The Feigenbaum Constant (4.669) - Numberphile
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The Feigenbaum Constant and Logistic Map - featuring Ben Sparks.
Catch a more in-depth interview with Ben on our Numberphile Podcast: • The Happy Twin (with B...
Ben Sparks: / sparksmaths
Random numbers: • Random Numbers - Numbe...
Mandelbrot Set: • The Mandelbrot Set - N...
Logistic Map graph: www.geogebra.org/m/wQbHRgye
Watch Ben build (from scratch) the Bifurcation Geogebra visualisation file he uses, on his channel here: • Bifurcation Diagram Li...
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Numberphile what would happen to the human population if they bred at this rate
yo @veritasium plagiarized your video!
16:08 "Actually, this is the mandelbrot set" Greatest plot twist of all time
Veritassium has a great video on this
Not exactly, it's the Z axis of the mandelbrot set, the axis most people never look at.
Top 10 Anime Plot Twists
Your comment made me laugh so hard IDK why. Well done :)
@@travisbrown6814 Two Ts. Which T am T going to T understandT?
3:05 "I'm not gonna read them out anymore"
*Reads them out*
weerman44 +
He's unpredictable ;)
take it easy, you millennial.....
Random whining? No, I have a feeling he wets himself on a regular basis.
fizixx Lol, it was just for fun ;)
This kind of stuff gives me the same goosebumps as when I discovered the pattern in my 9 times table twenty years ago.
+Friendly Metroid ha ha - nice
Friendly Metroid what? You mean that up through 20 all multiples of nine add to 9?
You mean the way the digits add up to 9?
Imagine a planet where they use hexadecimal, and some little alien child discovers a similar pattern in their F-times table.
Yes, maths is universal in that way.
Lol I thought you meant you found THIS pattern in your times table. I was very confused.
Lawrence D’Oliveiro hmmmm. Does it work in binary. Hmmmmmmm
Something I have realized about numberphile is that the videos that have a title with a number in it are always really good.
never would have guessed
I guess you can always count on them ;)
Is there a constant that relates the number in the title to the number of likes that video has? That's Widman's constant.
Tim Owen might have to map that... 🗺
@@maxonmendel5757 No point mate. It's clearer in my mind than it will ever be on paper.
this were the shortest fckin 18 minutes in my life
That's awesome
I saw your comment and was like there's no way that was 18 minutes, crazy
If you think this is interesting I suggest you look into difference equations and their stability.
Welcome to Numberphile
I think this is the most amazing mathematical thing I've ever seen
That's because the idiot in the video did such a horrible job of explaining it. Definitely try to find the follow-up video to that because the other guy does a MUCH better job of explaining the result.
Maruf Can Karatekin it makes sense because numbers are higher dimensional objects... -1/12 is like the first page on any book on string theory.... Reality is like 12 dimensions...
UstedTubo187
Dude
Said idiot has a ph.d and that number is shown in the book that every science students use
Also
He just used algebra laws to prove it, pretty sure that's not idiotic
UstedTubo187 the education and class ooze out of your comment like a putrid, liquefied innards of a rat mauled by a car wheel which just a second ago ran through a steaming, writhing maggot infested cow dung.
You're right, he did put in the hard work to become a PhD. I should've called him Dr. Idiot.
Wow! This is one of my favorite episodes. So cool!
Applied Science - i was just about to type this exact comment.
Applied science, one of my favorites as well. Also, I'm a post graduate engineering student. I'm about to check out your channel.
Watch chaos game by numberphile
17:09 Oh yeah, what if I write:
public static int Uhhh() {
return 7;
}
I was about to say, heh I had the same thought, then I realized that you are me from the past. :/
BTW, we know some Javascript now, so now we can just write:
function Uhhh() {
return 7;
}
@@MagnusSkiptonLLC You made my day ;)
@Michael Steshenko Sadly, I have not learned any new programming languages since then...
Maybe I could just do SQL:
SELECT 7 FROM dbo.Uhhh
But wait that would return one 7 per row in the table...
SELECT DISTINCT 7 FROM dbo.Uhhh
There we go :3
@@MagnusSkiptonLLC I've been following since 2017, and you're telling me I have to wait another 10 months?
