Fibonacci Numbers hidden in the Mandelbrot Set - Numberphile
ฝัง
- เผยแพร่เมื่อ 20 ก.ย. 2024
- With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
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Extra detail via Holly: Here's a link to an article (meant for a somewhat general audience) by Bob Devaney explaining the numbers of components, which are called periods: plus.maths.org...
And more from Bob: math.bu.edu/DYS...
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Editing and animation by Pete McPartlan
Farey Sums: • Funny Fractions and Fo...
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This video about Fibonacci numbers was as good as the last two combined!
not going to like because likes are at a fibonacci number
Underrated comment
It is so interesting how literally everything in math is connected and intertwined. This is really cool because if you don’t quite understand a certain topic or problem you can look at some things you do understand and connect it to what you are having trouble with.
That is the essence of what is known as the Langlands Program, named for Robert Langlands, who essentially created the whole schema...it relates to what are two entirely separate fields in mathematics, harmonic analysis and number theory, and the bridge that links them together.
EXACTLY! I also find fascinating how this figure is encoded in math and anywhere you go in the universe, the figure is still the same!
'B.' in Benoit B. Mandelbrot's name stands for Benoit B. Mandelbrot
raspi1983 Old joke.
Wait, so what does the second 'B.' stand for? :-)
the second "B" stands for Benoit B. Mandelbrot
observerms
th-cam.com/video/laHl-aFZUJI/w-d-xo.html The EDM in EDM Detection Mode stands for EDM Detection Mode.
I saw what you did there :)
Kudos to the animator. The scuttling mandelbug was a delight.
David Wiley The sound and the animation cracked me up.
No it was in fact the very opposite of a delight .
Yusss. I came down here to find the comments about it. That made me so happy. 4:24
It's a Miyazaki Mandelbug!
It's a Scuttlebug jamboree.
Two of my favorite concepts in one video. Today is looking like a good day.
Women and Paper?
Audio and Visual Stimulation
fibonacci and grills
markers and brown paper?
Fibonacci Numbers make it 3!
Everything about this video was great! The visuals were tuned perfectly. The explanation was thorough but succinct. And the enthusiasm of the presenter really brings it all together. Great work!
I love the little slot machine illustrating the iteration and the ping sound it makes. That's the way Mandelbrot sets should be computed.
Every time I’m feeling particularly sharp or intelligent, I click on one of these videos and it instantly puts me back in my place 😅
Still, for my limited understanding in advanced math, it was quite interesting.
7:20 Sometimes called the "naive sum" as well. It's also how you construct the Stern-Brocot tree, which enumerates all the positive rational numbers without repeating any.
Wow mind *BLOWN,* this is amazing
Who else just wanted it to keep on zooming in until infinity? [8:41]
You mean an infinitely long TH-cam video? No thanks.
Yeah. I wish it would've just kept doing numbers and faded out, to create the impression it could go on forever. Stopping makes it look like it fails at that number.
Nobody with half a brain thought it "failed" at that number
Here's one of the deepest zooms fellow Mandelbrot enthusiast th-cam.com/video/0jGaio87u3A/w-d-xo.html
+
It's pretty cool, that these two things have such a connection
But not terribly surprising, Fibonacci numbers pop up just about anywhere.
Nukestarmaster
I
do
not
think
so_about
these_numbers!
Fibonacci_numbers_are
definitely_not_anywhere,_you_idiot
it leads me to speculate that *everything* is, in fact, encoded in the Mandelbrot Set.
fukin druggos
@@albertb8999 I see what you did there, incorporating the sequence into your sentences.
Well played, Albert B, well played.
Riemann: My zeta function hides primes
Mandelbrot: My set hides Fibonacci
Ramanujan: -1/12 __
PlayTheMind riemann is way above mandlebort and ramanujan
Sharklops Haha.. nice one
What do you mean wrong, the limit of the nonconvergent sum of 1+2+3+4+5...+n where n=Alephnull-1 Does end up as -1*(1/12)
jawad mansoor YOU CANT JUST MAKE THAT CLAIM AND LEAVE
+jawad mansoor Riemann has done much more besides his hypothesis eg: introduced the term manifolds, riemann integrals, was one of the pioneers of non euclidian geometry (with gauss and some other russian guy), also physics and probably tons of things that im not aware of, he was one of the best mathematicians to ever live
I lost her at 1+1 is 2.
Nathan Thames
That's kind of Numberphile's comment section in a nutshell
"PewDiePie's personal account" kek
Muhammad Mamoon 2+2 is 4, -1 is 3, quick maths
Well, you have the basics down.
