelics have a different purpose than other drugs!! I've had philosophical realizations on LSD that to this day stand relevant
nintendo bouta sue scientists
*Nintendo bout to sue science
illegal eagle Who cares
@@UM7942 not sure, but that phrase sure does take the fun out of everything does it?
illegal eagle who cares
*Science bouta sue Nintendo... Wacław Sierpiński described the Sierpinski triangle in 1915.
Fractal Dimensionality, the new name of my band.
now thats epic
Not as epic as MY MOM
"Fractal" is a contraction of "Fractional dimension" or rather "Fraction dimensional". Rather than have say, 3 dimensions, you have say, 1.4 dimensions. But yes, it is quite a cool name. :)
Shanghaimartin that is SUCH a good band name 😂
Fractal Gates and Fractal Universe are already known metal bands so unless you're going for a different genre, I'd stay away from the whole fractal thing :D
"The neurons in our brain are fractal"
Where is that based on? Any serious research links or something to definitively support it ?
People like you need to just stop internetting.
@@leaffen9616 Personally I think this is a very interesting topic and I would like to have more info on it. The people that dedicated their time and energy to make this video could provide some links from the source of their research.
If you have any issues please come at me with evidence, research papers and data. That would be educational for both of us. Not some meaningless comment coming from the safety of your anonymity.
@@leaffen9616
"how dare you ask questions"
you got that backwards.
@@TheLummen. I share your fascination with this topic. I just came across this. Watching it now. Hope it's good.
"Fractals in Neurosciences by Dr. Antonio Di Ieva"-
ua-cam.com/video/6dFVA7jfMNI/v-deo.html Let me know what you think.
@@TheLummen. He spends the first twenty minutes giving us a decent overview of fractals, although it is good to have a healthy understanding of fractals going in. After that he talks about using fractal analysis on the brains blood vessels on both the micro and macro scales. The fractal analysts uses parameters such as circumference, density, branching, et al, from sources like brain slices and MRI images to determine if cancer is present and how far along the progression is. He, then, spends a few minutes discussing a couple of other related topics.
It was a fascinating talk. It helped to have a good understanding of neuroscientific vocabulary. If you like to geek out on fractals or neuroscience, or both you will enjoy the video more than once.
Robert Sapolsky also touches on this subject in his Human Behavioral Biology course of lectures available on UA-cam. Also a fascinating binge watch. Fractals are discussed in lectures "21. Chaos and Reductionism" and "22. Emergence and Complexity."
Loved the video, but I would like to make some observations:
- The dimension in fractals is different from the usual dimension;
- Fractals are not always self-similar.
I would recommend looking at "Fractals are typically not self-similar" to understand this concept better.
The tri-force of power
*The triforce is real*
The Sierpinski Triangle is real
Yep
"Just 20 Nanometers big" I know that too well.. :(
Cause its 10× the size of your dong?
Your pp non existent lmao
Mines 69x10^420 kilometers big ;)
@@Shorteagle mine is 6969*420^1000 lightyears big lmao
Thats what she said?
1:15 “You take a line, and divide it in half” That’s 2/3 of the line
Is zeno’s paradox a case of fractal? It has similar hallmarks.
3:43 no that’s the Triforce. lol
It wasnt wild it was breath of the wild
Literally, all I saw was the triforce, that's why I clicked the link... Geddit?? Heheh sorry
bahahahah, link
The Triforce is real!
No it's a Sierpinski Triangle
Im a material scientist, yet i struggle to understand some concepts in this videos like 1.58 dimensions (what that even means) and how fractals can improve electronic device? I understand structures give different properties in different atomic config... and each of them come with specific electron configuration, and i know we can arrange atoms, but, arrange electrons really?? Totally din't get how the triangle fractals config could improve efficiency of electronics. I think it's too brief info for common folks anyway, even for me.. interesting info, but leave me have way too much questions unanswered.. i just can't relate to it well yet to quantum mechanics principles i already know..
But thanks Seeker for putting down the journals so i can read more of the publications! Help me being a better scientist really to present these topics in attractive ways, otherwise i might have just skipped it when i read journals! I do get to know now we can arrange electrons (but im still confused abt the whole electron behaviour as a whole, aren't they supposed to be moving all the time) Anyway, Good Job!