@@elirockenbeck6922 I'd write it in VB (the first programming language I learned) but it would make my hands feel sticky.
"We are going to use rabbits because... well... they breed like rabbits"
Nailed it!
Anonymous h
this guy's a pretty good presenter
A complex subject explained in an understandable manner without losing any of its fascination. On the contrary, the radiance in his eyes and the intonation in his voice create the impression that he is speaking about something divine and awe-inspiring that he has just witnessed, commanding reverence and respect.
Eventually, in the future when we have discovered every single one of these important constants, we can add them all together and find that the answer is 42
Or... 23
😂😂😂😂😂😂
If you're including i, that already ain't happening
@TurboCMinusMinus might as well define the last important constant to be 42-x, where x is the sum of all the others
(just messing with you, for the record)
i reckon all the occult knoledge already has answers regarding this. And they've probably been steering humans how they want.
Interestingly, this _discrete_ logistic equation only models populations of animals that have a mating season. For other animals, including humans, the continuous logistic function is used and it's really boring in that it just converges and shows neither bifurcations nor chaos.
@@prassel6189 Agreed.
Yes, for continuous functions I think you need at least three different functions interacting in order to produce chaos, like the Lorentz attractor for example.
I am not a mathematician but trying to reduce this to something of meaning. I understand that this has been applied to other things than breeding animals. So, the equation is a model. The accuracy of the model, that is the equation, to reflect reality is probably key to any meaning. And a source of error in interpretation.
So in this model randomness increases but not randomly but actually at a fixed constant rate. And chaos eventually creates the non chaotic state - at a regular but increasing rate which falls apart. I was trying to understand this in terms of creation of order by accident. I guess that the equation predicts that something pre-exists but that order can evolve from chaos. For a spell. I was thinking of GUT theory of the Universe.
Would it not be true to say a number set, chaotic or ordered, cannot exist unless the model, the reality, the equation must exist first? Is there any mathematical way to support the Universe as an accidental appearance of order? Without a pre-existing mathematical equation or model?
I think this proves the possibility of order without design but of course leaves both options. But i think the subject speaks against creation without a previous ordered equation.
Introduce foxes.(i.e. predators, so known as predator pray model) :D you get bifurcations.
Because its humanitys destiny to overcome chaos (warhammer 40k reference)
Who's here after Veritasium's video?
Me!
yeahh
here
yess
It seems like he did a remake of this.
Yeah!!!
I remember re-discovering this constant in the 1980's on my commodore 64, playing around with iteratied logistic maps. At the time i had no notion of Feigenbaums work. Thanks for presenting this wonderful topic!
Wow, Ben Sparks is excellent at explaining things. He keeps it simple and ramps up the comprehension difficulty slowly/smoothly and just draws you in. I watched the whole 18 minutes with rapt attention even though I felt like I could have dropped out at any time and still have learned something interesting. Bravo!
title doesn't really make sense
is and 4.669 are the wrong way round
you don't make sense
Just letting them know jeeez
nope.. it's right both ways
No it isn't it sounds wrong with the question mark at the end
Absolutely beautiful video ! Thank you very much !
+Olivier Dutreuilh cheers for watching
Olivier Dutreuilh +
Here's a question... At what value of lambda does the average life of
rabbits become irrelevant due to the life period being less than that of
a Planck time?
Brucifer 42.
More interestingly...at what value of lambda does the duration between rabbits screwing become less than the Planck time? I propose calling this "the Hareporn Limit."
5:11 Brady doing a fair imitation of Elmer Fudd singing Wagner
I killed da wabbits..
This is mind-blowing! I remember when I first heard about chaos theory back in the 1990s. I told my boss it was one of the most important things I'd ever heard about. I'm not a mathematician, but I still intuit that is true.
Wow. Just Wow. That's really like best video ever about logistic functions and its connetion to mandelbrot's set. I am just proud of you.
Please do more videos about fractals/recursive/infinite things!
btw, sandpiles video was also great
What I liked was that I wasn’t *sure* it was about the Mandelbrot set until they mentioned it. They could’ve had a complete video without mentioning it. It shows how universal an idea can be.
@@maxonmendel5757 I
Finally a person who realizes the truth about Casio Supremacy.
