What Is A Fractal (and what are they good for)?

Рет қаралды 677,669

9 жыл бұрын

Fractals are complex, never-ending patterns created by repeating mathematical equations. Yuliya, a undergrad in Math at MIT, delves into their mysterious properties and how they can be found in technology and nature.
Learn more about all the stuff that MIT is doing and researching with fractals here: / what-is-a-fractal-and-...
----------
Find us online!
Facebook: / mitk12
Twitter: / mitk12videos
k12videos.mit.edu
----------
made with love at MIT
Creative Commons: CC BY-NC-SA, MIT
k12videos.mit.edu/terms-and-co...
Hosted by: Yuliya Klochan
Written by: Elizabeth Choe & Yuliya Klochan
Additional Scripting by: George Zaidan
Content Reviewer: Dr. Kwang Don Choe
Executive Producer & Doodles: Elizabeth Choe
Director: George Zaidan
Camera: Adam Morrell
Editor & Motion Graphics: Per Hoel
Theme song: Anthony Thomas & Neil Aggarwal
Music: “Unanswered Questions” by Kevin Macleod (incompetech.com/music/royalty-...)
Fractals in nature pictures: commons.wikimedia.org/wiki/Fil... and theyinfactor.files.wordpress.... (NASA/JPL-Caltech) and en.wikipedia.org/wiki/User:Tch... and upload.wikimedia.org/wikipedia...
Menger Sponge visualization from • Menger Schwamm (in Ble...
DNA chromatin fractal globule visualization courtesy of Maxim Imakaev and the Mirny Lab at MIT (mirnylab.mit.edu/)
Special thanks:
MIT Radio Club, Prof. John Essignmann & Ellen Essignmann, Dr. Kwang Don Choe, Max Imakaev

Пікірлер: 555

@casperado666 8 жыл бұрын

"Infinite perimeter but finite area" Mind blown

@MH.CLundy-Maurer 8 жыл бұрын

I'm an 8th grader trying to learn scientific and mathematical questions and problems :(

@giocodecorner 7 жыл бұрын

I think in this case both perimeter and area are infinite but bounded, hence not finite because it cannot be measured..

@Something_Disgusting 5 жыл бұрын

Gabriel's cake has finite mass but infinite volume...

@michaelwalters4749 5 жыл бұрын

@@throwaway3460 whata dick. I "Calculus bruh" do you even "respect bruh? " there's a way to teach without being an ass.

@giocodecorner 5 жыл бұрын

@@throwaway3460 ahaha thanks for the explanation

@chrismcguirk4031 7 жыл бұрын

This is like adding 1/10th to the previous number like 1+0.1+0.01+0.001 and never making 2

@RetroBackslash 6 жыл бұрын

Thank you, that actually helped it make sense!

@steffen5121 6 жыл бұрын

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...

@rick2267 5 жыл бұрын

Like an Asymptote?

@andyfung7878 5 жыл бұрын

thx

@palmtop_studios 5 жыл бұрын

@richardyoung5429 8 жыл бұрын

You deliver a clear and understandable message. Nice job!

@sonofgodsdad3227 5 жыл бұрын

Everything is made of math. Acid taught me that.

@pablolongobardi7240 5 жыл бұрын

acid makes you seek fractals for some reason...

@besserwisser4055 5 жыл бұрын

It's more likely to be the brain itself

@gyros69420 5 жыл бұрын

@@besserwisser4055 Breaks down reality/the simulation

@besserwisser4055 5 жыл бұрын

not this bullshit again..

@besserwisser4055 5 жыл бұрын

why would something that is part of simulation, when consumed, disrupt the simulation?

@Moepowerplant 5 жыл бұрын

Enough love triangles! Let's have a LOVE FRACTAL!

@jakeyjingles7521 4 жыл бұрын

Moepowerplant real shit!

@raydalio4172 4 жыл бұрын

Christopher Nolan, take a note

@Dr__Feelgood 4 жыл бұрын

That would be a mess, to the Nth power! Lmao!

@Urbancohort337 4 жыл бұрын

No thanks thats just infinite drama

@squiffy7559 3 жыл бұрын

quintiplesome?

@leomasciale5127 2 жыл бұрын

A short video, but with large amounts of clear precise information on the subject. Extremely well done.

@drikast 7 жыл бұрын

Well organized, informative and straight to the point. Thanks MIT and Yuliya.

@davidkccheng1975 7 жыл бұрын

drikast 😱😱😱

@TarePandaHelp 4 жыл бұрын

Im tripping on mushrooms right now and my mind is blown. Its so beautiful.

@xhocheinsdurchmol 4 жыл бұрын

NOICE

@notname4414 2 жыл бұрын

I wish i was trippinng on mushrooms right now :(

@tiffanyzyp6639 5 жыл бұрын

Wow wow wo ! You are making this stuff understandable which seemed so beyond my reach. Thank you for the great explanation!

@Logjam5 9 жыл бұрын

Listening to smart people is difficult for a simpleton.

