This maybe applies to the area of a Koch snowflake. But the perimeter actually diverges. Like the harmonic series: 1/2+1/3+1/4...=infinity. It's easy. After zero steps the Koch snowflake equals an equilateral triangle with perimeter=3. After one step perimeter=3*4/3=4. After two steps=3*16/9=5,333... And after n steps 3*4^n/3^n. So because 4^n diverges faster than 3^n it means that the expression 4^n/3^n also diverges and thus the perimeter of the Koch snowflake does also...
Very very very underrated video... This is a complex study involving years of research, yet communicated in a perfect, simple as well as interesting way...
1:18 the perimeter is unbounded doesn't follow from the equation shown, which doesn't account for decreasing side length. The math still works out if you write out the full equation: lim_n->inf ( 3 * 4^n / 3^n ) = lim_n->inf ( 3 * (4/3)^n ) = inf Nitpicky but needed if you want to do the same thing to show finite area.
Yes the limit of the sides >0. but the number of the sides approaches infinity. The key is that the sides approach infinity faster than the side length approaches zero. The perimeter increases by a factor of 6 with each iteration. Therefore the perimeter becomes infinite.
Don't let us fool you. We know way less than we want you to think we know. Every answer brings many more questions - which continues on indefinitely ...just like fractals. So remember: no one knows all the answers; even if we try to sound like we do.
It gets worse. I'm a simpleton even in spite of the fact that i understand fractals. You could say that my stupidity is a little like a fractal, being both infinite and contained.
You must all be " highly advanced intellectual individuals" and you are ahead of all humanity..jk you all aren't important and nobody knows any of you, you are nothing in the scheme of the universe and have no talents so you try to convince yourself that you are "smart" to make you forget the fact that nothing you do is important and nothing you do will ever matter
First time ever hearing about fractals and the statement "infinite perimeter but a finite area" has broken my brain ! Can someone think of an explanation that a dummy like me would understand? Also, 3:49 if you like science and comedy check out the British satire show "Look Around You," it pokes fun at the educational science videos we used to get in the 70's/80's, it's really weird and funny.
I can. Think of measuring a coastline. If you measure it in a broad map of the united states it will be a certain length based on the scale. But if you zoom in the scale, there are more fine details of the coastline that wouldn't appear in the less zoomed out scale, thus adding to the length of the coastline. Basically the more you zoom into the coastline, the more length it has growing to infinity as you zoom in. This is why coastlines and rivers have variable lengths according to the zoom, and why its impossible to truly measure the lengths of these objects.
*Love the fact that I'm able to easily understand every word you spoke. Thank you. I really enjoyed the way you laid all those facts out! I'm looking forward to seeing you again.* 👍😃👍😃👍😃👍😃👍😃👍😃👍
@@cookiedoughl_l were just talking surface area here, has nothing to do with the amount of matter, the matter stays the same while just the surface area increases. Everywhere we look infities are around us.
What would be the best whiskers pattern for a Channel Master TV antenna Yulia ?? The CM antenna has whiskers that are V-shaped like when you give the peace sign with your fingers. I am using the antenna to receive VHF-UHF signals for free to the air TV reception. Thanks
0:55 you mentioned that we can draw a fractional dimension on the computer using mathematical equations. I request you to make a tutorial on this or could you just tell me what software to use to make the graphs? it would be great help.
Thanks for your interesting explanation. After watching and doing some additional reading, I'm still not sure about my original question: is "fractal cauliflower" really a fractal or is it based on the golden ratio? Or is it an example of the Fibonacci sequence?
Yes, all plant life uses the golden ratio. Its explanation is quite apparent. And yes, they either use fibonacci or lucas numbers (sequence similar to fibbonaci)
2:23 it seems like the fractal antenna would produce a bunch of garbled noise because it's picking up FM, AM, TV, and whatever other signals there are. If I were to play an FM radio station and an AM radio station together, I wouldn't hear either one clearly. 🤔
i get that we can zoom to molecules or even plank size, but there is no smaller thing than quarks, so how can we zoom even more? maybe if we talk about universe zooming out and it beying inifine i would get, but how can some fractal be zoomed in infinitely?