Who thinks that’s funny?!!
She's so cool!
And cute!
@@fantasick8880 😍
Angelic.
and preeeeeety!!
Test question: In the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, what would be the next number?
Answer: So you take a point called c on the complex plane...
So is not a valid word with which to start a sentence except in very rare circumstances, for example explaining the purpose of doing something.
@@philpayton8965 It is valid for a joke though. The joke was that he's explaining a very easy concept in the most complex way imaginable using the most casual language possible.
@@nodezsh sorry man it was a bit pedantic of me it just used to be a pet hate of mine, probably fuelled by the fact I had a horrible micro-managing supervisor who started every sentence with "So...".
it was a me problem, not a you problem, just ignore me. was a long time ago now anyway.
The beauty of this math overwhelms me with emotion. Perhaps that seems strange, but the beauty of how all this works out makes me want to cry.
I thought I was the only one who feels this way! I completely agree! There is just so much order and beauty in all the world I don’t know how to take it all in emotionally.
Despite being quite familiar with both the Fibonacci sequence and the Mandelbrot set, my mind was indeed blown. It's even more amazing how "number games" like this can relate to the physical world (at least the one we can perceive).
This is one of the very best layouts of this fractal relationship with the Fibonacci sequence
A new video of Dr. Holly, aka she who commands my heart, mind and soul. This is a great week indeed.
I used to hate Mathematics. Long story short I developed Arithmophobia since an early age. Until tonight I watched a video about Fibonacci Sequence that introduces me a total new prospective of Math into my life. And for the first time in a long time 33 years more or less (I'm actually 37) I understood Mathematics 😱🤯😍 And after that I found this video is like a double 🤯🤯 sorry I had to is literally mindblowing. I think I can start saying I HAD Arithmophobia. Thank you!
I would 'guess'? it usually happens because of how cumbersome it is to get used to it from such a young age and to basically drill math into your skull by brute force.
Maybe, for whatever reason you had a knack for math but never developed the skill to use it because of some bad experience learning it growing up, at a very critical time. But this here, this makes no sense. It's like finding a glitch in the matrix. That's why it's so fun.
I would tell a joke about Fibonacci.
But it's as bad as the two previous jokes you heard combined.
Cyberspine #groan
You shouldn't start with two zeros... :D
0 + 0 = 0
Cyberspine and where does your joke end? If you are going to be funny, at least have an educated punch line to go with it. Those are hilarious
@@bradleylomas7525 HAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHA AHBAHSBHABSH HAHAHAHAHAHAH
Holly's laugh touches my cardioid :P
oof you better motice (this is not a typo)
Simp
@@dxrpz1669 incel
Incel
Thanks for the incredibly fascinating video. The more I learn about the Mandelbrot set, the more I like it. Dr. Krieger is excellent as always.
Everytime Holly laughs a furry baby kitten is born.
These inserted animations make all the difference - great thinking mr Haran!
Glad you liked them - they were done by Pete McPartlan
What I've learnt is no matter how many Mandelbrot videos I watch, I still have no idea how it's made. Only that it looks amazing on a projector!
Mandelbrot set is amazing. It's incredible how quite simple definition leads to infinitively complex structure.
i was obsessed with the fibonacci sequence when i was little and i'm obsessed with the mandelbrot set now, seems like a perfect video for me lol
Next: how to cut a cake via prime numbers, Graham's number created by Conway's game of life, and the fractal dimensions inside Parker squares.
Do you want existential crisises? Anyway, cool subjects!
…while doing a dice trick represented by playing cards printed on the surface of a Klein bottle.
*The reason I love mathematics*
"Is the universe a fractal that can be calculated in equation?
Is it Fibonaccis perfect golden spiral or is it just my imagination?"
From what I can tell, the world is defined by mathematics and patterns naturally. Math is the translation for the patterns that took the chaos or the earliest known parts of the universe up till as far as we can see. When Mathematics fails is the day I'm lost lol. @@microbuilder
Beautiful Ladies teaching us?🤫
Peng broads?
2:12 even non-mathematicians love this for different reasons xD
Shubham Shinde
Yes it is fun. They kind of look down on us as children.
When you really uncover it, it is for the same reasons, it is a way to describe or show the nature of the universe and consciousness. Just mathematicians see it in numbers and other people see it more spiritual, but it dissolves into the same sensations one has.