@metalwheelz 8 жыл бұрын

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.

@daraiekana2688 7 жыл бұрын

+metalwheelz your my favourite kind of person

@stewartsaurus5796 7 жыл бұрын

Dara the-opinionated-jerk they're are my kind of favorite kind of person too.

@Krazycutiegurlxxx 7 жыл бұрын

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.

@jakestephano3145 7 жыл бұрын

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

@KILLERSMITH111 3 жыл бұрын

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...

@mddell58 5 жыл бұрын

*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.* 👍😃👍😃👍😃👍😃👍😃👍😃👍

@RecruitingMaven 6 жыл бұрын

Thanks for delivering such a clear and concise explanation of fractals. Well done!

@emilyanncarman 6 жыл бұрын

Kudos for this video! You actually helped me understand fractals! After watching 4-5 other videos. 👏👏

@samarthraizada 7 жыл бұрын

That helped straighten things out. Thank you Yuliya. I was kinda confused on the iterations in Jurassic Park, but you explained it so simply.

@pierangelabarbanti7695 8 жыл бұрын

Thank you, Yuliya, and thank you MIT! this was great!!!!!!!!!!!!!

@halknowles1791 8 жыл бұрын

Fantastic explanation in an engaging video. Thanks Yuliya!

@Jamie-my7lb 8 жыл бұрын

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.

@chronicsnail6675 4 жыл бұрын

shut up nerd

@amsyarothman4312 4 жыл бұрын

@@chronicsnail6675 wtf you don't even have an idea about this lol

@garydegeorge5965 3 жыл бұрын

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.

@_valles3438 6 жыл бұрын

Thank you for making this video. It's crystal clear!!!

@The.Pickle Жыл бұрын

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.

@MrRussianDollOfficial 7 жыл бұрын

Amazing. Just the explanation for the purpose of fractals that I needed.

@karedlavaishnavi2118 5 жыл бұрын

you are so clear you've blown my mind into fractals

@ramjet4025 2 жыл бұрын

Julia, This was the best video I've ever seen on Antennas and was exactly what I was looking for.

@marlonlyn2719 3 жыл бұрын

This is awesome. Thank you for the video!

@nonsenseprogram8857 6 жыл бұрын

got motivated by this beautiful recursion,still working on it

@blogguiajapao7732 8 жыл бұрын

Great video and explanation! Thanks!

@sadeceyoutube2925 Жыл бұрын

Thanks for explain me this loop how was working.

@tmkim 2 жыл бұрын

Nice work Young one!!! Beautifully done! I learned something today!

@benjhanssen31 Жыл бұрын

I have trouble understanding this on my textbook. Thank you for a concise content!

@ArshiMorshi Жыл бұрын

Thank you for the video, very well explained 🙏🏻👏🏻

@johnmeye 4 жыл бұрын

Excellent presentation!!

@paramoreguate 6 жыл бұрын

Nice video, I loved every second of it :)

@brokenbrain3523 2 жыл бұрын

Thank you for the information

@AnkushSharma-zv5hv 7 жыл бұрын

extremely well explained

@AlisonBryen 5 жыл бұрын

Nicely explained!

@pappsco54 5 жыл бұрын

Thank you.......I actually understood this ......best video on thes explanation of fractal

@spade4acer 7 жыл бұрын

If fractals have infinite perimiter, are these so-called "fractal antennas" only objects that *resemble* fractals?

@junecroft8435 7 жыл бұрын

I think so. it wouldn't be physically possible to have a shape that goes on forever in the real world.

@Darqoni 5 жыл бұрын

@@junecroft8435 _man made that is_

@junecroft8435 5 жыл бұрын

@darqoni no i mean in general. there isnt infinite matter so nothing can constantly go forever

@dudel39 5 жыл бұрын

@@junecroft8435 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.

@BDF30 5 жыл бұрын

yes....

@VIRGONOMICS Жыл бұрын

Fantastic !!!! Well done !

@hiteshvaidya3331 7 жыл бұрын

very nice video. Is there in any classification in fractals? is it possible to see an image identify a fractal representation in that image?

@asprywrites 2 жыл бұрын

I loved your video, thank you!

@samidelhi6150 4 жыл бұрын

Really insightful

@fcass 3 жыл бұрын

So awesome and true. Thank you.

@jeremytorres1715 4 ай бұрын

This is one of the best explanations of fractals.

@adamross4295 7 жыл бұрын

Great video. Bravo

@thepessimist910 6 жыл бұрын

You did an awesome job

@userdeleteddd4633 3 жыл бұрын

very helpful thank you!

@LoganKM76 4 жыл бұрын

This presenter is excellent. Thanks for explaining it so well.

@tarunganesh8124 6 жыл бұрын

thanks this video helped for my examination

@romuloabarca8150 4 ай бұрын

Muy buen documental sobre los fractales...gracias.. Saludos 👍✌️✌️

@wuukaa9079 3 жыл бұрын

Such a nice video!