Its all theoretical, the equation states that the scale of replication is exponentially smaller each time: 0.1,0.01,0.001 and so on.... in theory you can do that forever without exiting your finite area. But thats only for a drawing in 2D. If that object had mass it couldnt exist. It would collapse on itself, kind of like a black hole. You cant keep cramming mass infinitely in a finite perimeter. Thats just not how the universe works. Inifinite math isnt really useful in everyday life
just increasing number of sides doesn't make perimeter grow (or as Greek said: Achilles can't catch a turtle); you also need to show it's length increased, in this case it is, so result is still correct
So is it like a tube, its the same diameter or circle but the pipe can go on for ever in length. thats what my mind thinks when you zoom in and loops the same thing we are pushing forward in space while the fractal is taking up like a square on the wall?
The perimeter of the snowflake isn't infinite because it has infinite sides, rather it's because the sum of the sides is infinite. There are infinitely sided shapes that do not have infinite perimeter, the easiest to think of would be a circle. There is a way to mathematically think of a circle as being a polygon with n sides, but in a circle's case, when n is infinity, the sides would be infinitely small. And when you sum them it would sum to a finite number.
No, using basic geometry we can determine that it's area is infinite. It can be proved quite easily by basic patterns of the simplicity of it and the limit of the function that derives it, ending up to infinity.
Using the snowflake example, the snowflake's area wouldn't be finite if you didn't draw a circle around it. It would keep growing indefinitely wouldn't it? Not just the perimeter but the inside (area), too.
I’m not surprised the fractal antenna came from somebody who wanted to work around their problems. It’s the same kind of logic that motivated a lot of inventions in the past.
If we write Pi=(F+U), Where F= Almost accurate value of Pi, and U=Remain uncertain value of Pi, Then we calculate Circumference(C)= 2(F+U)r= 2Fr+2Ur where 2Fr is a finite circle and 2Ur is an unknown shape which has a geometrical value, but not theoritical value, So U is another part of Pi and it has very small value with the help of radius r, it will look like straight line which carries unknown shape in it, So is it possible that everything you see is kind of unknown fractal of 2Ur because of approximity?????????????? Please reply
how fractal antenna pic up more and more signals after first iteration ----- one type(this is only one type) after second iteration ---- another type signal ,now in second iteration it can not pic up first iteration type signals the how can we say it pic up more number of signals
Wouldn't the perimeter also be finite as the side lengths are constantly getting smaller, so we could just use the sum of an infinite geometric sequence?
This video is quite misleading. The proper definition of a fractal, at least as Mandelbrot wrote it, is a shape whose "Hausdorff dimension" is greater than its "topological dimension". Therefor not all fractals are self similar. Besides, no. In our world perfect fractals cannot exist.
For self similar fractals it seems a little misleading when people say it has a finite area with an infinite perimeter. This is not true. By saying this you are saying that the shape has another dimension to hold this finite area, which would make it not self similar. It's like filling in a Koch-snowflake and calling it self similar. If we then consider it's topological dimension to be the dimension up to it being non-self-similar, than it would have infinite area as well as infinite perimeter.
The maths of fractals are not exactly easy: One way that fractals are different from finite geometric figures is how 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. Analytically, most fractals are nowhere differentiable. An infinite fractal curve can be conceived of as winding through space differently from an ordinary line - although it is still topologically 1-dimensional, its fractal dimension indicates that it also resembles a surface...
This is like adding 1/10th to the previous number like 1+0.1+0.01+0.001 and never making 2
Thank you, that actually helped it make sense!
This maybe applies to the area of a Koch snowflake. But the perimeter actually diverges. Like the harmonic series: 1/2+1/3+1/4...=infinity. It's easy. After zero steps the Koch snowflake equals an equilateral triangle with perimeter=3. After one step perimeter=3*4/3=4. After two steps=3*16/9=5,333... And after n steps 3*4^n/3^n. So because 4^n diverges faster than 3^n it means that the expression 4^n/3^n also diverges and thus the perimeter of the Koch snowflake does also...
Like an Asymptote?
thx
h
You deliver a clear and understandable message. Nice job!
Everything is made of math.
Acid taught me that.
acid makes you seek fractals for some reason...
It's more likely to be the brain itself
@@besserwisser4055 Breaks down reality/the simulation
not this bullshit again..
why would something that is part of simulation, when consumed, disrupt the simulation?
A short video, but with large amounts of clear precise information on the subject. Extremely well done.
Enough love triangles! Let's have a LOVE FRACTAL!
Moepowerplant real shit!