I'm a chemist, so I'll presume you have an understanding of material chemistry. I think how I would best use an analogy to help understand it. Is if you think of 1D as a line, and 2D as a sheet, the "in between" dimension is like a sheet with holes in it. You can't fully explore the 2D surface as it has constraints. Perhaps another way to think about this is if we take that 1D line and join it together into say a circle. It's now arguably a 2D surface, but if movement is still restricted to staying on that line then the shape isn't true 2D nor true 1D. It's somewhere in between. Fractals have these sorts of constraints but much more complex. Calculating it to be 1.58 is the level of "constraint" from 2D or the level of "freedom" from 1D. For the electron example given, the electrons can only move along the lines the fractal dictates. And we can improve electronics by understanding how to utalise those lines. I hope that makes sense and helps you visualise it? For further reading around the electronics I would recommend "Electronic band structure" and in particular "Valence and conduction bands"
For understanding that concept and many other in maths try watching the yt channel called 3 blue 1 brown. He has a vídeo on fractals too. Belive, it is way better than this one.
This is an attempt at creating micro circuitry which is compelling but calling it quantum is a bit of a stretch. If you are dependent upon a copper backing and the use of electrons for energy articulation than several key components are still within the atomic size range. For something to be truly quantum all its components and energy would need to be sub-atomic. I love the idea of using fractal patterns for creating micro circuitry but I hate when people make exaggerated claims about quantum computing.
Aditya Pradipta yay! The first post where someone doesn’t just comment on how much they are understanding the video; or how they took acid and just “see” this already and actually address the implications and the math and physics without trying to seem smarter than every other commenter! Thumbs up
@@fleecemaster Thanks for your explanation! however i still have few questions. im already familiar with how electron conducts electricity (valence, bands, etc), and in quantum dot material it's restricted to travel in only one dimension. in quantum wire it can only travel in both axis, due to de broglie wave restriction. so from what i understand, as long as a material have not reached a certain volume or length, it will not be conductive because the electron travel path is restricted; it cant travel if the size/dimension of the material is below it's de broglie wave length (different for each material); so maybe 1.58 dimension is a very small or restricted quantum wire? i still dont get why electrons being structured in a fractal could improve electronics? does it have to do with conductivity? less loss to restriction or something else? thanks man for spending time here
The Fibonacci sequence. Nature's beautiful impression of Phi, the Golden Ratio. Life is a fractal banging another fractal and creating a fractal of baby fractals.
Neurons are fractal? That might explain why I keep having nightmares of being able to enter a building but never able to find my way back out again. Thank you for the terminal prognosis!
On a related note, if the wrinkles on a brain were fractal, would that make someone infinitely smart, or just trap them in infinite indecision?
I appreciate your seeking curiosity and so I will answer you as a friend would.
Imagine if you will, the wrinkles of your brain as one long worm. A masterpiece of topological data which purpose is to send neurons through and around the loops at electrically charged speeds in order to give you a continual stream of conscious analysis through the connected senses of your nervous system. Now, the formation of the thoughts that occur to you are demonstrated to you through the reflection and refraction of various crystalline structures of the elements and molecules you introduce to your body, as the obstacles to your neurons firing through the loops.
There's a college lecture available in the UA-cam catalog titled something along the lines of "the geometry of the dmt experience" or something like that. You might take a particular interest.
Have a nice day.
there's a guy i know from high school who sells illicit substances at local dive bars who is a coke snowflake. is... is he a fractal? am i doing this right?
Majority of what you said is wrong. I’m questioning why people like you even speak when they have no idea what they’re talking about.
@@jordankelly4684 r/woooosh
@@jordankelly4684 why people like you are even on the Internet🤔
Yes he is. And yes you are....
@@jordankelly4684 are you on the spectrum? It was so obviously a joke lol..
Next week "How Jonny Mnemonic and the Matrix became reality"
Indeed
The way fractal dimensions work is based on scale; if you increase the size of a 1d object, its area increases by the same amount, if you increase the size of a 2d object, its area increases by that amount to the power of 2, if you increase the size of a 3d object, its volume increases by that amount to the power of 3; so in the case of the Koch snowflake, if you increase its size, its area increase by that amount to the power of 1.26...
