The Feigenbaum Constant (4.669) - Numberphile

[@numberphile]

Catch a more in-depth interview with Ben on our Numberphile Podcast: kzbin.info/www/bejne/Y6Wqn5xvhMd9jc0

[@vinster9165]

Numberphile what would happen to the human population if they bred at this rate

[@123coffeeshop]

yo @veritasium plagiarized your video!

[@Vodboi]

16:08 "Actually, this is the mandelbrot set" Greatest plot twist of all time

[@travisbrown6814]

Veritassium has a great video on this

[@galatei11]

Not exactly, it's the Z axis of the mandelbrot set, the axis most people never look at.

[@SmartWarthog]

Top 10 Anime Plot Twists

[@Its2for1]

Your comment made me laugh so hard IDK why. Well done :)

[@zixuan1630]

@@travisbrown6814 Two Ts. Which T am T going to T understandT?

[@fen4554]

This kind of stuff gives me the same goosebumps as when I discovered the pattern in my 9 times table twenty years ago.

[@numberphile]

+Friendly Metroid ha ha - nice

[@CraftQueenJr]

Friendly Metroid what? You mean that up through 20 all multiples of nine add to 9?

[@lawrencedoliveiro9104]

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.

[@maxonmendel5757]

Lol I thought you meant you found THIS pattern in your times table. I was very confused.

[@maxonmendel5757]

Lawrence D’Oliveiro hmmmm. Does it work in binary. Hmmmmmmm

[@kcwidman]

Something I have realized about numberphile is that the videos that have a title with a number in it are always really good.

[@remixener22]

never would have guessed

[@The_Feedy]

I guess you can always count on them ;)

[@SkillTimO]

Is there a constant that relates the number in the title to the number of likes that video has? That's Widman's constant.

[@maxonmendel5757]

Tim Owen might have to map that... 🗺

[@SkillTimO]

@@maxonmendel5757 No point mate. It's clearer in my mind than it will ever be on paper.

[@AppliedScience]

Wow! This is one of my favorite episodes. So cool!

[@earthbjornnahkaimurrao9542]

Applied Science - i was just about to type this exact comment.

[@acetate909]

Applied science, one of my favorites as well. Also, I'm a post graduate engineering student. I'm about to check out your channel.

[@777redhood]

Watch chaos game by numberphile

[@weerman44]

3:05 "I'm not gonna read them out anymore" *Reads them out*

[@isabellabornberg2153]

weerman44 +

[@Simpson17866]

He's unpredictable ;)

[@luisdiegocr]

take it easy, you millennial.....

[@fizixx]

Random whining? No, I have a feeling he wets himself on a regular basis.

[@weerman44]

fizixx Lol, it was just for fun ;)

[@pa20065]

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.

[@faastex]

I think this is the most amazing mathematical thing I've ever seen

[@UstedTubo187]

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.

[@hanniffydinn6019]

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...

[@uuu12343]

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

[@tabaks]

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.

[@UstedTubo187]

You're right, he did put in the hard work to become a PhD. I should've called him Dr. Idiot.

[@MagnusSkiptonLLC]

17:09 Oh yeah, what if I write: public static int Uhhh() { return 7; }

[@MagnusSkiptonLLC]

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; }

[@JamalAhmadMalik]

@@MagnusSkiptonLLC You made my day ;)

[@MagnusSkiptonLLC]

@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

[@elirockenbeck6922]

@@MagnusSkiptonLLC I've been following since 2017, and you're telling me I have to wait another 10 months?

[@MagnusSkiptonLLC]

@@elirockenbeck6922 I'd write it in VB (the first programming language I learned) but it would make my hands feel sticky.

[@ElektrykFlaaj]

this were the shortest fckin 18 minutes in my life That's awesome

[@marlenedietrich2468]

I saw your comment and was like there's no way that was 18 minutes, crazy

[@robin9740]

If you think this is interesting I suggest you look into difference equations and their stability.

[@diceLibrarian]

Welcome to Numberphile

[@DukeLaCrosse20]

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!

[@Joeobrown1]

this guy's a pretty good presenter

[@EmilMacko]

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

[@MrEfinel]

Or... 23

[@eternalkino34]

😂😂😂😂😂😂

[@Gold161803]

If you're including i, that already ain't happening

[@Gold161803]

@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)

[@bontempo1271]

i reckon all the occult knoledge already has answers regarding this. And they've probably been steering humans how they want.