Christopher Nolan, take a note
That would be a mess, to the Nth power! Lmao!
No thanks thats just infinite drama
quintiplesome?
Well organized, informative and straight to the point. Thanks MIT and Yuliya.
drikast 😱😱😱
Very very very underrated video... This is a complex study involving years of research, yet communicated in a perfect, simple as well as interesting way...
1:18 the perimeter is unbounded doesn't follow from the equation shown, which doesn't account for decreasing side length. The math still works out if you write out the full equation:
lim_n->inf ( 3 * 4^n / 3^n )
= lim_n->inf ( 3 * (4/3)^n )
= inf
Nitpicky but needed if you want to do the same thing to show finite area.
shut up nerd
@@chronicsnail6675 wtf you don't even have an idea about this lol
Yes the limit of the sides >0. but the number of the sides approaches infinity. The key is that the sides approach infinity faster than the side length approaches zero. The perimeter increases by a factor of 6 with each iteration. Therefore the perimeter becomes infinite.
Listening to smart people is difficult for a simpleton.
Don't let us fool you. We know way less than we want you to think we know. Every answer brings many more questions - which continues on indefinitely ...just like fractals. So remember: no one knows all the answers; even if we try to sound like we do.
+metalwheelz your my favourite kind of person
Dara the-opinionated-jerk they're are my kind of favorite kind of person too.
It gets worse. I'm a simpleton even in spite of the fact that i understand fractals. You could say that my stupidity is a little like a fractal, being both infinite and contained.
You must all be " highly advanced intellectual individuals" and you are ahead of all humanity..jk you all aren't important and nobody knows any of you, you are nothing in the scheme of the universe and have no talents so you try to convince yourself that you are "smart" to make you forget the fact that nothing you do is important and nothing you do will ever matter
Im tripping on mushrooms right now and my mind is blown. Its so beautiful.
NOICE
I wish i was trippinng on mushrooms right now :(
Wow wow wo ! You are making this stuff understandable which seemed so beyond my reach. Thank you for the great explanation!
First time ever hearing about fractals and the statement "infinite perimeter but a finite area" has broken my brain !
Can someone think of an explanation that a dummy like me would understand?
Also, 3:49 if you like science and comedy check out the British satire show "Look Around You," it pokes fun at the educational science videos we used to get in the 70's/80's, it's really weird and funny.
I can. Think of measuring a coastline. If you measure it in a broad map of the united states it will be a certain length based on the scale. But if you zoom in the scale, there are more fine details of the coastline that wouldn't appear in the less zoomed out scale, thus adding to the length of the coastline. Basically the more you zoom into the coastline, the more length it has growing to infinity as you zoom in. This is why coastlines and rivers have variable lengths according to the zoom, and why its impossible to truly measure the lengths of these objects.
Thanks for delivering such a clear and concise explanation of fractals. Well done!
Thank you, Yuliya, and thank you MIT! this was great!!!!!!!!!!!!!
Julia, This was the best video I've ever seen on Antennas and was exactly what I was looking for.
That helped straighten things out. Thank you Yuliya. I was kinda confused on the iterations in Jurassic Park, but you explained it so simply.
*Love the fact that I'm able to easily understand every word you spoke. Thank you. I really enjoyed the way you laid all those facts out! I'm looking forward to seeing you again.* 👍😃👍😃👍😃👍😃👍😃👍😃👍
If fractals have infinite perimiter, are these so-called "fractal antennas" only objects that *resemble* fractals?
I think so. it wouldn't be physically possible to have a shape that goes on forever in the real world.
@@cookiedoughl_l _man made that is_
@darqoni no i mean in general. there isnt infinite matter so nothing can constantly go forever
@@cookiedoughl_l were just talking surface area here, has nothing to do with the amount of matter, the matter stays the same while just the surface area increases. Everywhere we look infities are around us.
yes....
you are so clear you've blown my mind into fractals
Fantastic explanation in an engaging video. Thanks Yuliya!
Thanks for explain me this loop how was working.
I have trouble understanding this on my textbook. Thank you for a concise content!
What would be the best whiskers pattern for a Channel Master TV antenna Yulia ?? The CM antenna has whiskers that are V-shaped like when you give the peace sign with your fingers. I am using the antenna to receive VHF-UHF signals for free to the air TV reception. Thanks
Thank you for making this video. It's crystal clear!!!
