Turning Math Into Art With Beautiful Fractals

Here's a compilation of the algorithms used to obtain the most famous and beautiful fractals, a clear example of how one can turn mathematics into art!
#maths #art #visualization #geometry #python #visual #algorithm #fractal #fractals #dragon #tree #snowflake #hilbert #fractalgeometry #coding #programming #visualprogramming #relaxing #manim
Visualization Tool: Manim library, Python

[@zordon2311]

Hold on this isnt 3Brown1Blue

[@Numb3rTr33]

I wish it was! 3blue1brown is a genius

[@JJHJKM]

@@Numb3rTr33Almost Same with their videos

[@yonaoisme]

WOW, what gave it away?

[@enzorak]

There was no talking and also no 3blue1brown animation thing

[@zordon2311]

@@enzorak can't make Jokes in 2023 nowadays can i

[@deathbreach3448]

Not only are fractals a mathematical expression and art, they also express the kind of perfection that living organisms strive to replicate

[@goutgueule9197]

Hi

[@circumplex9552]

​@goutgueule9197 can I be in the letter pfp club even if im not on fire

[@goutgueule9197]

yes but you will melt@@circumplex9552

[@DJPastaYaY]

Whats fascinating is that if there wasn't a limit to how many times we could fold paper, we could make the dragon curve just by folding a piece of paper over and over again!

[@Mikelaxo]

How?

[@AxoYT_4]

@@Mikelaxounbreakable charm of strength

[@finnianreilly1831]

There is a fun software called Matryoshka that allows to play with geometric fractals using photo montage.

[@Tarou9000]

I made abstract art with neural networks, for each pair of x and y values it return rgb values, beautiful!

[@Darsh.r.m_20]

I love how simple yet complicated they are at the same time

[@capncaramell]

This is beautiful, I hope your channel gets more recognition!

[@Numb3rTr33]

Thanks a lot! Unfortunately I don't have a lot of time to create stuff, but I always try to work on something

[@TylevGD]

why does it feel like this is the perfect video to put a jumpscare

[@decract]

Congregation jumpscare?

[@EntergeticalakaBot]

Make the colors a image of congregation so it slowly dissolves into congregation

[@antoniothegunexpert5955]

Only if math was like this...i would have actually learnt

[@paulfeeder4262]

i once did the pythagorean tree but with the angle being random between like 30° and 60°. it was rlly nice bc you always got a new variant, but it was still clearly a tree

[@Numb3rTr33]

Obviously 😆

[@Darsh.r.m_20]

Where did you do it?

[@circumplex9552]

​@@Darsh.r.m_20they probably just wrote their own program

[@MintAnimatesRebooted]

beautiful. The fact that you can make this with ANY shape blows my mind. i hope you make more videos like these!

[@cwone3160]

how is it that the levy curve is just the path that was traced by the Pythagorean tree in the first part when it kept expanding thats just amazing

[@aravindmuthu95]

I heard somewhere that fractals are the arch nemisis of the derivatives Where derivatives let things get simpler as we zoom in, fractals get more complicated as we zoom in

[@Sinner487]

There's another pattern in all of these. One that is also perfect. The sine wave. The sound we crave. The sound you feel in your soul. How good your singing voice is, literally depends on how close it is to a sine wave. Listen to super auto tuned voices.

[@mikaerehodgetts]

1 thing I noticed is that the Koch curve 85 shows up in the Pentaflake, and that the Koch snowflake shows up in the Hexaflake. I just think it's so cool that another Fractal show up in another.

[@Numb3rTr33]

That's right!

[@themountaindude]

2:30 man don't be so harsh on my guy Fibonacci

[@lypths]

i was just vibing to this melancholy music. but the fractals are also beautiful ❤️

[@veronicawilliamson4526]

How would you calculate/draw these?

[@Numb3rTr33]

I use the python library Manim, but to create these fractals there's still quite a lot of code. Different algorithms for each one

[@veronicawilliamson4526]

@@Numb3rTr33 thank you

[@polsiv]

Enjoyed the video!

[@samsongao366]

Oh yeah! This actually relaxes my brain without going outside. hahaha

[@WAHAHAHAHAHAHA-Man]

3:41 IS THAT THE CURVE OF 85?!?!!🤯🤯🤯

[@Numb3rTr33]

It is!

[@ruthmaryrose]

There is so much beauty in the world it’s not possible to experience it all! R. L. Stevenson wrote❤ “The world is so full of a number of things, I’m sure we should all be as happy as kings.” Thank you for sharing some of that beauty to help spread happiness!

[@worldview12]

So mesmerising...

[@Mag3.1415]

They’re so pretty!

[@Noob_TopDaBatata]

You need atleast 100k subs now, i love this interesting math videos, especially the ones with an amazing edition like your!

[@Numb3rTr33]

Thank you! Really appreciated!

[@bach2mach]

This is awesome!!! What is the music in the background? Thanks.

[@Numb3rTr33]

Hi! the music is called "Cancion Triste 1502". Thanks!