The measurement of area (or volume) is done by using unit squares, or lines, or cubes or whatever, you count how many squares (or whatever) the object is touching at various sizes and you calculate the proportion of that number to how much you changed the size of the object; and the bigger you make the object the more accurately you can calculate the dimensionality of the object.
Thank you, Maren Hansenberger. Your narration and handling of this subject was both delightful and enlighting.
The camera loves you; and your MIT association is admirable. I've only had the occasion to visit MIT, would love to have attended, but lacked the credentials. You; on the other hand, you clearly made the grade. Well done:-)
Also; I must say, I admire people like Yuliya, who get to do undergraduate work in the field of fractal research, and at MIT no less. Well done again:-)
0:16 actually fractals arent usually self similar.
WarioGiant ...She said that natural fractals aren't totally self similar" all the way", but mathematical ones are, or can be, because they are designed to be, like the Mandelbrot Series.
In Theory you can do a lot, with mathematical precision, in practise, nature goes so far as it needs, and doesn 't then, get bogged down in Rules , - it makes the rules . Maybe this is why we find things like quantum mechanics so enigmatic!
.
THE TRIFORCE!!! AT THE ATOMIC LEVEL
Why are fractals in nature? Why are the same patterns in your ear in the same patterns on a snails shell? Why do you see fractals when you take dmt or shrooms? Life is a mystery we need to solve
It's all about using the least amount of energy, Maan. So just chill and enjoy the colours. ¦¬}
Because fractals represent an infinite, creative universe.
@@MrApotator God is math lol he Asian
Life's structure comes from DNA, if DNA give a recursive instruction then you'll see a fractal. There's a video about Fibonacci spirals that talks about why plants all seem to spiral the same way. But if your outcome depends on your last two outcomes, you'll probably see some sort of Fibonacci pattern.
Because fractals are structures that can be described with much less information then they appear to(because of their self symmetric nature). Structures in nature all arise from a simpler set of laws so complexity can either arise from those laws creating chaos( giving uninteresting noise or turbulence) or by recursion, creating fractals.
Scroll on through the video and you get a slightly different yet repeating explanation of what came a minute before, Amazing!
Can you force fractal structure onto matter with the application of specific audio frequencies?
#Cymatics
That looks like the triforce!
Looks more like a Sierpinski Triangle
Sigh...
So the Sierpinksi Triangle is basically a fancy Triforce? Can we get a Zelda theory on that?
EchoFlower Productions you got it backwards
Theory: it symbolizes how infinite the power of the Triforce is.
2:50: "It's weird I had literally no idea it was possible"
But that's the definition of a fractal. Fractal means fractional dimension, that's why it's called FRACTal.
That's just a naming coincidence.
I made a model MIPS more than a decade ago to see if I could figure out how to conceptually capture how lighting works based on how I see light interactions on a macroscopic scale.
While I can't see molecules, I know how they impact the world because I used to basically see Cherenkov radiation pretty much everywhere. This got me interested in lightning specifically (after I learned about radiations influence on matter). I noticed this effect much more strongly around stormy weather. Some days I could see working electronics through otherwise opaque matter even several feet away. I always assumed my skin had something to do with this sensory perception and perhaps my hydrophobic skin layers played a role in this when the nano structures were more tightly grouped together (when I was smaller/younger)?
Hydrophobic materials suspend liquids by not breaking their surface tension. This is possible because of micro-optic or sub-optical structures sometimes comprised of single atom thick splines organized in specific patterns typically aligned in a single orientation like those found on the leaves of lotus plants. I posted a video about how my skin suspends water droplets and how water can move almost frictionlessly after my skin is exposed to water.
After being struck by lightning I studied ways to interfere with its formation and I can say that I'm very sure about how this can effectively be disrupted, but I'll leave it at that.
I believe that I'm not the only or first human with this ability (though most who I think had this ability are now dead). I assume most other humans who had this ability helped make massive strides in making electricity useful for the rest of civilization. So it's not all bad.
I do think the ability fades over time as the skin grows and those nanoscale splines spread farther apart from eachother. I have never seen people's skin repel water nor have I heard about this or any medical conditions associated with this (see here: ua-cam.com/video/rUuM5yqLwSA/v-deo.html wow, just noticed this video was private since upload, that's how weird I think this is). I likely have a few tissue disorders plus a known benign congenital bone/limb deformity too... So it's not all good either.
