i have a tattoo of this curve in my shoulder because i believe is one of the most beautiful i know of. this video helped a lot in explaining why i wanted this to my not so mathy friends. as always, your videos are amazing. keep up the good work.
Think Twice its the perimeter of the figure when the iterations tend to infinite, of course the details is limited why the tint and skin, so it isnt infinitely detailed, but its a good work, its look as detailed as the last iteration in the video
Think Twice if you want a fractal, i would say this one, or the burning ship or the triangle one. Those are quote aestetic. Or maybe euler identity? A sine wave is also nice
you you are doing phenomenal stuff I guarantee after some time you will be dead famous this is soo elegant I have no words for it i just wanna thank you before you are world-famous already
Beautiful animation of Heighway's Dragon curve, showing very clearly why it comes from paper-folding! And also the link with complex multiplication, by (1+i). That explains the root 2 and the rotation and spiral....
This is so profound. Thank you for the reflective music that honours this sacred geometry with the audio it deserves, and allows us to drop into the deep stillness it evokes.
Thanks for the support:) still pretty much the same as before, I just got to be patient and wait as there is no medicine :/ Hopefully ill get better during the upcoming months. Thanks again
dragon curve is copied on one end and rotated 90°, julia set is complex square rooted, which is halved angles on one point and copied 180° around it and square rooted distances. dragon curve kinda looks like julia sets. I'll try make a mandelbrot set for dragon curves and see if it's fractal or something boring like circle. the most obvious way of doing it with moving the point of copy and rotate is circle.
The ratio is based on the bounding box he drew, aka by sidelength. And it ends up to √2, cause only that number has this property of unfolding into itself. For example the ratio between standard metric A4 paper is 1:√2, because when you fold this paper in half, lengthwise, you get an A5 paper, and the ratio of the sides of that A5 paper are the same; 1:√2, just scaled by a factor of -2
I was about to ask a question but then I read the description!(what'd happen if we rotated 45º.) In the description instead of "patter", shouldn't it be "pattern"? Nevertheless, if we rotated 45º instead of 90º, how would the scale be? √(2) as well? or 2 or 1?´ Edit: Now that I'm seeing better, if we rotated 45º, it'd intersect itself... right? Wow 70 hours to render? o.O? DOes the Cinema 4d use more CPU or GPU? And how much time do you take animating? Do you need to program or just know how to use cinema4d? Glamorous as always! How do you find these topics about non euclidean geometry?
Yes you're right it's "pattern", my bad. To be honest I'm not sure about the scale of the pattern, if we rotate by 45 degrees. I would imagine that the curve produced by using 45 degree angle instead of 90 degree angle would look a lot different. :) I didn't render the whole animation in one go, but overall it took around 70 hours. You don't need to know how to program to use cinema 4D, and it is not hard to learn how to use it. But there is an option there to use python for your animations. Cinema 4d uses both CPU and GPU but I'm using a laptop to do everything so I can only use my CPU haha. Having a GPU would definitely speed things up. I stumbled upon this topic in a book I recently bought on amazon, however It was not really worth buying , because the dragon curve was the only interesting topic there imo. In general books and google are my best options on learning about new topics like this. Thanks for asking :) feel free to contact me anytime.
Think Twice, Thanks! If you wanted, you could always show some euclidean geometry proofs (by Euclids for sure) :P. Keep your amazing work! I was about to ask if you were better but brian nguyen already did! However hope you get better! estuardoremi, very interesting! Thanks, it looks like the function, sin(|x|), in a way, I mean the produced fractal from [0;180]º its the same as [180;360]º
Just beautiful
thank you:)
android neko !
i think it's neat how the segments never repeat, and every iteration fits perfectly
Coming here from 3blue1brown.
I simply HAD to check out this video!
Obligatory "username checks out" comment
Dude forms of "Dragon Curve" are my username all over the place I love dragon curves
same here bro
I love how it nestles into itself perfectly every iteration.
your feelings are irrational
@@Fire_AxusYour face is irrational
So satisfying to watch
It is! Had fun animating that.
@@ThinkTwiceLtu how do you make these animations? Like a software or some programming language?
