Unfolding The Dragon | Fractal Curve |

  Рет қаралды 191,539

Think Twice

Think Twice

6 жыл бұрын

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 :)
_________________________________________________________________
Any further questions or ideas:
Email - thinktwiceask@gmail.com
Twitter - / thinktwice2580
_________________________________________________________________
Render time: ~ 70 hours
Programs used:
- Cinema 4D (3D animation)
- Adobe Premiere Pro (Editing)
_________________________________________________________________
Music by: AlanKey86
Time Passes - • "Time Passes" - Alan S...
/ @alankey86

Пікірлер: 203
@dragoncurveenthusiast
@dragoncurveenthusiast 6 жыл бұрын
Coming here from 3blue1brown. I simply HAD to check out this video!
@nicogutholz9399
@nicogutholz9399 5 жыл бұрын
Obligatory "username checks out" comment
@andrewprahst2529
@andrewprahst2529 4 жыл бұрын
Dude forms of "Dragon Curve" are my username all over the place I love dragon curves
@Great_Rising_Sun
@Great_Rising_Sun 3 жыл бұрын
same here bro
@cubicardi8011
@cubicardi8011 6 жыл бұрын
Just beautiful
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
thank you:)
@noidentity7873
@noidentity7873 3 жыл бұрын
android neko !
@yorkeR177
@yorkeR177 6 жыл бұрын
So satisfying to watch
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
It is! Had fun animating that.
@ryanbell3704
@ryanbell3704 3 жыл бұрын
@@ThinkTwiceLtu how do you make these animations? Like a software or some programming language?
@shaunyap4090
@shaunyap4090 3 жыл бұрын
i think it's neat how the segments never repeat, and every iteration fits perfectly
@weesalikesmilktea4829
@weesalikesmilktea4829 4 жыл бұрын
I love how it nestles into itself perfectly every iteration.
@Fire_Axus
@Fire_Axus 3 ай бұрын
your feelings are irrational
@attackofthejiggli
@attackofthejiggli 2 ай бұрын
​@@Fire_AxusYour face is irrational
@MagicGonads
@MagicGonads 6 жыл бұрын
Now to tessellate it
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
I was going to include that but my pc was just too slow at rendering ;/
@neidenMetalun
@neidenMetalun 6 жыл бұрын
*thing unfolds for the third time "well this is gonna be pretty"
@notsodailydiscorddump1610
@notsodailydiscorddump1610 3 жыл бұрын
Ngl I was worried something would happen
@Lukoro1357
@Lukoro1357 6 жыл бұрын
This is the most beautiful shape I have yet encountered, and seeing this video made it even better.
@facundobiaggio8439
@facundobiaggio8439 6 жыл бұрын
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.
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
Thank you:) that's awesome! Can I ask you how many iterations does your tattoo have?
@facundobiaggio8439
@facundobiaggio8439 6 жыл бұрын
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
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
That's nice, I'm considering a math tattoo myself.
@facundobiaggio8439
@facundobiaggio8439 6 жыл бұрын
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
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
FACUNDO BIAGGIO thanks for suggestions:)
@dejnol
@dejnol 6 жыл бұрын
How is it possible that You have so little views?!
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
Takes time to build an audience I guess, spread the word :)
@mrduuud
@mrduuud 4 жыл бұрын
@@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..
@Great_Rising_Sun
@Great_Rising_Sun 3 жыл бұрын
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
@_Vortex___
@_Vortex___ 6 жыл бұрын
Crazy, soothing music with amazing math, this is my favorite place
@lopezb
@lopezb 4 жыл бұрын
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....
@dubarnik
@dubarnik 6 жыл бұрын
Simply extraordinary.
@eloyam9973
@eloyam9973 5 жыл бұрын
Absolutely beautiful
@ve.n
@ve.n 5 жыл бұрын
I like every video of yours before even watching.... coz its incredible Every time!
@Shubham_pandey-nk1un
@Shubham_pandey-nk1un 4 жыл бұрын
Just Amazing 🌟✨ Never saw such things ever before
@Mrkontrol007
@Mrkontrol007 6 жыл бұрын
Best channel ever! Thanks.
@maluithil
@maluithil 4 жыл бұрын
Beautiful!
@ChompChickadee