I hate my brain sometimes. I understood that fractals appear in the body but I didn't think of extrapolating that over to the brain. I'm totally glad you mentioned that. Thanks. I'm definitely gonna try to apply that to my very own style of artificial neural network.
(It could just be that I'm up late but I don't know if that's true right now since I've "sleeping around the clock" for the past week and a half (that's what I call pushing my bed time later and later almost every other day.) I might fall asleep at 10am or noon. idk)
Diiiiiiid someone say........... "ILLUMINATI CONFIRMED"!!!!
Finally, Scientific evidence of the power of the Triforce, all those hours of playing Zelda were not wasted!
UA-cam : Seeker AND Numberphile post a video about maths
Me : *How can they achieve so much power*
It would be nice if seeker sought out a little research before dropping a video about maths.
I dunno, maybe know what Mandelbrot *actually* said about fractals before sh*tting out another half-assed pop-science video full of errors.
@@badlaamaurukehu
Did you write a message to Seeker with your criticism?
[opens the locker]
"All hail J!"
[mind is blown]
For the Cantor set you do not divide it in half, you take out the center third of each piece.
Fractals do not have to be self-similar!!
ua-cam.com/video/gB9n2gHsHN4/v-deo.html&vl=en
2:04 you just explained the coastline paradox.
"We have 19048738429 km in coastlines"! And it's actually true
@@TheHellogs4444 yes but it grows the more you zoom in and decreases the more you zoom out. I know there is an agreed way to measure them but nonetheless the paradox exists.
It looks like a Triforce inception. A Triforce within a Triforce within a Triforce...(Within a Triforce)
Triforce multi-verse proven by science
This is how you get tons of damage man
I've never heard of it called triforce I've always known it as serpinkskis triangle
I would listen to you make sense of this for hours.
It's like "shocking" a piece of wood with electricity and getting cool patterns
Anyone that's played Zelda knows that's not a Serpenski Triangle...it's a TRIFORCE :-p
well yes but actually no
Neurolink ?
:)
:^)
Dark link
@@dalton2578 w==3
^ heh
It's not just wild
It's: *_Breath of the_*_ wild_
I demand the immediate release of the trapped electrons!
This is just an excellent video. It goes above and beyond the subject, it is informative and fun!
Fractals are amazing and since you need a minimum level of technology, mathematics to visualise them. I think they are important and useful.
Cmdr Benkai or do some good acid
But Fractals aren't Typically Self Similar
Yeah I wish they did their research
@@cirlex5104 Shhh... don't melt the snowflakes.
Thank you 3b1b
Today's fact: The Sun City Poms is a cheerleading squad in Arizona that only people 55 or older can join.
Please tell me their coach is English.
I bet they eat a lot of cornflakes
Facterino Commenterino
Sounds sexy
Today’s Fact: I don’t give a shit because the comment has nothing to do with the topic of the video.
K G Today’s fact: that’s the joke you inbred stain
I work as a currency trader and fractals appear in an almost ever repeating pattern. As you zoom into the volume /price data, the same fractals appear inside fractals until you zoom into the smallest measurement of price, a tick.
By using this geometry, traders are able to anticipate price movements.
What's curious to me is why the fractals occur in the first place. These patterns are everywhere, what's weird is they don't just show up in stock prices, you can pick any data from the weather to school attendance figures and the same fractals exist.
From a fundamental perspective, the price of an asset is influenced by human behaviour. However, the presence of these fractals allows us to build machine learning algorithms to trade the markets.
The brain is a fractal antenna.
The more and more we discover and learn I wonder what limit we are ever gona reach seeker somtimes seems like final fantasy episode explained in short
The Mandlebrot is iterative, not recursive.
Shhh, snowflakes think cute=science don't melt their entire reality.
To program fractals, you have to make the formula recursive. So yes, actually the Mandelbrot set is recursive (and iterative).
@@badlaamaurukehu shh people with small dicks feel the need to call everyone a snowflake
@@Matt_Legler you're doing a transformation...
@@Epicvampire800 shh snowflakes also feel the endless need to White Knight for others.
This is just the Tri-Force...
No it's just a Sierpinski Triangle
I'm calling it now, this formula will be used in world creating in future video games
This is probably the first implementation of every data visualization class.