I just love how the graph quickly became a fractal. Fractals are the best.
I love it. I remember vaguely when I first heard about fractals and the weird unpredictable behaviour they can produce, but this gave the same feeling all over again. The crazy simplicity of it and the infinite chaos it breeds is just awe-some. The extra pieces of sudden order in the middle of it just adds to the mystery. Great stuff. Very good video
This might be one of my favourite numberphile videos in the last year or so. Great subject, well explained, some mystery and a charismatic host. Thanks!
I'm so glad you made the video this length and didn't split it into several parts. Ben does a great job of explaining it and it feels like we get to go on the journey from its first discovery, to uncovering its strange properties, to seeing how they're used at the end. So many unexpected things happen here that I think splitting the video would've made them feel unrelated.
As soon as I saw the function I got excited. I absolutely love the graph at the end. It's like the hipster version of the Mandelbrot set. It's equally nerdily beautiful but much less known :P
Glad you liked it!
It's not a function though, technically speaking. Which makes me wonder, why do we spend so much time teaching kids what functions are?
it is a function if you consider f(λ) to give the sequence of answers (a single thing) and this is just a particular visualization of it.
It is tidy and logical. But you're not thinking fourth-dimensionally, Marty!
And, being hipster, it's actually a dumbed down version of the bigger thing
For those who stopped watching when the sponsor message plays: Fan service starts at 18:37 ...
Thank you I almost missed that :')
4.669/4 Would pet chaotically.
Thanks dude
Oh man. Thank you!!!
I was about to write "I think Fractals have something to do with this"
Then he said it actually IS the Mandelbrot set.
Awesome video!
The number of times concepts and visuals I've known casually have been linked together by a Numberphile video is Huge, but this video beat them all. I've heard of this constant before, but didn't know it was not only related to population maps, but Every Single quadratic map... Then hearing that the map shown produces a one-dimensional analogue to the Mandelbrot set? That's crazy.
Keep on enriching my life, Numberphile!
That was an awesome video! Your channel is not getting old, keep up the good work!
is it because it has 69 in it?
Because theres 69 in the end :)
A. Rashad
69's not the end 😉
69 is just the beginning :>
I see what you did there :D
does it have a creamy ending?
CHAOS THEORY! I've been waiting for a video on this for so long, thanks so much!
Thank you so much, I've heard about this formula some years ago, but did not remember it and did not quite understand it. Now everything is explained beautifully!
Numberphile, you never fail to find something new and exciting to find out in math! :)
And we all would like to hear more from today's professor.
Excellent video! Possibly the best video on this channel yet!
As a Math/CS major, I really loved that ending! Great to see how everything is connected!
6:55 It's hilarious how excited he is at the idea of showing us a graph XD
I'm not mathematically savvy at all, but I'm fascinated by the reality that numbers are a universal constant. Your videos are excellent, i enjoy them immensely. Keep it up please
Ben Sparks is simply fantastic. Top notch.
I like the videos about mathematical constants.
The fact that so much math links up like that shows that math isn't something we humans made up. It is something that is innate to the universe and we are just discovering it.
BrotherAlpha Or it could just show commonalities in mathematical reasoning. But if you need to make math seem "mystical" for it to be meaningful to you that's cool too.
He's not presenting it as mystical. Quite the opposite. He's just saying it's inherent in the way things work. Math is the most mundane thing there is.
BrotherAlpha or we are living in a sim created by lazy developers. just kidding.
All of math is just different expressions of the same 9 axioms, of course you're gonna see similar structures pop up in places you thought to be different. Because you've invented two different views of a particular set of conclusions, and called them two "branches" of mathematics (like geometry and topology, investigating two different aspects of forms), that doesn't mean there's an actual divide between them. It only makes sense that different conclusions will turn out to be versions of the same idea under different perspectives, it all comes from the same place.
BrotherAlpha , we humans made up notation and techniques for manipulating those symbols that represent quantities and relations between quantities, but of course, those quantities and relations already exist out in the world independent of us.
This is why I watch numberphile. Thank you for making this. Fascinating stuff.
So fascinating. You're fostering my new found love for maths. Thank you guys so much for sharing your passions.
Thanks for watching us.