@ChompChickadee 4 жыл бұрын
This is so satisfing to watch and so cool an good animation
@briann363
@briann363 6 жыл бұрын
I love your videos so much! Any updates on your conditions?
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
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
@yossi_cohen
@yossi_cohen Жыл бұрын
Amazing video! I've subscribed!
@navneetmishra3208
@navneetmishra3208 6 жыл бұрын
Never expected tht!!!👌
@stenoch
@stenoch 5 жыл бұрын
Thank you. That made my day.
@troubleshootinglife361
@troubleshootinglife361 Жыл бұрын
Perfection!
@chinmaychandraunshuh
@chinmaychandraunshuh 6 жыл бұрын
Beautiful
@_Vortex___
@_Vortex___ 6 жыл бұрын
My favorite😁, watching for fifth time.
@jpolimaciel
@jpolimaciel 4 жыл бұрын
Amazing!
@alexismiller2349
@alexismiller2349 6 жыл бұрын
That's a *thicc* piece of paper
@enzoleonardo2197
@enzoleonardo2197 6 жыл бұрын
Amazing how everything falls into place
@mattkafker8400
@mattkafker8400 4 жыл бұрын
Beautifully done.
@ThinkTwiceLtu
@ThinkTwiceLtu 4 жыл бұрын
Thank you:)
@HypercatZ
@HypercatZ 3 жыл бұрын
So satisfing!
@vpambs1pt
@vpambs1pt 6 жыл бұрын
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?
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
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.
@estuardodiaz2720
@estuardodiaz2720 6 жыл бұрын
Check out this video, with the different curves for different angles :D kzfaq.info/get/bejne/eLuHmKWlzMzIep8.html
@vpambs1pt
@vpambs1pt 6 жыл бұрын
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
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
Thanks man:) Do you have a favorite proof or topic that you would like to see a video about?
@vpambs1pt
@vpambs1pt 6 жыл бұрын
Actually I don't, I haven't studied it in depth yet. But I will!
@anamarijavego6688
@anamarijavego6688 5 жыл бұрын
amazing!
@caad5258
@caad5258 Жыл бұрын
beautiful
@debracarter7290
@debracarter7290 Күн бұрын
Love this ❤
@gotmilk9843
@gotmilk9843 6 жыл бұрын
This video was very therapeutic
@krystawisner6043
@krystawisner6043 6 жыл бұрын
amazing!!!!!
@maut_
@maut_ 3 жыл бұрын
Omg! This is insane
@NarutoShippudenIntro
@NarutoShippudenIntro 6 жыл бұрын
Loving the music!
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
Thomas ftw
@goldfish9773
@goldfish9773 4 жыл бұрын
Why is this so melancholic
@comteqfr525
@comteqfr525 Жыл бұрын
I love how they fit without superposing
@typobad
@typobad 6 жыл бұрын
yes, so satisfying
@thegrandestbazaar4800
@thegrandestbazaar4800 3 жыл бұрын
Very good
@s888r
@s888r 6 ай бұрын
Did this process upto 19 iterations on AutoCAD and the result looks amazing
@arush-adityarao5212
@arush-adityarao5212 3 жыл бұрын
they actually show this in every chapter of the original Jurrassic Park book
@AgentMidnight
@AgentMidnight 6 жыл бұрын
Very beautiful :)
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
Thank you!
@ashleylee217
@ashleylee217 6 жыл бұрын
so good wtf
@ohno4458
@ohno4458 6 жыл бұрын
This channel breaks my mind
@jfg8890
@jfg8890 5 жыл бұрын
Hermoso!
@cubicardi8011
@cubicardi8011 6 жыл бұрын
Finally a new Video!!!
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
Hope it was worth the wait.
@cubicardi8011
@cubicardi8011 6 жыл бұрын
Think Twice Yes it was!!!
@vpambs1pt
@vpambs1pt 6 жыл бұрын
From Think Twice, the videos are always worth the wait (; .
@ilprediletto
@ilprediletto 6 жыл бұрын
Maybe width of the partial dragon curves are numerators of partial continuous fractions of the root of 2? 1, 2, 3, 5, 7, 10 ?
@salvatorepitea5862
@salvatorepitea5862 3 жыл бұрын
So simple ,,,yet so complex
@CandyFlossWizard1928
@CandyFlossWizard1928 2 жыл бұрын
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
@wallywutsizface6346
@wallywutsizface6346 3 жыл бұрын
1:34 Never knew about this part! Is that ratio by area or by side length?
@pranavkondapalli9306
@pranavkondapalli9306 2 жыл бұрын
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
@chuckles1252
@chuckles1252 6 жыл бұрын
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?
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
I was rendering it on my laptop, so It took a while.