This is the most beautiful shape I have yet encountered, and seeing this video made it even better.
i have a tattoo of this curve in my shoulder because i believe is one of the most beautiful i know of. this video helped a lot in explaining why i wanted this to my not so mathy friends. as always, your videos are amazing. keep up the good work.
Thank you:) that's awesome! Can I ask you how many iterations does your tattoo have?
Think Twice its the perimeter of the figure when the iterations tend to infinite, of course the details is limited why the tint and skin, so it isnt infinitely detailed, but its a good work, its look as detailed as the last iteration in the video
That's nice, I'm considering a math tattoo myself.
Think Twice if you want a fractal, i would say this one, or the burning ship or the triangle one. Those are quote aestetic. Or maybe euler identity? A sine wave is also nice
FACUNDO BIAGGIO thanks for suggestions:)
Now to tessellate it
I was going to include that but my pc was just too slow at rendering ;/
*thing unfolds for the third time
"well this is gonna be pretty"
Ngl I was worried something would happen
you
you are doing phenomenal stuff
I guarantee after some time you will be dead famous
this is soo elegant I have no words for it
i just wanna thank you before you are world-famous already
Crazy, soothing music with amazing math, this is my favorite place
they actually show this in every chapter of the original Jurrassic Park book
How is it possible that You have so little views?!
Takes time to build an audience I guess, spread the word :)
@@ThinkTwiceLtu lol.. Maybe there is a wisdom in the pattern in the video to give you a technique to multiply your audiences.. If you want that..
Simply extraordinary.
Beautiful animation of Heighway's Dragon curve, showing very clearly why it comes from paper-folding! And also the link with complex multiplication, by (1+i). That explains the root 2 and the rotation and spiral....
I saw this video in 2020. Now it makes me nostalgic. Yep, nostalgic for 2020.
Absolutely beautiful
Did this process upto 19 iterations on AutoCAD and the result looks amazing
I like every video of yours before even watching.... coz its incredible Every time!
I love how they fit without superposing
That's a *thicc* piece of paper
Why is this so melancholic
Amazing how everything falls into place
This is so profound.
Thank you for the reflective music that honours this sacred geometry with the audio it deserves, and allows us to drop into the deep stillness it evokes.
Just Amazing 🌟✨
Never saw such things ever before
I love your videos so much! Any updates on your conditions?
Thanks for the support:) still pretty much the same as before, I just got to be patient and wait as there is no medicine :/ Hopefully ill get better during the upcoming months. Thanks again
Best channel ever! Thanks.
0:15 woah, hold on there buddy
Amazing video! I've subscribed!
Beautifully done.
Thank you:)
dragon curve is copied on one end and rotated 90°, julia set is complex square rooted, which is halved angles on one point and copied 180° around it and square rooted distances. dragon curve kinda looks like julia sets. I'll try make a mandelbrot set for dragon curves and see if it's fractal or something boring like circle. the most obvious way of doing it with moving the point of copy and rotate is circle.
This channel breaks my mind
The most epic introduction for a laptop ( play from 1:44 at 2x)
Edit: Edited timestamp
Never expected tht!!!👌
This is so satisfing to watch and so cool an good animation
1:34
Never knew about this part! Is that ratio by area or by side length?
The ratio is based on the bounding box he drew, aka by sidelength. And it ends up to √2, cause only that number has this property of unfolding into itself. For example the ratio between standard metric A4 paper is 1:√2, because when you fold this paper in half, lengthwise, you get an A5 paper, and the ratio of the sides of that A5 paper are the same; 1:√2, just scaled by a factor of -2
My favorite😁, watching for fifth time.
For a wierd reason that i dont know if i get sort of nearvos around large fractals if you start to zoom far into it
This video was very therapeutic
Beautiful
Beautiful!
I was about to ask a question but then I read the description!(what'd happen if we rotated 45º.)
In the description instead of "patter", shouldn't it be "pattern"? Nevertheless, if we rotated 45º instead of 90º, how would the scale be? √(2) as well? or 2 or 1?´
Edit: Now that I'm seeing better, if we rotated 45º, it'd intersect itself... right?
Wow 70 hours to render? o.O? DOes the Cinema 4d use more CPU or GPU?
And how much time do you take animating? Do you need to program or just know how to use cinema4d?