[@lagduck2209]

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.

[@lagduck2209]

Please do more videos about fractals/recursive/infinite things!

[@lagduck2209]

btw, sandpiles video was also great

[@maxonmendel5757]

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.

[@omnathbhandari3434]

@@maxonmendel5757 I

[@DeJayHank]

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

[@kokopelli314]

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!

[@Wargon2013]

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!

[@antivanti]

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

[@numberphile]

Glad you liked it!

[@twiedenfeld]

It's not a function though, technically speaking. Which makes me wonder, why do we spend so much time teaching kids what functions are?

[@Tupster]

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.

[@kennethsizer6217]

It is tidy and logical. But you're not thinking fourth-dimensionally, Marty!

[@sashimanu]

And, being hipster, it's actually a dumbed down version of the bigger thing

[@andrew_owens7680]

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.

[@alexhenderson3364]

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!

[@tzokke]

"We are going to use rabbits because... well... they breed like rabbits" Nailed it!

[@rishabhrajprakash7213]

Anonymous h

[@SomethingUnreal]

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.

[@unvergebeneid]

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.

[@tratbagd4500]

@@prassel6189 Agreed.

[@johntate6537]

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.

[@donhill3915]

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.

[@hachat1]

Introduce foxes.(i.e. predators, so known as predator pray model) :D you get bifurcations.

[@mykalkelley8315]

Because its humanitys destiny to overcome chaos (warhammer 40k reference)

[@swampedg0d]

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

[@olivierdutreuilh6535]

Absolutely beautiful video ! Thank you very much !

[@numberphile]

+Olivier Dutreuilh cheers for watching

[@isabellabornberg2153]

Olivier Dutreuilh +

[@sjcwoor]

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?

[@tabaks]

Brucifer 42.

[@RadicalCaveman]

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."

[@lpsp442]

Those are truly the best calculators. Introduced to them in high school around 2005, and I've never needed another model.

[@Kalobi]

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".

[@ObeyCamp]

I just love how the graph quickly became a fractal. Fractals are the best.

[@PC_Simo]

Truly. I’m watching this, in a K-Hole; which means that my life is a fractal. 👍🏻

[@ChannelEmrakul]

As a Math/CS major, I really loved that ending! Great to see how everything is connected!

[@cazadorcrazy9194]

Ever since I was 16 a flunked out of almost every math class I took. Supplementary education programs and summer school were the driving forces behind the miracle that was my high school graduation. I always hated math to the point where it was a deciding factor of what career I wanted. Fields such as engineering and most sciences were out of the question due almost completely to the amount of math involved. The channel Veritasium introduced me to the Feigenbaum Constant and for the first time in my life I looked for more videos about it which was how I ended up here, at 1 in the morning, watching videos about what was unanimously my most hated school subject for 3 years. I wonder why they didn't teach us this stuff in schools. Being able to more accurately predict what a population of rabbits is going to be in 5 years is way more useful for a biologist or ecologist than the ability to find the area of a triangle or solving a logistic function. Thank you for helping me find a new love for learning when I thought my time was already up.

[@hd_inmemoriam]

For those who stopped watching when the sponsor message plays: Fan service starts at 18:37 ...

[@diligar]

Thank you I almost missed that :')

[@WarmongerGandhi]

4.669/4 Would pet chaotically.

[@TheLordoftheDarkness]

Thanks dude

[@maxonmendel5757]

Oh man. Thank you!!!

[@theaddies]

Ben Sparks is simply fantastic. Top notch.

[@Griemz]

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

[@therunetruekinght]

sometimes art won't be understood, but it can still be appreciated

[@blump5080]

As a musician, I love mathematicians. We are all just trying to discover what's going on in the world around us using different methods. It's so exciting and a never ending journey

[@shakesmctremens178]

5:11 Brady doing a fair imitation of Elmer Fudd singing Wagner I killed da wabbits..

[@picknikbasket]

Again the best is held till the last, well done Brady this is epic storytelling.

[@sugarfrosted2005]

Finally a person who realizes the truth about Casio Supremacy.

[@TheTCKreen]

Wow. I didn't think I'd be so enthralled by 4.669 - thanks Brady&co! :D

[@gigglysamentz2021]

6:55 It's hilarious how excited he is at the idea of showing us a graph XD

[@StephenKatt]

I really enjoy the enthusiasm of these videos. I'm not even a math guy, but still, this stuff is fascinating and weird.