Is that the tri force?
No it's a Sierpinski Triangle
@@TheOmniWasher breh that isnt a woooosh
Jew star
The woman presenting this is so cute! (Yeah, I kinda followed the science, and was interested, but I am concerned about interfacing electronics with the human brain.)
So refreshing to have a female presenter that doesn't up talk. Very clear easy to listen to accent.
Zelda’s world confirmed. Also, I clicked because of the TriForce.
"you take a line and divide it in half" sees a line being split in to two 1/3 pieces over and over again
Maren + Fractals + Quantum Science = Heartblow
Triforce existence confirmed
The triangle is the ultimate form of reality... The Tri-Force...
How about mimbari triluminary in Babylon 5 lol
@@neilmurphy966 Wow! It's a strange one... The symmetry got me confused.
*Legend of Zelda exist*
Mathhhhhhhh is everywhere. That was so cool! And you covered background wonderfully. Great scicomm writing.
What is your target audience?
Chickens? Hire a better host one who doesnt cluck
shut up loser lmao
starts off with non factual definition of a fractal... it doesn't have to be self similar by means of smaller versions within itself...
I don't know how this got left in but it really should be corrected, teaching wrong is worse than not teaching
synonyms:
the Zelda fractal
the Triforce fractal
You can see really complex fractals while under the influence of psychedelics ✨😌✨
Exactly!
To explain the infinite perimeter and finite area, think of this:
There are two kinds of infinities:
The small infinity
1,2,3,4,5,6,7,8.......
And the large infinity
1.
1.0000000000......1
1.0000000000......2
1.0000000000......3
............
1.9999999999......9
2.
It would take an infinite amount of time to reach the number two in this example.
Fractals have the larger infinity for its perimeter, which is why it would take forever to measure as it keeps getting smaller and smaller to an infinite amount of decimals (as a number).
I love I found this video.
People seem to be afraid of my image like its some kind of satanic symbol.
I took this shop class, when I was young, and our instructor assigned us a special project. He had us make these small bridges out of paper. We all came up with our shapes. I don't even remember what my shape was. After we were done we put the strength of the bridges to the test by stacking weight on them. The weights were textbooks. Most of our bridges collapsed from one book. Then, there was this student who made the structure of triangles holding the bridge up. We kept stacking books on it and it finally give at around five books.
Imagine this microscopic shape building up to a macroscale bridge support.
You use 3blue2browns image of a fractal, but didn't even watch the video where the title was "Not al fractals are self similar"
The TRIFORCE. I knew it. Summon the Hero of Time!
Great but fractals aren't typically self-similar though
*pretends that wasn't from another youtube video*
Could it be tactical, or even practical, to try and fractal a pterodactyl?
No more bandwidth problems when hooking our brains up to a computer
Who else clicked this because of the triforce fractals
Now I remember Ant Man
Frak'n Fractals can really Frak with your mind.
nice article. I've known about fractales for awhile now, but i didn't know about fractional dimensionality. I'm an intrigued.
Maybe crop circles are just aliens having fun.
An infinite line has infinite "perimeter" and zero area. Blew you mind eh?
Torricelli's trumpet.
Planck scale... But infinite sounded good right?
It blows my mind because its not intuitive, if the perimeter is expanding shouldn't there be more area(however miniscule) as it grows?
@@madscientistshusta , with the Koch snowflake as its perimeter increases its area does too, but its area approaches the limit of a circle.
If you add 1/2 + 1/4 + 1/8 + 1/16 ... it always gets bigger but approaches 1, never quite reaching it.
The *Menger sponge* is like a 3D Sierpinski triangle.
It starts with a cube, and exponentially smaller cubes are removed ad infinitum.
It has infinite surface area, occupies a volume, yet has zero volume.
It didnt. Because an infinite line is not a closed figure so there is not much point in talking about its area.
She's so cute and smart
Thirsty ass.
She's reading off a script
Just like heather Swanson
A J P ???
I feel like I'm starting to understand
no fractals are typically not self-similar
ua-cam.com/video/gB9n2gHsHN4/v-deo.html&vl=en
I cannot wait to modify my body with fractal implants ...
Everyone else be like, mandelbrot sets aint self similar and im just here zooming into my 17th mandelbrot recursion.