Glamorous as always!
How do you find these topics about non euclidean geometry?
Yes you're right it's "pattern", my bad. To be honest I'm not sure about the scale of the pattern, if we rotate by 45 degrees. I would imagine that the curve produced by using 45 degree angle instead of 90 degree angle would look a lot different. :)
I didn't render the whole animation in one go, but overall it took around 70 hours. You don't need to know how to program to use cinema 4D, and it is not hard to learn how to use it. But there is an option there to use python for your animations. Cinema 4d uses both CPU and GPU but I'm using a laptop to do everything so I can only use my CPU haha. Having a GPU would definitely speed things up. I stumbled upon this topic in a book I recently bought on amazon, however It was not really worth buying , because the dragon curve was the only interesting topic there imo. In general books and google are my best options on learning about new topics like this. Thanks for asking :) feel free to contact me anytime.
Check out this video, with the different curves for different angles :D th-cam.com/video/BUWeBtgfdJk/w-d-xo.html
Think Twice, Thanks! If you wanted, you could always show some euclidean geometry proofs (by Euclids for sure) :P. Keep your amazing work! I was about to ask if you were better but brian nguyen already did! However hope you get better!
estuardoremi, very interesting! Thanks, it looks like the function, sin(|x|), in a way, I mean the produced fractal from [0;180]º its the same as [180;360]º
Thanks man:) Do you have a favorite proof or topic that you would like to see a video about?
Actually I don't, I haven't studied it in depth yet. But I will!
Now I understand what Ian Malcom was trying to say
Perfection!
Didn’t expect the destroyer of Pythagoras and his beloved rationals to appear.
Loving the music!
Thomas ftw
Maybe width of the partial dragon curves are numerators of partial continuous fractions of the root of 2?
1, 2, 3, 5, 7, 10 ?
Omg! This is insane
So simple ,,,yet so complex
Love this ❤
So satisfing!
beautiful
Got randomly recommend to me, I know what my geometric patron for my mathematics based wizard is now.
Song????
Finally a new Video!!!
Hope it was worth the wait.
Think Twice Yes it was!!!
From Think Twice, the videos are always worth the wait (; .
Thank you. That made my day.
Very good
Very beautiful :)
Thank you!
That's some mathemagic
This is interesting way to calculate sqrt(2)
Terimakasih infonya Maha Besar Allah meliputi segala sesuatu dan membuat kita saling mengenal
0:13 I'm not sure I like where this is going.
0:15 I thought this was gonna turn into a freaking swastika
Omg I can see that
grandpa chill
Common Square root of 2 occurance
amazing!
Tidak memiliki suhu thermal?
could something like this be found in the mandelbrot set?
My man turned a (-) into a ( 🐉 )
ok, this is epic
yes, so satisfying
so good wtf
This is gunna be a fractal
Scary how these are all maths, no design, no simple things, just maths
sir , what software you use for visualization
Можно ли это считать переходом от Хауса к порядку?
amazing!!!!!
Make the thickness the value of the house turning angle
what is the angle between the mini-dragons?
Sinx 45 degrees
But WHY is the factor √2?
This is beautiful, but how did the render take 70 hours?? Was it rendering on your personal machine, or was it some sort of cloud render?
I was rendering it on my laptop, so It took a while.
Here from the Curiosity Box!
:)
Sooo, zero iteration is crown?
I came
wait
Why is your username the same?
Came here from Jurassic Park (the book)
Enzo Leonardo
It’s just Chaos theory at work (or something)
That's the reason I clicked
This makes me feel uncomfortable and relaxed at the same time
Hermoso!
And that... that’s Chaos theory.
I'm stoned rn and this is amazing
This is insane. Even if fractals aren't typically self-similar.
You know there's a god in heaven when math works this well!
This is what Jeff Goldblum was trying to warn us about.
instructions unclear, instead of following along and making a dragon fractal i made a dragon
Wheres the dragon?
I've seen these in my dreams, it scares me
Why do I feel like Fez is simmilar to this?
Fez the Hungarian city?
Как представляет мая бабушка новый ковёр
PLEASE APPLY A NOISE FILTER
woowowowoowowoow
:)
this is you you'll have to open laptops in 2050
2000th like.