Today let’s have some

fun with fractals. To start with,

what are fractals? You’ve probably seen tons

of fractals in nature, but you just did not know

that they were fractals. One example is a

fern in this image. Here’s what a whole

fern looks like. Now if we zoom into

one leaf, look, it looks like the whole fern. Now let’s zoom in even more. And look at this. It looks like the fern again. Some flowers are also fractal. At first sight if we see

this bunch of flowers we can see that the bunch is

made up of many small flowers. But actually, if

you look closer, each of the small

flowers is made up of even smaller portions. Just the same way that

each portion makes up the small flowers,

each small flower also makes up the whole bunch. So each of these

smaller portions is in fact similar to

each of the flowers, and even to the bunch. This is also an example

of a fractal pattern. Another fractal is a broccoli. And don’t we all

really love broccoli? As you can see, each of

the heads of the broccoli resembles the

vegetable as a whole. Now that you’ve seen these

examples of fractals, you can probably spot your next

fractal in nature by yourself. So what exactly are fractals? The word fractals comes from

the Latin verb to break. Fractals are geometric

patterns in which every smaller part

of the structure is similar to the whole. How do we actually

create a fractal? Let’s first look at the

Sierpinski Triangle. It does look complicated,

but we can create this in a few simple steps. Let’s start with

the black triangle. We can mark the center of

each side of the triangle, and connect the dots to make

a new upside down triangle. We then remove this triangle

and are left with three smaller, black triangles instead of one. We take the centers of each

of the three new triangles and again connect the

dots to make three new upside down triangles. Let’s remove the upside

down triangle at the top. Look, we get three new triangles

instead of the one at the top. We can now remove the

one at the bottom left, and, finally, the one

at the bottom right. You’ll notice that each time

we remove an upside down triangle we get three

new black triangles. So now we have a total of nine

even smaller black triangles. Let’s see the triangles that we

will remove in the next step. Now we can again take the

top part of the big triangle and remove the upside

down triangles. We can continue on to

the bottom left, and then the bottom right. We already have 27

black triangles. If we keep going we can make

more and more black triangles at each step. And if we keep

doing this forever we’ll have an infinite

number of triangles, and all inside the one big

triangle we started with. Let’s have another example. This one is called

the Von Koch Curve, named after the Swedish

mathematician who came up with it. This time we start with a

line and divide it into three. We mark these points,

then take out the middle. We take a line of

equal length to the one we just removed and put it

at an angle of 60 degrees. We can now connect

the two lines, and this line happens

to be equal in length to the line we just removed. So instead of one

middle line, we have two new ones

at the same length, making the curve longer. And notice that instead

of one line segment, we now have four line segments. Now take each of these four new

lines, divide them into three, and take out the middle

from each of them. Starting from the left let’s

put in two new lines instead of the middles. You’ll see that

each of these lines is equal to the length of

the ones we just removed, which means that the length

of the curve increased again. We already have 16 line

segments to work with. Let’s take each of these

and repeat the same steps. It’s starting to look pretty. You can see that at every

step each time we add segments we make the curve longer. If we keep repeating

the steps we make the curve

longer and longer. Since we can keep

repeating this forever, the length of the

curve becomes infinite. This is what makes

fractals special. Now we can move on to a more

complicated and more beautiful structure, the Mandelbrot Set. As we can see if we

zoom in, we recognize the original structure again. If we zoom in again we again

recognize the same structure as the original image. This keeps happening as we

zoom in again and again, and at each step the image

retains its beauty as well. In this video we saw

the beauty of fractals. We showed you how to

recognize them in nature, and even how to create

some simple fractals. We hope you had some

fun with fractals.

very good video!

fractal this

フラクタル萌え

fun vid thanks

Im inlove with the speaker 🙂

Thank you very much. This is my new knowledge.

Wow! I'm a fractal of God!

no just no

Where's the fun?

Acid

everything has rhythm. amazing evolution of life!

fuck the music r.i.p ears

This is fun!!!

Thaaaanks. I had fun with fraaaactals.

check out the paisley patterns made in cloth ,its in the brain, hot wired long before computer imagine-it would take a life time to work out on paper this is old maths before technology-blows me,its all thrue nature.

The dictor has nice voice and accent.

Holy triforce

You're at risk that I kiss you to death, sweet voice.

awesome teaching style!!! 😀 soo good hehe!

