Thanks man. If it wasn't for your explanation of the paper folding analogy I probably wouldn't be able to write an algorithm for rendering this fractal. Once again, thank you!
Fractal research can lead to new discoveries in the microscopic and macroscopic level. In fact its the only way to truly understand the mechanics of the Universe
A much simpler way to generate dragon is to consider a taxi in Manhattan on a street grid. You generate binary sequence to direct right or left turn at each intersection encountered. Let 1 = left turn, 0 = right turn. Sequence generated as follows: code for order 1 dragon is a single 1. To generate code for dragon order N+1, take code for order N, spread bits apart, and insert 1, 0, 1, 0, ... starting with the first 1 before the (N-1) code sequence, inserting alternating 1s and 0s between bits of the the (N-1) code, and ending with a 0 at the end. Examples for the first few orders. To show process, I denote the new inserted bits as i and o for 1 and 0. 1: 1 2: i1o = 110 3: i1o1i0o = 1101100 4: i1o1i0o1i1o0i0o = 110110011100100 These dragons are set of "L-code" fractals. There are related dragons when the paper is folded into 3rds in a "U" shape, & folds opened 120 degrees, and other folded in 3rds in "Z" shape, and folds opened to 60 degrees.
If the one of the isosceles right triangles have to be half as big as the other, why are you denoting the dimensions by 2 and X, not 2 and 1 (or any equivalent)...? Seems odd.
Now we're talkin! I love shit like this. More cool vids like this please on cool math concepts. I'd personally like to hear your perspective on concepts like solving elemnetary differential equations. linear algebra, the mathematical principles behind Maxwell's, Einstein's & Schrodinger's equation(s), etc. Also maybe you can share & discuss some of the problesm you work on as a grad student.
Nope! I could see how they might look so however, since they are close to being golden: A golden spiral's radius is multiplied by a factor of φ (≈1.618) for every 90° of rotation. These spirals' radii are multiplied by a factor of 2 for every 90° of rotation.
Nice tutorial. I have been drawing illusions in AutoCAD and can show you how to draw an impossible triangle and a spiral illusion. Drawing something like this in AutoCAD will allow you to draw this to a very far zoomed in level.
phantom effect in fractions, cool, i draw these but starting from the center going outwards and the outsides fit the coped effect over and over, eventually it creates a circle with diamond clarity, its awsome, must be a gift to craft gems and stones, gonna stick with drawing, never get that job 0_o
I find it a bit funny (no offence, the video is great!) how you see "parts" on the fractals' designs... "Sierpinski's triangle is made out of 3 copies of itself." It's is actually made out of infinite copies of itself! :)
interesting. There was a crazy ted talks I watched where they can make pillars from computer models that would be impossible to sculpt without our technology. They are pretty much fractal calculations that could be sculpted into rock. Some fractals have so many intricacies that it would be impossible to accurately draw one. Some fractals are incredibly complex. Cool video though the guy knows what he is talking about.
Thanks for posting! The paper folding analogy 1:00 explained it all... finaly! ^^ Isn't this the same fractal used in the SF novel Jurassic Park by M. Crichton? o°P The star nebula version of the Mandelbrott at the end is really beautiful!
im sorry i have to do a fractal for a math assigment, but i need to do it in half of cardboard! how do i make this one bigger? what measures should i use to start please help!!!
Fractal geometry existed in Africa long before the Europeans discovered it. Just look at the history of african art, social design structure, architecture.
Dat Intro....
best intro ever
Hahahaha
PhunkDumpOfficial wirklich so
Yes boi
the fact that this came out a day after i as born is absolutely awesome
he should've apologized in advanced for that intro WTH 😂😂
Best intro ever 😂
Well, I’m 13 years late to the party, but...
NATE THE MATHEMATICS GUY
NATE THE MATHMATICS GUY
NATE NATE NATE NATE NATE
MATH RULES
NATE NATE NATE NATE NATE NATE
NATE THE MATHMATICS GUY
Oh YEAH
Thanks man.
If it wasn't for your explanation of the paper folding analogy I probably wouldn't be able to write an algorithm for rendering this fractal.
Once again, thank you!
Impressive
Incredible video
i looked at this problem, for a short while. I have what i believe is the solution.
But no way of testing it.
Excellent video.
I wish I was high on potenuse
i wish i was high on potenuse *but spoken louder so the class hears it and laughs uproariously*
Fractal research can lead to new discoveries in the microscopic and macroscopic level. In fact its the only way to truly understand the mechanics of the Universe
thanks man! Always wanted to draw fractals but I never quite understand how I should draw them xD
A much simpler way to generate dragon is to consider a taxi in Manhattan on a street grid. You generate binary sequence to direct right or left turn at each intersection encountered. Let 1 = left turn, 0 = right turn. Sequence generated as follows: code for order 1 dragon is a single 1. To generate code for dragon order N+1, take code for order N, spread bits apart, and insert 1, 0, 1, 0, ... starting with the first 1 before the (N-1) code sequence, inserting alternating 1s and 0s between bits of the the (N-1) code, and ending with a 0 at the end. Examples for the first few orders. To show process, I denote the new inserted bits as i and o for 1 and 0.