Thank you ! I learned something new here.
Really interesting, great episode.
This guy explained it so clearly and concisely, awesome video
Those are truly the best calculators. Introduced to them in high school around 2005, and I've never needed another model.
Is there a way to show how that graph is the mandelbrot set?
Memington upload.wikimedia.org/wikipedia/commons/b/b4/Verhulst-Mandelbrot-Bifurcation.jpg
Wow! Very cool.
Why did this make me tear up?
I always hated math in school, was terrible at it, but that gif absolutely blew me away. Amazing.
jordan fink Thank you. Amazing link.
Is there a reason that the bifurcations aren't symmetrical? At 15:10 for example the bottom fork diverges by a much larger amount than the top. Is that some integral part of the function or just controlled randomness?
ALSO THERE"S A LIL PUPPY OMG I LOVE PUPPY
Ok I'm done
Around 8:06 where he first shows a repeating set of four numbers, there's .50, .87, .38, and .82; and what you see on the graph are those four numbers presented along the y-axis numerically.
what does "controlled randomness" mean?
It IS symmetrical in a way. the higher the previous fork was, the larger the difference between the offshoots is.
WOW! The first time I heard about this Feigenbaum fractal was in the mid 80es together with the Mandelbrot set. But I had no idea that both are connected. Great video. Thx!
The BEST numberphile video in quite a while. Loved it.
The best feeling I get is when i discover stuff like this in mathematics or physics or whatever subject from the internet. I feel like i'm witnessing the universe on a deeper level, but then I get super sad when reality hits me: I realize I am just an electrician, never learned any maths or physics beyond the basics and thus won't ever properly understand any of it, let alone explore it on my own.
But I feel like it's somehow worth to try to understand it at least, it makes me happy for some reason :D
sometimes art won't be understood, but it can still be appreciated
"So what do you like to do in your free time?"
"I watch a lot of TH-cam..."
"Ha ha, like funny Vines and memes, right?"
"... videos about math."
@Pybro Ambiguous 😊
I have been away from formal work in mathematics and am grateful to know we use the nomenclature ‘pseudo random numbers’. Thanks!
This very much reminds me of a root locust of a control system. As you increase the system gain a system can go from exponetial decay (stable), to constant oscillations (marginally stable), to exponentially growing oscillations (unstable). The points where the solutions split remind me of a discrete sample of a sinusoid or a marginally stable system.
This escalated quickly.
Great video. One of my favourite Numberphile videos for ages :). Thanks!
+Justin Murtagh glad you liked it
Thanks for this, one of the best brideos in a long time. I would also love to see you guys in casual settings + drugs.
I love the plots that come out of this thing. Really interesting.
I think it's famous because Numberphile did a video on it.
Aapo like the the Parker square 😝
I think this has become one of my all time favorite Numberphile videos. Very interesting. Is the GeoGebra file available for download anywhere?
One of the best videos yet. I really liked this one.
This is AMAZING to see. I can't believe how well that equation describes population and biology
Robert May's BBC Radio 4 Life Scientific interview remains one of my favourites. He went on to model HIV for the UN
Unique feeling. New Numberphile video :D
This is legitimately the most interesting and fascinating mathematical thing I have ever seen.
brilliantly explained - superb - thank you so much
Can you make a video about why Lamda can't be >4?
Because it grows exponentially at that point
I believe it is just because it pushes into negatives, and you can't have a negative population
It's because the starting value of 0.5 would give you a population of > 1 in the following year, and we want the population to be between 0 and 1. If you make Lambda even bigger, even more values would surpass 1 the following year.
spaghetti +
By completing the square, you can quickly see that the value of x that gives the maximum for x(1-x) is x = 1/2 - thus the maximum for this quadratic is 1/4. We have to make sure that lambda * x * (1-x)
6:00 - Am I the only one who thought:
- Duck season!
- Rabbit season!
- Duck season! etc. :)
Elmer Season!
Again the best is held till the last, well done Brady this is epic storytelling.
This was one of our tasks at programming course (figuring out behavior, calculating constants).
Ah yes, 4.669. Almost as famous as Scott of the Antarctic.