2:00 TRIFORCE!!

I give you a thumbs up for opening my eyes to the fractal triforce.

What is "linth"? She says it quite a bit. Btw dont bother responding because I know the answer, I'm just being an ass.

That's not broccoli that's poccoli

"Lenth"?

Broccoli? What kind of broccoli are you eating????

WHAT COLOR IS THE DRESS?!?! Its obviously Green!

The key term is self similarity.

thats a zoomed in piece o bud , not bro colii

you can learn this all by droppin acid too, probly how she learned

I love me some fractals

is that song pi?

That's romanesco not brocoli

Had fun with fractals!:D

So basically, the Illuminati are infinite!

this made me itchy

Very informative. Nice!

I don't understand the last one

that's not broccoli

Ma te ma ti co!!!!!

1:56

You could stop there and leave it as a triforce. It's way cooler.

Where is fun?

I love broccoli

Very well done. Nice job:) Keep up the good work…

1:56 or the triforce?

What type of broccoli are you eating? That ain't broccoli.

cute and great info

How could someone down vote this? what were they looking for or let down with Fun with Fractals?

Good job, took a complicated mathmatical concept and explained it while still being fun and SHORT. The expediency of the explanation is almost as interesting as the video.

But like…. whats the point?

the triangle is triforce LEGEND OF ZELDA FRACTAL ADVENTURES CONFIRMED LOL

fucking awful

waste my fuckin time

1:55 – Razor1911 rulez!!!!!

Well done and interesting

Fractals are typically not self similar

the 'lenth' of the curve

The broccoli creeps me out

i love this so much!!

not broccoli. Cauliflower….

2:19 a triforce of triforces! Zelda FTW!

The word "fractal" comes from contracting "fractional" – because it refers to a geometric object with fractional dimension.

The triangular Swiss cheese, and the van Koch fractal, e.g., each have dimension between 1 and 2, because each has infinite length, but 0 area, all within a finite 2-ball (circular disk).

BTW, your justification for infinite length of the van Koch fractal is non sequitur. Just because it gets longer at each of infinitely many steps, doesn't guarantee that its length is infinite.

But the fact that at each step its length gets multiplied by 4/3 > 1, does, because, as n→∞, so also (4/3)ⁿ→∞.

Isnt this kind of like a ception because it has a something in something in something forever

Dumb as shit comments section omfg… broccoli, triforce, "fractals typically not self similar", try to be goddam original for crissake.

How do u make the last one mandelbrot

this is soooo fricken cool 🙂

1:51 the Triforce can teach you about fractals kids, so use this as a reason for getting a legend of Zelda game.

Actually, please don’t, because this obviously won’t work.

romanesco is even better than standard broccoly

romanesco is even more tasty than standard broccoli

1:37 tak. Nie ruski, nie amerykański *POLSKI*.

1:55 https://youtu.be/VPU4k63YLfA?t=2s

ITS NOT BROCCOLI, ITS ROMANESCO

Fractals are terrifying

beautiful

1:50 Meet the Black Triforce.

1:40 it was created before first fractals that were called fractals

Maths student here to tell you that fractals are not fun 😪

its not broccoli… its a cauliflower. Cauliflower heads resemble those in broccoli, which differs in having flower buds as the edible portion.

tayeul

Triangle fractal is just a ultra triforce to me

1:56 what happens to the triforce when ganon touches it. It shatters into billions of pieces. Great job now link has to fish up about a bazillion more shards of the triforce.

that is not what a fractal is

How it feels to chew 5 gum

I just watched this on 5 hits of really good lsd

When you say you love Broccoli, are you thinking of Dwight Schultz?

Was promised fun, got broccoli.

At least it had fractals!

Do you have to be from MIT to make this

thank you for the explanation but the vid is poorly titled and the person narrating really sounds like someone reading a paragraph or two. You didn't tell me how to have fun with them either —-I was waiting the whole time. It is the only reason I watched. Why didn't you call it "a quick explanation on what a fractal is"?

you can have fun with fractals with the help of our friend lucy

Subhanallah

(Flicking through recommended vids in 2018) is it just me or are fractals kinda scary?

uhh, plants aren't fractals, some of them are just self-similar which does not mean that they are fractals.

ThAt music at the end was disturbing

just like humans with limbs and fingers right?

0:40 What is the flower?

1:07 that’s a cauliflower….

Unti you did amazing 😄😃😀