Humans are like fractals, we occupy a finite area, yet we have infinite potentials inside.
true dat
Bro...u have no idea how deep that is...
@@Isaac-mi5wq Thanks man, stay safe :D
Not like, they are. Society is a chaotic system chasing it's owl tail.
Still some are lazy as hell 😂
very nice video. Is there in any classification in fractals? is it possible to see an image identify a fractal representation in that image?
0:55 you mentioned that we can draw a fractional dimension on the computer using mathematical equations. I request you to make a tutorial on this or could you just tell me what software to use to make the graphs? it would be great help.
Try desmos.
3:22 what river is that? It seems too perfect to be real
This is one of the best explanations of fractals.
Nice work Young one!!! Beautifully done! I learned something today!
Thanks for your interesting explanation. After watching and doing some additional reading, I'm still not sure about my original question: is "fractal cauliflower" really a fractal or is it based on the golden ratio? Or is it an example of the Fibonacci sequence?
Yes, all plant life uses the golden ratio. Its explanation is quite apparent. And yes, they either use fibonacci or lucas numbers (sequence similar to fibbonaci)
Kudos for this video! You actually helped me understand fractals! After watching 4-5 other videos. 👏👏
This is awesome. Thank you for the video!
got motivated by this beautiful recursion,still working on it
Amazing. Just the explanation for the purpose of fractals that I needed.
Julia is the perfect name for a teacher who explains fractals
2:23 it seems like the fractal antenna would produce a bunch of garbled noise because it's picking up FM, AM, TV, and whatever other signals there are. If I were to play an FM radio station and an AM radio station together, I wouldn't hear either one clearly. 🤔
Language has infinite perimeter and finite area (fixed amount of words, infinite combinations).
Tony Marsh well said
I disagree. If you have finite words, you have a finite number of ways you can combine those words.
Jenah Dooley yes I thought that too the permutations are finite
+Jenah Dooley
This would apply only if each word could be used a given amount of times
Which is never the case (except for style exercises)
lol no
3:23 That's not a river system, its a mandelbrot fractal but coloured to look like a satellite picture.
i get that we can zoom to molecules or even plank size, but there is no smaller thing than quarks, so how can we zoom even more? maybe if we talk about universe zooming out and it beying inifine i would get, but how can some fractal be zoomed in infinitely?
Its all theoretical, the equation states that the scale of replication is exponentially smaller each time: 0.1,0.01,0.001 and so on.... in theory you can do that forever without exiting your finite area. But thats only for a drawing in 2D. If that object had mass it couldnt exist. It would collapse on itself, kind of like a black hole. You cant keep cramming mass infinitely in a finite perimeter. Thats just not how the universe works. Inifinite math isnt really useful in everyday life
yeah thats what i thought, but some people thinks this explains infinity easily :D
just increasing number of sides doesn't make perimeter grow (or as Greek said: Achilles can't catch a turtle); you also need to show it's length increased, in this case it is, so result is still correct
Education channels:
I fear no man.
But that thing
*fractals*
It scares me..
Nicely explained!
extremely well explained
I loved your channel, is very good. I am Brazilian and I manage to understand what you say , because I love videos like this. Arranged a new fan
+Amanda Mata Uhul
Excellent presentation!!
Thank you.......I actually understood this ......best video on thes explanation of fractal
“infinite perimeter, but a finite area” is a great summary. just as humans are. 1:38
Great video and explanation! Thanks!
So is it like a tube, its the same diameter or circle but the pipe can go on for ever in length. thats what my mind thinks when you zoom in and loops the same thing we are pushing forward in space while the fractal is taking up like a square on the wall?
This presenter is excellent. Thanks for explaining it so well.
Thank you for the information
The perimeter of the snowflake isn't infinite because it has infinite sides, rather it's because the sum of the sides is infinite. There are infinitely sided shapes that do not have infinite perimeter, the easiest to think of would be a circle. There is a way to mathematically think of a circle as being a polygon with n sides, but in a circle's case, when n is infinity, the sides would be infinitely small. And when you sum them it would sum to a finite number.
No, using basic geometry we can determine that it's area is infinite. It can be proved quite easily by basic patterns of the simplicity of it and the limit of the function that derives it, ending up to infinity.
I’m thinking a Zeno’s paradox situation. But I’m not a mathematician.
How does it have finite area if the perimeter increases with each repetition?