[@joebykaeby]

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

[@xaytana]

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.

[@omikronweapon]

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.

[@martixy2]

Sometimes there are these lulls in content, but right now numberphile is on a ROLL. This was amazing.

[@HalcyonSerenade]

"So what do you like to do in your free time?" "I watch a lot of KZbin..." "Ha ha, like funny Vines and memes, right?" "... videos about math."

[@kbruh3057]

@Pybro Ambiguous 😊

[@margarett.newman7574]

I have been away from formal work in mathematics and am grateful to know we use the nomenclature ‘pseudo random numbers’. Thanks!

[@pugazharasuad]

Who's here after Veritasium's video?

[@kiwiklogg]

Me!

[@haphaja3352]

yeahh

[@Snowflake_tv]

here

[@shalabhsingh5007]

yess

[@nethacker91]

It seems like he did a remake of this.

[@Zoxical-g6w]

For those wondering what happens at values of lambda past 4, the function blows up to infinity (or rather, negative infinity). Since the initial population is 0.5, if we plug in a number greater than 4 as lambda in the formula, you'll notice that, initially, it goes to a value higher than 1. 4.1×0.5×(1-0.5) = 1.025 Now, it's really easy to notice that the next iteration, the population will become negative, since you now have to do 4.1×1.025×(1-1.025), or 4.1×1.025×(-0.025). The population for this iteration will now be something around -0.1, which makes no sense. The numbers after this iteration will all be negative, since in the formula you multiply two positives (4.1 and (1-x) (since x is negative, you're basically doing 1+x)), and a single negative (x). You can verify this with a calculator. I used Google's calculator for accessibility's sake.

[@owenwilliams6306]

title doesn't really make sense

[@owenwilliams6306]

is and 4.669 are the wrong way round

[@aleksganev]

you don't make sense

[@owenwilliams6306]

Just letting them know jeeez

[@aleksganev]

nope.. it's right both ways

[@owenwilliams6306]

No it isn't it sounds wrong with the question mark at the end

[@JeremyForTheWin]

The entirety of Numberphile is secretly the story of the evolution of Ben's hair.

[@n0lain]

Can you make a video about why Lamda can't be >4?

[@animowany111]

Because it grows exponentially at that point

[@nikoyochum6974]

I believe it is just because it pushes into negatives, and you can't have a negative population

[@boghag]

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.

[@isabellabornberg2153]

spaghetti +

[@niallegan4073]

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)

[@Ax1007]

This is legitimately the most interesting and fascinating mathematical thing I have ever seen.

[@althaz]

Great video. One of my favourite Numberphile videos for ages :). Thanks!

[@numberphile]

+Justin Murtagh glad you liked it

[@dAvrilthebear]

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.

[@HarukiMiyazawi]

I like the videos about mathematical constants.

[@d0tz_]

the mindblowing just goes on non-stop in this video, my jaw literally dropped when he revealed this is the real# part of the Mandelbrot set.

[@BrotherAlpha]

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.

[@ldskjfhslkjdhflkjdhf]

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.

[@KaitouKaiju]

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.

[@nosuchthing8]

BrotherAlpha or we are living in a sim created by lazy developers. just kidding.

[@Kabitu1]

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.

[@NoActuallyGo-KCUF-Yourself]

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.

[@ronaldc8634]

Put the following in the console (press f12) and paste this in to try it out yourself: function logisticMap(x1) { return function f(n,r) { if (n

[@Memington]

Is there a way to show how that graph is the mandelbrot set?

[@tunateun]

Memington upload.wikimedia.org/wikipedia/commons/b/b4/Verhulst-Mandelbrot-Bifurcation.jpg

[@Memington]

Wow! Very cool.

[@robinsparrow1618]

Why did this make me tear up?

[@MichaelFoleyPhotography]

I always hated math in school, was terrible at it, but that gif absolutely blew me away. Amazing.

[@cfebresmol]

jordan fink Thank you. Amazing link.

[@pythagorasaurusrex9853]

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!

[@DaBoff99]

Robert May's BBC Radio 4 Life Scientific interview remains one of my favourites. He went on to model HIV for the UN

[@EeroSoralahti]

Excellent video! Possibly the best video on this channel yet!