[@dianapeck3820]

4:25 turn and see something that looks like a n

[@Ssacabambaspis]

Wow i wish i had any clue about what is happening in front of me right now so I could fully grasp how insane this is. Crazy good animation btw! Instant sub

[@eklavyamotghare]

8 mins of utter peace

[@I-have_phonophobia]

It was until stupid lil angela said ‘hey gouis win 5000 miny in comp dress’ in that 321go voice

[@komolkovathana8568]

Branches in plant/tree's Roots and Trunks, Organ branch in Animal's Lung, Kidney, Capillary branches of Blood vessels.. Mollusc' s Shell..(Ammonite) !?!

[@blazingstar9638]

This is so beautiful

[@TypicalPythonCoder]

This is beautiful

[@magefreak9356]

Beautifully made

[@Numb3rTr33]

Thanks a lot!

[@nightflareplayz2009]

what a well made video! you deserve more credit!

[@Numb3rTr33]

Thanks! Hopefully I'll grow more

[@KojiWada060724]

I think, Koch's Anti-Snowflakes looks like "Koch's MITSUBISHI"

[@royphjd]

Beautiful 😊

[@kidredglow2060]

COOL! :)

[@catcherintheeye]

These are simply beautiful. Great job! (and may I know the background music you used? It sounds very peaceful)

[@Numb3rTr33]

Thank you! The background music is called "Canción Triste 1503"

[@catcherintheeye]

​@@Numb3rTr33Welcome, your work totally deserves everything. And for the song, thanks!

[@glitching_teapot]

Levy Curve is just a buffed up guy who’s showing off his muscles

[@sureshbabu-yl6ve]

Good work, continue 👍👏🏻💐

[@Numb3rTr33]

Thanks a lot, I will!

[@CeresouslyAnimates165]

Some curves on the Koch Anti-Snowflake look like the Koch Snowflake

[@Numb3rTr33]

It is the same curve reversed!

[@CeresouslyAnimates165]

What’s your favorite fractal ​@@Numb3rTr33

[@eilandihis4696]

this is amazing... also is it to see that by playing around myself with coding random stuff in python I "reinvented" some of those... 😒 very nice video :)

[@Numb3rTr33]

Reinventing fractals is wonderful! You sometimes find some crazy intriguing images no one ever found before!

[@eilandihis4696]

the best is when you try to do something, don't make it, but find plenty of interesting patterns on the go, thus making you test more... letting you explore the fractally multiplying branches of possibilities. If that makes sense 🤔@@Numb3rTr33

[@mysyntax1311]

could you opensource the code we can learn from it

[@Numb3rTr33]

Sure, I will next time!

[@ceejay8328]

3:17 the way I shouted “MITSUBISHI”

[@leonciopina3618]

Entonces debo suponer que la estructura de un átomo debe responder a un modelo fractal, ya que en su gran mayoría el "volumen" que abarca un átomo está vacío como se representa en la ilustraciones de los fractales

[@pvzpokra8602]

beautiful is all i have to say about this

[@konohappiness7481]

I cried watching this

[@Numb3rTr33]

I'll make you cry even more with the next video coming in a few hours 😁

[@shellcooke6606]

6:06 hilbert curve is like a maze

[@Numb3rTr33]

True! 🤭

[@pvzpokra8602]

to me, the second iteration looks like a castle (it is upside down in this video)

[@Mr.Smiler1]

I made reverse version of the triangle 5 pixel up and 1 pixel right at the corner same as the left one and repeat

[@4U70_DeadAuto]

fun fact: the quad koch curve is ALSO known as the "seed"

[@SuperMario-vc4ew]

Fun Fact: If you tilt your screen sideways when the H-I De Rivera Fractal shows up, it looks like a Detailed I-Beam

[@thepixelatedpacman]

underrated

[@redtreestimeline8960]

Hexaflake=David’s Star Maximus

[@geeteevee7667]

You aced 3B1B’s style PERFECTLY!

[@Numb3rTr33]

Thank you! However 3b1b is able to create very complex and clear animations which require a lot of time (that I don't have unfortunately). Furthermore, Grant Sanderson is an extraordinary expositor. I'll try to get better at these things as well, right now I ask you guys to like share and sub to support me, hopefully I'll become a high quality creator at some point ☺️

[@I-have_phonophobia]

So calm a single ad could scare you

[@Perplaxus]

Please more of this relaxi g math animations

[@Numb3rTr33]

Working on a new one!

[@WAHAHAHAHAHAHA-Man]

5:50 So that's why mazes look strange.

[@Kostya8888]

I cried from such sad music

[@Satie84]

The hexaflake looks like a snowflake with a koch snowflake with a koch snowflake and so on to infinity koch snowflakes.

[@Numb3rTr33]

That's the beauty of fractals! They're so mind-blowing...😵‍💫

[@CeresouslyAnimates165]

The Levy Curve looked like it was shrinking

[@Numb3rTr33]

It did. The whole image was not maintained at the same size, but rescaled accordingly to the new fraction size

[@Tk42tk]

Could anyone tell me the name of song playing in video.sound really peaceful for me.