Nice video, I loved every second of it :)
Fantastic !!!! Well done !
When you show up for a relatively simple yet elegant concept and then suddenly it dawns on you.
Using the snowflake example, the snowflake's area wouldn't be finite if you didn't draw a circle around it. It would keep growing indefinitely wouldn't it? Not just the perimeter but the inside (area), too.
Really insightful
Can you figure out the asymptote of the reach limit of the fractal triangle?
I loved your video, thank you!
Such a nice video!
2:41 When the math starts copying the 5th Dimension scene from Interstellar
Nice Educational Video!
You did an awesome job
thanks this video helped for my examination
Muy buen documental sobre los fractales...gracias..
Saludos
👍✌️✌️
As Edwin Starr would say, “I said, fractal, huh (good God, y'all). What is it good for? Absolutely nothing, just say it again.”
Nothing
When compared to a bow-tie antenna, how much more gain will the fractal be able to get ???
I’m not surprised the fractal antenna came from somebody who wanted to work around their problems. It’s the same kind of logic that motivated a lot of inventions in the past.
Thank you for the video, very well explained 🙏🏻👏🏻
Great video. Bravo
Thank you Julia❤
Awesome! :) Keep at it!
how do u make a solid finite object like a attena shaped like an infinite never ending one?
well described.Keep going
If we write Pi=(F+U), Where F= Almost accurate value of Pi, and U=Remain uncertain value of Pi,
Then we calculate Circumference(C)= 2(F+U)r= 2Fr+2Ur where 2Fr is a finite circle and 2Ur is an unknown shape which has a geometrical value, but not theoritical value, So U is another part of Pi and it has very small value with the help of radius r, it will look like straight line which carries unknown shape in it,
So is it possible that everything you see is kind of unknown fractal of 2Ur because of approximity?????????????? Please reply
very helpful thank you!
It's amazing how many ppl get fractals wrong. Self similar is neither a requirement nor determinant for fractals.
So awesome and true. Thank you.
Thank you Dearest!!!! Love this❤❤❤
Whoa, the Koch snowflake is pretty basic but then the video escalates to using fractals for signal antennae, very coooooool
I feel like I learnt more than anyone, though I literally know everything about this already
how fractal antenna pic up more and more signals
after first iteration ----- one type(this is only one type)
after second iteration ---- another type signal ,now in second iteration it can not pic up first iteration type signals
the how can we say it pic up more number of signals
Great video i learned alot
Wow this is an excellent video! :) You are going to be an excellent mathematician!
Very cool video
Wouldn't the perimeter also be finite as the side lengths are constantly getting smaller, so we could just use the sum of an infinite geometric sequence?
Nicolas Castaneda google the "coastline paradox" for an explanation on that
How is it possible to exist an infinite perimeter and limited area?! Wow! Amazing!! Mind blown!!!!! Absolutely! 😻
This video is quite misleading. The proper definition of a fractal, at least as Mandelbrot wrote it, is a shape whose "Hausdorff dimension" is greater than its "topological dimension". Therefor not all fractals are self similar. Besides, no. In our world perfect fractals cannot exist.
For self similar fractals it seems a little misleading when people say it has a finite area with an infinite perimeter. This is not true. By saying this you are saying that the shape has another dimension to hold this finite area, which would make it not self similar. It's like filling in a Koch-snowflake and calling it self similar. If we then consider it's topological dimension to be the dimension up to it being non-self-similar, than it would have infinite area as well as infinite perimeter.
@@aaronspeedy3087 thank you I appreciate that! 🪐🧝🤍🌱✨🌍
Who came here from the oneoddsout
1OddsOut! Never heard of 1OddsOut...
me
samee
Meeee!!!!
i did
thanks for the vid
Well done!
thanks a lot. that was well explained
bfhgj
Can someone explain how a river system is a fractal? I dont follow that part. Or maybe i'm off on the definition of fractal.
This girl is very pleasant to watch and listen to 😍
The maths of fractals are not exactly easy:
One way that fractals are different from finite geometric figures is how 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.
Analytically, most fractals are nowhere differentiable. An infinite fractal curve can be conceived of as winding through space differently from an ordinary line - although it is still topologically 1-dimensional, its fractal dimension indicates that it also resembles a surface...
This is so trippyyyyyyy
this is so clear than my mind blown
good one.. thanks
Interesting video