@hopesouthstar4304 8 ай бұрын

Thank you Julia❤

@Chrisymcmb 7 жыл бұрын

Awesome! :) Keep at it!

@laur-unstagenameactuallyca1587 2 жыл бұрын

thanks for the vid

@naisookdeo4558 6 жыл бұрын

Great video i learned alot

@tantrika.exotica 2 жыл бұрын

Thank you Dearest!!!! Love this❤❤❤

@boatpizza2801 6 жыл бұрын

Nice Educational Video!

@PavanMehat12 6 жыл бұрын

Wow this is an excellent video! :) You are going to be an excellent mathematician!

@user-fr9jt8bt3f 4 жыл бұрын

well described.Keep going

@donvandamnjohnsonlongfella1239 6 жыл бұрын

Came to you because of the word Fractal used in a Robin Williams interview. :) THANKS ROBIN! AND THANK YOU LADY FOR explaining this to me. :)

@thesunstartstoset 9 жыл бұрын

thanks a lot. that was well explained

@amoleleleivai305 8 жыл бұрын

bfhgj

@MrAnantjain 4 жыл бұрын

good one.. thanks

@shaynefinley4231 3 жыл бұрын

Well I love fractals And u did a kickers job of describing them 👏 and two thumbs-up👍 up

@GoodMusicManiac999 5 жыл бұрын

Well done!

@victoryfirst2878 5 ай бұрын

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

@ForeverMan 8 жыл бұрын

I find this channel awesome...

@kornbread5359 4 жыл бұрын

3:22 what river is that? It seems too perfect to be real

@boorayin2773 5 жыл бұрын

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?

@user-ox4ii2bw6x 5 жыл бұрын

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)

@honestabe5153 4 жыл бұрын

Very cool video

@vexcarius7100 5 жыл бұрын

Humans are like fractals, we occupy a finite area, yet we have infinite potentials inside.

@andrewooton7275 4 жыл бұрын

true dat

@Isaac-mi5wq 3 жыл бұрын

Bro...u have no idea how deep that is...

@vexcarius7100 3 жыл бұрын

@@Isaac-mi5wq Thanks man, stay safe :D

@zerosd15ds43 Жыл бұрын

Not like, they are. Society is a chaotic system chasing it's owl tail.

@prithvirajabnave6073 10 ай бұрын

Still some are lazy as hell 😂

@UnTizioACaso1 2 жыл бұрын

Julia is the perfect name for a teacher who explains fractals

@spicebeargamingyt8660 3 жыл бұрын

Clean video, and like @casperado666 my mind is a little bit blown. I'll be sure to show off my new knowledge of fractals!

@Cam-ej1cu Жыл бұрын

Interesting video

@amandamata 9 жыл бұрын

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

@richaellr 8 жыл бұрын

+Amanda Mata Uhul

@biggerthaninfinity7604 3 жыл бұрын

Can you figure out the asymptote of the reach limit of the fractal triangle?

@dumdum6215 7 жыл бұрын

This is so trippyyyyyyy

@nevidomyvitaliy Жыл бұрын

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

@anilkumarsivarathri7928 5 жыл бұрын

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

@gayglekillgoogle9611 5 жыл бұрын

how do u make a solid finite object like a attena shaped like an infinite never ending one?

@syntrexfpv1347 2 жыл бұрын

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?

@mehersingh3010 3 жыл бұрын

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.

@adityabadole7221 2 жыл бұрын

Try desmos.

@bowgyu 3 жыл бұрын

I feel like I learnt more than anyone, though I literally know everything about this already

@mentalthrillness2484 6 жыл бұрын

I love this video so much and this was so helpful. Also you are so delightful like girl I want to be your friend

@mariothane8754 6 ай бұрын

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.

@waheedrather8883 5 жыл бұрын

Which is more mind blowing Eulers sum of infinite series (e) Or concept of fractals

@giancarloandrebravoabanto7091 4 жыл бұрын

this is so clear than my mind blown

@honestabe5153 4 жыл бұрын

Thanks

@NostalgicMem0ries 6 жыл бұрын

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?

@mr.coffee6242 5 жыл бұрын

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

@NostalgicMem0ries 5 жыл бұрын

yeah thats what i thought, but some people thinks this explains infinity easily :D

@TashaHarrisTashaluvsyou 3 жыл бұрын

@hareecionelson5875 3 жыл бұрын

Whoa, the Koch snowflake is pretty basic but then the video escalates to using fractals for signal antennae, very coooooool

@coolmarchpakistan7564 2 жыл бұрын

thanks dear for xplanationa

@scootermom1791 28 күн бұрын

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. 🤔

@yongsong5745 4 жыл бұрын

nice!

@christopherparks4342 5 жыл бұрын

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.

@coleslaw7662 5 күн бұрын

“infinite perimeter, but a finite area” is a great summary. just as humans are. 1:38

@scootermom1791 2 жыл бұрын

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.