not just you.

True lol

Its not too hard to understand just look at the seed example:)

Fortnite

Yeah pretty much

Leave it to a computer scientist to iterate a joke into the ground.

Tadesan lol

Flow🐍 is ❄flake.

Joke! XD

Good point comrade.

I would never get any shit done lmao. But on the other hand my anxiety and depression are at an all time low!

Imagine getting stuck in the those fractal shapes

Loading tips!

Genius

So underrated

uh oh

Curves!😏

O-O

I don't get it, I'm not too young, I just don't get it, someone please explain. Goddamn why does nobody believe me

Switch the first two letters

@@Steffy07 Snow flake :P

@@Steffy07 Who are you talking to?

@@NoriMori1992 you?

1:10 Triforce. I know it's "Sierpiński triangle," but I'm a gamer. It's "Triforce" to me.

+Kabitu1 It is wild, isn't it? With fractals, rather than talking in terms of area, the more natural notion seems to be fractal dimension (and I guess the measure according to that fractal dimension).

+Kabitu1 And not only does it have a non-0 area, it has an infinite circumference.

+3Blue1Brown, I'm a little late to the party, but is the box dimension of the non-zero angled curve equal to one for theta equal to some small number, then jump to 2 for theta equal to zero? Or does the box dimension approach 2 as theta approaches 0, equal zero at theta equals zero?

+

Kabitu1 you might need to slow down

I wonder what function gives the dimension when the angle is the input.

I just worked it out. It’s D=ln(4)/ln(2(1+sin(θ/2))).

Well the dimension formula is D=ln(n)/ln(s) where n=the number of copies to make the original and s=the scaling ratio of those copies. Because the seed always has 4 evenly sized line segments, n=4. The scaling ratio will be the length of the seed relative to to the lines that make it up. That length is 2(1+sin(θ/2)). Putting it all together, you get D=ln(4)/ln(2(1+sin(θ/2))).

xenontesla122 wow that is amazing

@@xenontesla122 That's a neat idea. I'll try this on my students for an illustration of what fractal dimension is.

wait till you hear about Borwein integrals

Makes a bit of sense though, because a curve is kinda like a snake, and fractals kinda flow from segment to segment.

Sounds like an EDM composer nickname

+Hwd405 Yor profile pic matches perfectly

***** gorgeous tbh

God i hope he didnt have a Spyro profile pic when he said that

Axrah at the time it was Jesy Nelson from Little Mix doing the "Balegdeh" face I think? I barely remember this comment

@@Hwd405 oh thank god, i also like how you reply to a comment to your 4 yo comment in under 1 hour

trueee

how

how is this porn?

@@Distantexplosion1076 porn = pleasure , this = pleasure pretty easy to understand

Dante Pedersen it’s a joke

@@lilyerwin8114 ok

+electrocat1 Until someone's reading your internet history.

+electrocat1 it's been changed *for some reason*

+Mormeemo_ Nooo. Now I wanna know what the original title was ...

Globalplayer1102 Fractal porn: Space filling curves

@@jumbochamploon2591 thanks

This is a sick idea. Wait. After thinking about it, I'm not sure if it could geometrically work.

Neat

What would it look like

Vectors are useful tools for solving two-dimensional problems. Life, however, happens in three dimensions. To expand the use of vectors to more realistic applications, it is necessary to create a framework for describing three-dimensional space. For example, although a two-dimensional map is a useful tool for navigating from one place to another, in some cases the topography of the land is important. Does your planned route go through the mountains? Do you have to cross a river? To appreciate fully the impact of these geographic features, you must use three dimensions. This section presents a natural extension of the two-dimensional Cartesian coordinate plane into three dimensions.

Agreed agreed

+Chandler Gloyd I need to know what the title was! Could you please tell me?

***** Fractal porn: Space filling curves

Chandler Gloyd LOL! I see, thank you.

+Chandler Gloyd Perhaps the related videos were a little... inappropriate?

+JSQuareD I consider that a bonus.

4 years later and nobody is here to answer his question. Is there no such thing as joy in this universe?

I was waiting answer for 2 years

Shazam doesn't pickup anything

Ohh wow... That's depressing

I guess we will never know... :sadface:

+hama prgasc What's it called?

+XxCLIqGamerxX I answered this question ,but someone(idiot) deleted my comment. AGAIN you can do this in these software : 1. Processing 2. Structure Synth 3. Apophysis

Jetset Willy Yeah it says removed as spam, but thanks

thank you, I never knew those programs existed, just downloaded all 3.  they rock

Robbie Devine Aslo VVVV will do the job. vvvv.org you can import Structure Synth code to VVVV via the integrated module and animate the whole. watch?v=3h8PvAbTLAw

He writes some of his own stuff github.com/3b1b/manim

+Nikhil Sasi Rajan I would start by ensuring that your fundamentals are sound. It's much too easy to excitedly learn about what is interesting, with not enough time spent on exercises and foundations. With some admitted bias, I'd recommend Khan Academy for that. I am also a big Art of Problem Solving fan. They are aptly named, and provide a seemingly endless source of interesting problems that help to gain different perspectives on math. And as general advice, always be ruthlessly honest with yourself about whether or not you understand something, and be patient enough to insist on a deep understanding before you move on.

+1 for AoPS!

Do you have an AoPS account?

You can define the speed of convergence rigorously, describing how fast the distance between the n-th curve and the final curve decreases

It is mathematically rigourous. You're trying to find an n such that for all x > n, a certain area a following a curve PHCx would map out the unit square.

Same lol

TheRedstoneTaco I don't know man Because it would be greater than 3d So I wonder how would we perceive it

Try tau dimensional first.

@@kulak8548 But tau is larger than 6.. We can't even begin to comprehend. Better start with e

*"porn"*

im pretty sure everyone knows what the triforce is

+Bhagirath Solanki We get the most boring fractal of all: A line.

xso.

its area is boring, but its 'node' spacing may be interesting

the previous video goes into more detail. If you've watched that already, then I'm sorry, but I find it weird that you comment this on this video(which is more of a visual show-off than anything else)