Noah Topper It's been 22 days I am dying for a new episode
Almost as famous as the Parker Square
(@Connor Hill) I find it mildly sad that in the (as of right now) 7 hours since this comment was made, it's only been thumbed-up 10 times, including mine.
mpperfidy 13 hours later, 69 likes
Sorry, I was referring to Connor Hill's "Almost as famous as the Parker Square" which is still grotesquely unloved, compared to what it deserves.
After reading "Chaos" by James Gleick, when I was in 8th or 9th grade, I wrote an Atari Basic program to demonstrate / illustrate the bifurcating results of that very equation!
JB Lewis I did the same thing, only on an Apple ][+.
8th or 9th grade? I found it hard going to read that after 2nd year at university! I would have loved to learn some basic programming when I was at school and was a little jealous of some boys in my maths class having programmable calculators, and impressed by one who wrote a computer program to investigate a number series and came with a very long printout with a list of numbers! I did get a programmable calculator eventually - I think it was in my first year at uni. I still write visual basic programs on it now but can do most maths I want to do using formulas and graphs on Excel. Windows doesn't let you write programs. At uni I got to learn a bit of Pascal programming first... then Fortran... then C+ or C++. I've forgotten those languages now. Still know a bit of html for making basic Webpages. Visual basic on the calculator is enough for the little bits of maths I want to do that needs a bit of programming (and Excel of course!)
This reminds me of Lotka-Volterra equations (one of my favorite biological math equations) which explores the relationships between the populations of predators and prey with some initial assumptions about the stability of an ecosystem being made (It's been awhile). If you're into this type of stuff, I highly recommend reading about it. It has interesting history/inspiration and probably has interesting applications.
Oh my ! This is profound and spectacular ! I have been trying this out on matlab and its wonderful ! Thanks guys !
If I remember correctly, this is referenced in the great novel The Curious Incident of the Dog in the Night-time
7:29 "It's life, Jim, but not as we know it!"
I love that two people working on fractals at the same time are called Feigenbaum and Mandelbrot, which are German for "fig tree" and "almond bread".
The content of this video was fantastic!
Here from Veritasium :)
"It doesn't have an 'uhhhh' function." --I like that explanation.
Wow. I didn't think I'd be so enthralled by 4.669 - thanks Brady&co! :D
last 2 videos have been brilliant. fascinating stuff!
I made a bit of a typo in the last video. Yes 2.9999 is 3, but the important part is 1.9999. Because you gave to shift the idea of base 10 back and forth to have base ten reveal itself. And that makes 1 then "2" but it's a special type of infinity you need to define a number. They bookend each other abd and in 1d, tge singularity is a number. Square or 2, literally allows you to go up a dimension. Primes in the first base 10 sequence are like hiw to jump dimensions
Holy shit! watching this video is like watch an epic movie in theater. it has everything: the set-up, tension building, climax, twist and a reward ending. am i having a nerd-gasm?
This is why I love math
Holy crap that is absolutely beautiful. Maths is absolutely amazing. Thanks Brady for bringing this to us :D
Wow, one of the best videos of numberphile! Awesome! :D
"Let's go with rabbits, cause they breed like a-uhh"
WHAT? SAY IT!
Make a video with Hannah in it! I really liked the secret Santa video BTW
Let's be honest, Hannah Fry is the most seductive thing that ever happened to mathematics and I'm including Euler's identity here.
Penny Lane - I'm adding Kelsey Houston-Edwards from PBS Infinite Series to my list of math babes. It now has two on it.
One of your best videos, fascinating.
Absolutely amazing. Thank you!
Which software did he use to plot?
Who's here after youtube recommended this video, you were about to skip but then started thinking"wait a minute,thats the number from Veri..."
This is my favorite Numberphile video so far.
Saw a talk by this man about the origin of numbers; I never knew he did a Numberphile video! Would recommend going to see the talk it if you have the chance.
15:05 To Infinity and beyond!
What software did you use at 14:30? Is it Geogebra? If so, would it be possible to share the source file? Thanks!
ikr
Lysergesaure1 Check video description!
Great, thank you very much! Interesting to play with.
This is awesome! Thanks for sharing!
Ooh there's a cricket bat on the back. Oddly enough feels like home to me now.
Fascinating to know about the dual fixed point constant.