@@pizeblu well.. except that the way mathematicians see it actually makes sense, the way you see it doesn't.. it really have nothing to do with consciousness, the nature of the universe... It's just math
As a non matematician myself I love it because it shows how something so complex and weird can come up from such a simple rule.. also because fractals are just weird, counterintuitive and fascinating.. but nobody who understand this even a tiny bit would say that it's connected with things like consciousness or the nature of the universe.. get your feet on the ground mate
@@raffaelepiccini3405 I just don't understand how so many people who had never communicated before are able to "figure out" fractals and how they relate to consciousness on their own.
Numberphile really nails it by explaining math in an entertaining and lighthearted way.
Amazing.... please do more videos about the Mandelbrot set. It is the most interesiting mathematical object I know of, in my opinion...
Loving your videos!
I wrote a program to generate the Mandelbrot set many years ago and the interesting part was outside the iconic shape - the colours are formed as visual representations of the number of iterations (like a contour map) with the iconic shape merely the set of values that kept on iterating. They were the boring bit! Thank you for showing me what I was missing. I'll have to revisit that code with these extra features to explore!
2:13 made me smile
The Mandelbrot Set will never be as beautiful as Dr. Holly.
I disagree :Ü™
oh yes, Holly Krieger
IBMicroapple There needs to be more Dr. Krieger videos.
I think I have a new crush.
@TheronQRamacharaka I'm guessing it's a perfect match. But something tells me the carpet is gone.
IBMicroapple simp
@@takotaw8453 still a virgin
The best Mandelbrot tour guide EVER!
Glad to see her again!
Dr Holly Krieger and the Mandelbrot Set, name a more iconic duo... I'll wait.
I can see that nail and gear flag in the background :)
and a Reunion swamp hen!
This recall me how I solve the dimension of cantor set when I was undergraduate.
I used the following model to find the dimension of cantor set.
Consider there is a creature that will reproduce themself 1 sec after they born. After 1 sec they have born, they will start make one new born baby in each sec. And their new born baby will start to reproduce themself 1 sec after they born.
first sec, only 1 new born baby, number of creature is 1.
next sec, only 1 creature ready to reproduce (mature), number of creature is 1.
next sec, 1 new born baby and 1 mature, number of creature is 2.
next sec, 1 new born baby and 2 mature, number of creature is 3.
next sec, 2 new born baby and 3 mature, number of creature is 5....
It end up number of creature in everysec is following fibonacci sequence.
Intelligence makes people more beautiful
Racial purity makes humanity beautiful
@AccuracyIsGone I agree... come go after the heretic of the g4y empire
@@NwoDispatcher the exact opposite is true. Racial purity leads to an amplification of genetic defects over time. The largest gene pool is the healthiest.
@@NwoDispatcher If you truly believe that, don't ever have a DNA testing. You'll find out that you're anything but.
Most of your ancestors had more IQ than you and had this idea that screwing around is more fun than raging about a concept that doesn't exist.
@@NwoDispatcher come on, evolution needs tension. How about you leave it be when it's so minor
Great explanation, thanks. By this construction the numerators are also the Fibonacci sequence, two terms behind the denominators. Since the ratio of subsequent terms in the Fibonacci sequences approaches the Golden Ratio as n --> infinity, this means that the ratios that you are considering approach the Reciprocal of the Golden Ratio, Squared. [I think this is right - and surely pretty well known. I just realized it from your presentation.]
Love you Dr Holly!
Mandelbrot set, you're a Rorschach test on fire, you're a day-glo pterodactyl, you're a heart shaped box of springs and wires, you're one badass f**king fractal
Zedi gan thank you. I read the comments specifically to not repeat that if someone beat me to it. 💜💜💜
The picture of the freshman sum they showed was wrong. Is it a Parker freshman sum? 🤔
I was searching for the comment pointing that out, wonder who misunderstood the freshman sum joke
For some reason they showed the multiplicative
Mind blown! I think it's so incredibly cool how sites like Numberphile, 3 Blue 1 Brown, and Brilliant are making mathematics fun and inspirational. If you haven't checked out Brilliant's site, I highly recommend it for any curious minds.
Math is amazing. Who even discovers this stuff?!
Soumil Sahu mathematicians
+Cellkist obviously, but who goes out of their way to say, "today im gonna pull out the Fibonacci sequence out of a weird shape"
Soumil Sahu They don't. They explore a weird shape and say "Wow! Fibonacci sequence relates to it!"
How do they find the weird shape to being with? Well, mathematicians make random problems up and hope they lead to something interesting. The Mandelbrot set was a lucky discovery!