1: 1
2: i1o = 110
3: i1o1i0o = 1101100
4: i1o1i0o1i1o0i0o = 110110011100100
These dragons are set of "L-code" fractals. There are related dragons when the paper is folded into 3rds in a "U" shape, & folds opened 120 degrees, and other folded in 3rds in "Z" shape, and folds opened to 60 degrees.
beatiful
Mathematics as art. Really interesting!
Thank you, I've been trying to remember the triangle method. Very helpful!
thanks a lot. That's awesome how mathematics and art look so close
Most excellent thing to do with my math classes
Amazing intro
If the one of the isosceles right triangles have to be half as big as the other, why are you denoting the dimensions by 2 and X, not 2 and 1 (or any equivalent)...? Seems odd.
Bruh what was that intro? I love it
Hmm.. Fractal art. If there were an exhibition, who would be the artist?
love it ! great stuff!
my favorite is the Julia set
Great vid. really helped with math homework!
Now we're talkin! I love shit like this. More cool vids like this please on cool math concepts. I'd personally like to hear your perspective on concepts like solving elemnetary differential equations. linear algebra, the mathematical principles behind Maxwell's, Einstein's & Schrodinger's equation(s), etc. Also maybe you can share & discuss some of the problesm you work on as a grad student.
that intro tho
Nope! I could see how they might look so however, since they are close to being golden: A golden spiral's radius is multiplied by a factor of φ (≈1.618) for every 90° of rotation. These spirals' radii are multiplied by a factor of 2 for every 90° of rotation.
Nice tutorial. I have been drawing illusions in AutoCAD and can show you how to draw an impossible triangle and a spiral illusion. Drawing something like this in AutoCAD will allow you to draw this to a very far zoomed in level.
phantom effect in fractions, cool, i draw these but starting from the center going outwards and the outsides fit the coped effect over and over, eventually it creates a circle with diamond clarity, its awsome, must be a gift to craft gems and stones, gonna stick with drawing, never get that job 0_o
I am going to master this, i have to.
Awesome. Thanks.
2007 be like
I find it a bit funny (no offence, the video is great!) how you see "parts" on the fractals' designs...
"Sierpinski's triangle is made out of 3 copies of itself."
It's is actually made out of infinite copies of itself! :)
Just to answer the last question in the video. The reason it works the same as paper folding is because paper sizes are based on the square root of 2.
Isn't that the fractal that's in Jurassic Park?
interesting. There was a crazy ted talks I watched where they can make pillars from computer models that would be impossible to sculpt without our technology. They are pretty much fractal calculations that could be sculpted into rock. Some fractals have so many intricacies that it would be impossible to accurately draw one. Some fractals are incredibly complex. Cool video though the guy knows what he is talking about.
Any chance of you doing a similar video, but using the Golden Dragon fractal?
Thanks for posting! The paper folding analogy 1:00 explained it all... finaly! ^^
Isn't this the same fractal used in the SF novel Jurassic Park by M. Crichton? o°P
The star nebula version of the Mandelbrott at the end is really beautiful!
This thing does take a long time to draw by hand... I drew one in my notebook and it took my almost 4 hours...
im sorry i have to do a fractal for a math assigment, but i need to do it in half of cardboard! how do i make this one bigger? what measures should i use to start please help!!!
so really we could call the Dragon Fractal, the 'RIght Triangle Fractal'?
is that correct?
this messes with your brain. I have to say that was awesome, and I tripped when I found out they turn into the same shape. It is infinite.
Group theory! - I had to look it up, forgot the name. Maybe something on that.
@danielatha4 have mythbusters disproved lim (1+1/n)^n=e yet?
How did you get the colours at 1:40?
What, this video is from 2007
WHERE AM I?????
2020 !
That was very cool! And nicely presented. Very pleased that you subscribed to my videos. Thanks.
Thanks! Are the spirals golden?
Is he going to respond?
@KernsNoel they disproved Daniel had a brain
@makersmark90 Well, but that pushes the question. The fractals arise out of logical necessity; does that mean God is elevated above logic?
what is this whole thing for ? O_O
Anyone watching this in 2020? xd
its a fact that no matter the size of the paper you cannot fold more then 8 times
i know right
10 years
Question of the day:
Why is this in my recommendation ?
Fractal geometry existed in Africa long before the Europeans discovered it. Just look at the history of african art, social design structure, architecture.
yeah but did they understand the math behind it, and be able to aply to real world problems, or did they just think it looked cool?
Of course I have a paper that I can fold in half infinitely many times. :)
Я из Росси и не чего не поняла уже на второй минуте...😅
Tell that to Britney Gallivan
La intro más perturbadora que vi :v
I know why
Why the hell im i hereee youtube ???
you can only fold paper or anything 7 times never 8 ry it my teacher taught me this in art class MR BRADDOCK GIRARD PA 5th grade
Firewall - Sincere (Lange Mix)
/watch?v=3Un4vLSYbdI
rip-off of Bill Nye and ViHart
By the way he made videos long before vi. But they are both awesome
atleast look at the upload date before saying bullshit