Unfolding The Dragon | Fractal Curve |
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- Опубліковано 21 жов 2017
- Dragon Curve is one of many self-similar fractal curves. It is also an example of a space-filling curve. The curve never crosses itself and does not meet at the ends. The same pattern is scaled by square root of two and twisted by 45 degree angle.
You can build your own dragon curve by folding paper in half many times, and then unfolding it by 90 degrees. Learn more: en.wikipedia.org/wiki/Dragon_curve
Thanks for watching :)
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Any further questions or ideas:
Email - thinktwiceask@gmail.com
Twitter - / thinktwice2580
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Render time: ~ 70 hours
Programs used:
- Cinema 4D (3D animation)
- Adobe Premiere Pro (Editing)
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Music by: AlanKey86
Time Passes - • "Time Passes" - Alan S...
/ @alankey86
Just beautiful
thank you:)
android neko !
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 think it's neat how the segments never repeat, and every iteration fits perfectly
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?
*thing unfolds for the third time
"well this is gonna be pretty"
Ngl I was worried something would happen
Now to tessellate it
I was going to include that but my pc was just too slow at rendering ;/
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:)
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..
Crazy, soothing music with amazing math, this is my favorite place
That's a *thicc* piece of paper
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
Simply extraordinary.
Just Amazing 🌟✨
Never saw such things ever before
Absolutely beautiful
I like every video of yours before even watching.... coz its incredible Every time!
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....
they actually show this in every chapter of the original Jurrassic Park book
Best channel ever! Thanks.
Amazing video! I've subscribed!
Beautiful!
This is so satisfing to watch and so cool an good animation
Never expected tht!!!👌
0:15 I thought this was gonna turn into a freaking swastika
Omg I can see that
Perfection!
Beautiful
Amazing how everything falls into place
Thank you. That made my day.
So satisfing!
Amazing!
My favorite😁, watching for fifth time.
Now I understand what Ian Malcom was trying to say
I love how they fit without superposing
amazing!
This video was very therapeutic
beautiful
Why is this so melancholic
Omg! This is insane
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
Did this process upto 19 iterations on AutoCAD and the result looks amazing
amazing!!!!!
Beautifully done.
Thank you:)
yes, so satisfying
Very good
This channel breaks my mind
Hermoso!
So simple ,,,yet so complex
so good wtf
Loving the music!
Thomas ftw
I came
wait
Why is your username the same?
Didn’t expect the destroyer of Pythagoras and his beloved rationals to appear.
That's some mathemagic
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 ua-cam.com/video/BUWeBtgfdJk/v-deo.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!
Very beautiful :)
Thank you!
ok, this is epic
Came here from Jurassic Park (the book)
Enzo Leonardo
It’s just Chaos theory at work (or something)
That's the reason I clicked
Got randomly recommend to me, I know what my geometric patron for my mathematics based wizard is now.
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 (; .
And that... that’s Chaos theory.
Terimakasih infonya Maha Besar Allah meliputi segala sesuatu dan membuat kita saling mengenal
This is gunna be a fractal
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.
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 is interesting way to calculate sqrt(2)
The most epic introduction for a laptop ( play from 1:44 at 2x)
Edit: Edited timestamp
Maybe width of the partial dragon curves are numerators of partial continuous fractions of the root of 2?
1, 2, 3, 5, 7, 10 ?
WOW :D
Wow
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
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
I'm stoned rn and this is amazing
0:15 woah, hold on there buddy
could something like this be found in the mandelbrot set?
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.
😍
sir , what software you use for visualization
2000th like.
Scary how these are all maths, no design, no simple things, just maths
This makes me feel uncomfortable and relaxed at the same time
woooooow
Here from the Curiosity Box!
:)
I've seen these in my dreams, it scares me
Make the thickness the value of the house turning angle
Noice
woowowowoowowoow
:)
My man turned a (-) into a ( 🐉 )
what is the angle between the mini-dragons?
Sinx 45 degrees
Song????
This is what Jeff Goldblum was trying to warn us about.
Oooh
Tidak memiliki suhu thermal?
But WHY is the factor √2?
I'm tripping and ahhhhb
This is insane. Even if fractals aren't typically self-similar.
Можно ли это считать переходом от Хауса к порядку?
Fibonacci did it again
almost like a julia set
You know there's a god in heaven when math works this well!
Me seeing the first two parts: NATZI NATION