Soumil Sahu sometimes it's a Mathematician, sometimes a "non- Mathematician" notices a pattern and wants to know: "does this 'thing' ever stop or does it go on forever?" They may get bored of it, or keep studying it, or even become obsessed with it (especially if their pattern appears to present itself everywhere; it's a constant reminder.)
People who think it's amazing
We also have the start of the Fibonacci numbers 0,1,1... in the complex plane. The zero in the centre can represent t=0 the moment of now in an individual reference frame. We also have negative 1 and positive 1 with a rotation 2π that is a constant represented by ħ=h/2π. Therefore we even have the start of the Fibonacci numbers 0,1,1,2,3,5,8,13,21... forming spiral on all levels of creation!
Person: "what the heck happened to your mind?!"
Me: "oh dont worry it was just blown"
Love these videos. But. Is it just me, every time I watch Dr Holly Krieger, I cannot help thinking about Nicole Kidman. The resemblance, the attitude, the mysterious charm. It is as mesmerizing for me as the Mandelbrot set. Am I alone? Anyone else?
4:30 theory of T H I C C N E S S
Not only is the maths in this really cool, but I also loved the cheeky Nail and Gear hiding in the background :)
she is BACK
I could listen/watch Dr Holly Krieger all day.
listen? yeah right
ik i dont understand what they are saying on numberphile but i still like to watch the videos
Just noticed that at 6:07, the hyperbolic component labeled as 1/5 is actually the 1/4 component and the next largest one the right is actually the 1/5 component.
So I guess it's time to fall in love again...
Mobin92 simp
Simp
Simp
Hi
Ha ha ha - he may be a math geek and be on about that !
I have said it before and I will say it again. Dr Holly might as well be Amy Adam's more academically inclined sister. If Dr Holly ever makes a discovery worthy of a Hollywood movie, we know who to cast in it.
when shits stormy outside but a new numberphile video is up
Just letting people know that the Brilliant site is very cool and offers a very brief bit of access before having to go premium with a subscription. I ended up not paying, but I can certainly see why it's worthwhile for mathematics fans.
*Brady always asks some great questions.* Correct me if im wrong but his qualifications are in engineering and not math(s)? He obviously has some math skills or at the very least a good math instinct, but how good are his actual math skills? Has he done any papers and if he has has he been cited much?
he is a journalist
Bengineer8 He is but im pretty sure ive heard before that he has a qualification in engineering. And most journalists dont know anything about maths. It got me wonderin
*NEW RECORD* - Congratulations Numberphille. Only 12 seconds to completely confuse every atom in my head.
I await your next video.
Dr. Haran really makes great questions
He is not a doctor.
Wise Guy he is indeed
You could draw a straight line from 1/4 to the waist. Since the map is 1/2-sqrt(1/4-z), the straight line from 1/4 is still straight in the circle. And an arc subtends half the angle from a point on the circumference that it does from the center. So the bearing of the point on the circle from 0 is the same as the bearing of the point on the cardioid from 1/4.
Math never ceases to amaze me.
Fabulous presentation, thank you for the intellectual depth charge -> factual recognition time bomb of realization.
Because we keep going between two fractions, does the fraction approach something?
trekky0623 I believe it approaches 1 - 1/φ, where φ is the golden ratio (1 + sqrt(5))/2.
So when do we get a zoom in at the golden ratio?
Approaches 1
zoom in infinitely and you will get the golden ratio.
Fractal sets and the Fibonacci sequence seem to be a base geography of our world. In this video you seem to show that the Fibonacci sequence auto-magically flows out of the Mandelbrot set. Extremely fascinating, thanks.
You had me at Fibona..wow those eyes...
OK, I see the Fibonacci series in the hyperbolic components along your circular transformation, but I still don't understand what it has to do with the number of antenna branches. Did I miss that, or did you forget to explain it?
Please don't misunderstand me, I am always enthralled by the content of these videos. However, between Dr Holly Krieger, and the absolutely lovely Dr Hannah Fry, I could even watch with the sound off!
Your homework will be to find the Prouhet-Thue-Morse constant in the Mandelbrot set. That is, the thing you might recognize as what Matt Parker called a fair sharing sequence, written as a binary number like 0.0110100110010110…₂. It's quite satisfying.
But why should the Mandelbrot set have tendrils that coincide with their Fibonacci position?! I feel like I was told I’d get an answer and all I got was an amazing new mystery
Rick Weber Isn't that all what answers are?