@zashtozaboga
@zashtozaboga 5 жыл бұрын
ok, this is epic
@penguingamer9882
@penguingamer9882 3 жыл бұрын
0:15 I thought this was gonna turn into a freaking swastika
@NUISANCE_ANIMAL
@NUISANCE_ANIMAL 3 жыл бұрын
Omg I can see that
@Pumpkin-man
@Pumpkin-man 3 жыл бұрын
Got randomly recommend to me, I know what my geometric patron for my mathematics based wizard is now.
@abdielmartinez6964
@abdielmartinez6964 4 жыл бұрын
Now I understand what Ian Malcom was trying to say
@JediJess1
@JediJess1 5 жыл бұрын
could something like this be found in the mandelbrot set?
@mrduuud
@mrduuud 4 жыл бұрын
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.
@brucewani2639
@brucewani2639 6 жыл бұрын
That's some mathemagic
@Green24152
@Green24152 3 жыл бұрын
Didn’t expect the destroyer of Pythagoras and his beloved rationals to appear.
@ratuadilFF
@ratuadilFF Жыл бұрын
Terimakasih infonya Maha Besar Allah meliputi segala sesuatu dan membuat kita saling mengenal
@danielpalecek4090
@danielpalecek4090 6 ай бұрын
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.
@prashanthkumar0
@prashanthkumar0 5 жыл бұрын
sir , what software you use for visualization
@alexkuznetsov4254
@alexkuznetsov4254 3 жыл бұрын
This is interesting way to calculate sqrt(2)
@back_the_bone
@back_the_bone 3 жыл бұрын
This is gunna be a fractal
@enzoleonardo2197
@enzoleonardo2197 6 жыл бұрын
Came here from Jurassic Park (the book)
@venomissocute3448
@venomissocute3448 6 жыл бұрын
Enzo Leonardo It’s just Chaos theory at work (or something)
@davincent98
@davincent98 3 жыл бұрын
That's the reason I clicked
@oliot4814
@oliot4814 6 жыл бұрын
I came
@averyatkinson862
@averyatkinson862 5 жыл бұрын
wait
@denverf9
@denverf9 5 жыл бұрын
Why is your username the same?
@Goblin-vs4wc
@Goblin-vs4wc 3 жыл бұрын
Можно ли это считать переходом от Хауса к порядку?
@sinx2247
@sinx2247 6 жыл бұрын
what is the angle between the mini-dragons?
@ThinkTwiceLtu
@ThinkTwiceLtu 6 жыл бұрын
Sinx 45 degrees
@arienkano6002
@arienkano6002 6 жыл бұрын
Wow
@jpolimaciel
@jpolimaciel 4 жыл бұрын
Song????
@mbroooky2064
@mbroooky2064 5 жыл бұрын
Make the thickness the value of the house turning angle
@user-vt4bz2vl6j
@user-vt4bz2vl6j 3 ай бұрын
The most epic introduction for a laptop ( play from 1:44 at 2x) Edit: Edited timestamp
@igrer
@igrer 6 жыл бұрын
WOW :D
@badhbhchadh
@badhbhchadh 5 жыл бұрын
But WHY is the factor √2?
@user-bv9xc6cb5o
@user-bv9xc6cb5o 4 жыл бұрын
I've seen these in my dreams, it scares me
@MidWestGem999
@MidWestGem999 2 жыл бұрын
I'm stoned rn and this is amazing
@ratuadilFF
@ratuadilFF Жыл бұрын
Tidak memiliki suhu thermal?
@Squonka
@Squonka 6 жыл бұрын
This makes me feel uncomfortable and relaxed at the same time
@errinbeck7136
@errinbeck7136 3 жыл бұрын
Here from the Curiosity Box!
@ThinkTwiceLtu
@ThinkTwiceLtu 3 жыл бұрын
:)
@huaiscrblol5077
@huaiscrblol5077 6 жыл бұрын
woooooow
@ackkipfer
@ackkipfer 2 жыл бұрын
😍
@cr0w_ns48
@cr0w_ns48 3 жыл бұрын
0:15 woah, hold on there buddy
@girlfriend2287
@girlfriend2287 3 жыл бұрын
Scary how these are all maths, no design, no simple things, just maths
@pinkraven4402
@pinkraven4402 5 жыл бұрын
Sooo, zero iteration is crown?
@1.4142
@1.4142 5 жыл бұрын
2000th like.
@BearshiMisnes
@BearshiMisnes 6 жыл бұрын
This is insane. Even if fractals aren't typically self-similar.
@robertass5040
@robertass5040 6 жыл бұрын
Noice
@venomissocute3448
@venomissocute3448 6 жыл бұрын
And that... that’s Chaos theory.
@h.a6859
@h.a6859 Жыл бұрын
My man turned a (-) into a ( 🐉 )
@Ferkeshu
@Ferkeshu 6 жыл бұрын
Why do I feel like Fez is simmilar to this?
@erik-ic3tp
@erik-ic3tp 4 жыл бұрын
Fez the Hungarian city?
@xilvos
@xilvos 3 жыл бұрын
woowowowoowowoow
@ThinkTwiceLtu
@ThinkTwiceLtu 3 жыл бұрын
:)
@ReservoirDolphin
@ReservoirDolphin 2 жыл бұрын
This is what Jeff Goldblum was trying to warn us about.
@Xahster
@Xahster 3 жыл бұрын
Как представляет мая бабушка новый ковёр
@UrMom-bc6pd
@UrMom-bc6pd 2 жыл бұрын
I'm tripping and ahhhhb
@muizmuhammad4578
@muizmuhammad4578 4 жыл бұрын
Wheres the dragon?
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