[@Numb3rTr33]

It is called "Cancion triste 1502"

[@victorhmingthanmawia4773]

Trigogogo

[@Wangbw]

I need more, pls. pls

[@Just_Json]

*The Hilbert Curve creates you a perfect maze*

[@trifonmag4205]

Not really a maze since you can't get lost in it, just walk along the path and you'll eventually exit it

[@Just_Json]

Perfect maze for babies I think

[@CeresouslyAnimates165]

THE HILBERT’S CURVE IS MY FAVORITE FRACTAL!!!!!!!!!

[@CeresouslyAnimates165]

Although the Moore Curve stole from it

[@CeresouslyAnimates165]

😡

[@lauracarroll3276]

Interesting

[@khoale5071]

Love

[@shikaishik]

綺麗ですね

[@VladVideos0]

there are infinity koch snowflakes in the hexaflake

[@muhammadbinshfique740]

your work is genius i might end up being ur student

[@Numb3rTr33]

You're too generous! That was pure coding😁

[@muhammadbinshfique740]

@@Numb3rTr33 i am rn learning coding as a self taught dev i will be interested in learning how and u did it

[@Numb3rTr33]

@@muhammadbinshfique740 sure. I'm a self-taught as well. This one has been created with Python, using the library Manim

[@eggheadusa9900]

One time I fell through the floor once and three times and four nights I knew it, the key was three

[@rqns]

This music makes me feel uncomfortable 💀

[@Numb3rTr33]

Why is that?😔

[@humbertorodriguezperez1214]

Starburst dendrimers

[@ar25k46]

I don’t see the pattern in quadrisnowflake, why aren’t there more iterations

[@Numb3rTr33]

Hi! The quadriflake starts with a square, then, it divides itself into 4 smaller self-similar parts, rotated by 45 degrees. Each one of these squares does the same and it keeps going on the same way!

[@ar25k46]

@@Numb3rTr33 so in the final fractal after infinite iterations, does it look like 45 degrees turned or no?

[@Numb3rTr33]

@@ar25k46 no, it would still look like a cross made up of infinitely small squares, like what you see here😄

[@ar25k46]

@@Numb3rTr33 ohh ok thx

[@Numb3rTr33]

@@ar25k46 you're welcome! And by the way every fractal you see here is already close to convergence

[@nbon-]

3:19 mitsubishi

[@mathanimation7563]

Could you provide me code of this video

[@antimateriaali]

Dragon curve looks more like a sea horse curve

[@Numb3rTr33]

Nice observation!

[@freon8933]

Song?

[@tasnimfarah6139]

❤

[@royphjd]

Plankton

[@Tiger_131_88]

3:18 Sponsor By Mitsubishi😂

[@oni0ni0n]

Such a beautiful art. But this recall me trypophobia

[@MKXD2010]

1:31 triforce

[@anakinmeh928]

you are a fucking genius

[@Numb3rTr33]

Thank you sir, I wish I was actually 😆

[@firmanirawan9843]

Bro its more like broccoli😂

[@viewanaprapa887]

Didn’t know Brent had a secret sibling named H-I de

[@AlekBernardOfficial9]

Oh look here are youre friends.

[@crazydog1750]

You can't imagine the shock I had when I saw the subscriber count was less than 1,000... I thought you were one of those popular guys with like 100K subs while I was watching and was somehow wrong about it.

[@Numb3rTr33]

That really makes me glad and gives me hope! To be honest, half of my actual subs and these 36k views came in one week with this video which suddenly "exploded". Hopefully it's going to get more popular. At the moment I'm working on another one!

[@crazydog1750]

@@Numb3rTr33 Yeah, I feel that. I was mega tiny for a long time then all of a sudden after

[@number61802]

2:02 It's not Sierpinski Carpet, it's Menger Sponge.

[@Numb3rTr33]

Try to google it! 😄

[@CeresouslyAnimates165]

3D Sierpinski Carpet is named Menger Sponge

[@royphjd]

Wow that happened

[@demoncoregiblet]

where's mandelbrot, Numb3? Where are my rabbits?

[@Numb3rTr33]

I knew someone would ask me that at some point 😄 it's already planned and in work in progress for the future!

[@redstocat5455]

You are an tree made from number, are you ?

[@Numb3rTr33]

I am🤭

[@redstocat5455]

@@Numb3rTr33 I undercover your cover !

[@theman34234]

this seems really cool to code but im learning java and im only a beginner :(

[@Numb3rTr33]

Little by little you can get very far!

[@iamthechannel5885]

tree 3 is just tree tree 2 and tree 2 is just tree (tree 1 + tree 1)

[@weskerwillie9044]

Life...

[@dianapeck3820]

It is Growing But start srinking 7:08

[@dianapeck3820]

………coolness………..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

[@gottanimate]

Porque caralhos eu vi 8 minutos de formas geométricas se moldando? *por que sim*

[@user-vy5ev8nt6k]

ㅊㄱㅍ 수면유도

[@Neptune455]

Y 4:57

[@on2.2]

the first one is just fractal christianity