That explanation just made me more confused. The explanation seems like an even crazier way for numbers to function.
There's just no competition. NONE of the other female mathematicians giggles as adorably as Holly.
She has one of the cutest laughs
Your a creepy dude
Michael Eaves what? Why?
@@dmytronadtochyi9116 haha incel
I love how Brady has the Nail & Gear in the background.
Gotta love that 9:59
Can you imagine how blown away Fibonacci would be if he could see the Mandelbrot set...
SHE BLINDED ME WITH SCIENCE!!
This is math, you’re even blinded by vocabulary.
Thomas Dolby......luv science
I enjoy Dr Holly's videos. Brillance is when you can solve known math, Genius is when you discover/invent NEW math,
Exactly 10 minutes...
😍 it's beautiful
Jan Sanono It's actually 9:59
You are probably a physicist
If you take the frame count of 14975 @ 25 fps it's exactly 9:59, no .something, so John Ox is correct.
10minutes is the threshhold for more money/view
And the video isn't bad either.
Elegant, beautiful illustration of how math describes our universe. And, how most everything is connected. Thanks for the deep sense of awe I'm feeling right no.
Nail and Gear!
at 6:17, the components labeled "1/5" and "4/5" should actually be labeled "1/4" and "3/4". the "1/5" and "4/5" components are the next larger components down elephant valley.
I'm watching this on high, sounds awesome
8:45 the 144 should be to the right of the 89, not to the left. The one to the left is 89 + 34 = 123, not 144. Then the next one which you wrote 233 should be more like 212 and less like 233.
Hey, thanks as always
It’s easy: Just take a point called Z in the complex plane, let Z1 be Z^2 + C. Z2 is Z1^2 + C. Z3is Z2^2 + C... and so on. If the series of Zs will always stay, close to Z and never trend away, that point is in the Mandelbrot Set!!
Ah, Dr. Krieger! Must be my lucky day!
@TheronQRamacharaka jeez chill haha
We should all be so lucky.
I love mathematics because there’s so much hidden beauty and unexpected patters recur in seemingly unrelated systems. One can keep digging deeper and deeper and still find unexpected patterns that’ll keep you busy for a lifetime... if you let it! :)
This was very interesting and well presented 👍🏻
Great now Jonathan Coultan's "Mandelbrot Set" song is going to be stuck in my head all day. :P (Yes I know the song is wrong. It describes a Julia Set)
Anyways it's cool to see how things like the Fibonacci numbers and Mandelbrot set are intertwined.
Fun Fact, this video was released on 10/5, but in the 510th Fibonacci number, there are 2 "17'"s. (2017) (there are also 5 0's)
So mandelbrot set which is supposed to be the equation that eliminates the electronic interference that is heard when transmitting by wire has nothing to do with the way electricity behaves or anything to do with atomic numbers or weight.
0:45 What's up with the up-arrow-paper appearing in all the videos lately? Oh, and 7:32 should be 1/2 + 1/2 = 2/4.
MasterHigure, That's funny, do more arithmetic.
Freshman Sum Freshman Sum!
Baaahahahahahahahahajahahahahahahajajaja
I mean, you messed up a Freshman sum. That's basically a Parker freshman sum right there.
Yeah, you said that Freshman Sum was in a certain way and showed it differently.
my mind is blown off right now.
I am amazed and mesmerised
almost ecstatic to find out the relation between Julia, Mendelbrot and Fibonacci
Thanks a lot
Holy $^@=!!! I'm very much a humanities individual.. waited until my senior year to take college algebra, etc. I was watching this really cool show on HGTV where this treehouse expert built a treehouse for these Montessori students, and he included the Fibonacci sequence in this awesome bench he made near the reading nook up in this treehouse..I discovered that the Fibonacci sequence is ALL OVER nature etc. in the shape of leaves, etc. I discovered the Mandelbrot Set quite by accident, as, for some strange reason, I've grown really attracted to math... so that I can understand it. If the Fibonacci Sequence is all over nature... where else is it??? The exact idea of the Mandelbrot Set did NOT occur to me, but my small, feeble noodle is TOTALLY in overdrive as I watch this..Love your videos, Dr. Krieger!!
Judy Carter Holy Krieger
Starting with 2/5 and moving against 1/2 I will find /7, /9, /11 and so on. Going clockwise moving against 1/3 I get /8, /11, /14 and so on.
It seems any fraction can be found, not only fibonacci fractions. It all depends on the direction pattern. The fib pattern is left, right, left,...
The pattern I found is just left all the time. Or right.