[@MrMakae90]

This escalated quickly.

[@harmony.enforcer]

This is AMAZING to see. I can't believe how well that equation describes population and biology

[@Henu_K]

I think it's famous because Numberphile did a video on it.

[@iminni3459]

Aapo like the the Parker square 😝

[@dustinsc2023]

This guy explained it so clearly and concisely, awesome video

[@JBLewis]

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!

[@daicon2k6]

JB Lewis I did the same thing, only on an Apple ][+.

[@yahccs1]

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!)

[@georgehornsby2075]

One of the most interesting numberphile videos I've seen, not that I'm biased.

[@NoahTopper]

Ah yes, 4.669. Almost as famous as Scott of the Antarctic.

[@Kire1120]

Noah Topper It's been 22 days I am dying for a new episode

[@mpperfidy]

(@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.

[@thatoneguy9582]

mpperfidy 13 hours later, 69 likes

[@mpperfidy]

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.

[@robertharaway8196]

+

[@normILL]

This is why I watch numberphile. Thank you for making this. Fascinating stuff.

[@harryscully3642]

If I remember correctly, this is referenced in the great novel The Curious Incident of the Dog in the Night-time

[@jmcbresilfr]

That was an awesome video! Your channel is not getting old, keep up the good work!

[@willk7184]

Really interesting, great episode.

[@tracyhouser3138]

So fascinating. You're fostering my new found love for maths. Thank you guys so much for sharing your passions.

[@numberphile]

Thanks for watching us.

[@heliocentric1756]

Thank you ! I learned something new here.

[@imnotnia]

This is my favorite Numberphile video so far.

[@TheDeadOfNight37]

is it because it has 69 in it?

[@Ayplus]

Because theres 69 in the end :)

[@jwhite973]

A. Rashad 69's not the end 😉

[@RDSk0]

69 is just the beginning :>

[@MyYTwatcher]

I see what you did there :D

[@Feta_Cheezz_Montgomery_Burns]

does it have a creamy ending?

[@thomassynths]

The BEST numberphile video in quite a while. Loved it.

[@bsul03420]

7:29 "It's life, Jim, but not as we know it!"

[@bill794]

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.

[@xjdfghashzkj]

"It doesn't have an 'uhhhh' function." --I like that explanation.

[@nafi4932]

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.

[@LarsStokholm]

I think this has become one of my all time favorite Numberphile videos. Very interesting. Is the GeoGebra file available for download anywhere?

[@RaphaelBarboza77]

Very nice, Brady! One of Numberphile's finest.

[@Lysergesaure1]

What software did you use at 14:30? Is it Geogebra? If so, would it be possible to share the source file? Thanks!

[@salut730]

ikr

[@sparkytheteacher]

Lysergesaure1 Check video description!

[@Lysergesaure1]

Great, thank you very much! Interesting to play with.

[@YtseFrobozz]

The last time I saw this graph was in a physics book... like 20 years ago. When he started to draw it again and it split the first time I got this eerie feeling like... I don't know what it is, but I know I've seen it before. Then when he drew the second split I said, "Oh this is chaos!"

[@Robi2009]

6:00 - Am I the only one who thought: - Duck season! - Rabbit season! - Duck season! etc. :)

[@RDSk0]

Elmer Season!

[@ericdunn9001]

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.

[@arun2686]

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..."

[@venkatbabu186]

Each constant is a behaviour constant. Phi is a random behaviour constant. Just like Brownian motion trajectory. Transcendental is a behaviour of jitters in electronic dynamics. Distance requirements for separation and reduce jitters. FB constant is like leaves growth.

[@Deguiko]

This is quite an amazing video for such a boring title.

[@completeandunabridged.4606]

Bruno Bandeira Pulse :)

[@Ddiaboloer]

Bruno Bandeira Has the title changed or did I misremember the title being more boring than it is now?

[@HalcyonSerenade]

That's about the best way to describe math.

[@EtzEchad]

That is fascinating. I'm a computer scientist and I was familiar with that form of a pseudorandom number generator, but I didn't know the mathematical background behind it. I could see people spending a lifetime studying this.

[@genrole]

"Let's go with rabbits, cause they breed like a-uhh" WHAT? SAY IT!

[@joegermany471]

LOVE the reference to "ummmm seven"!

[@iviasterzox22]

I am not gona read them now out .. - continues to read them out loud.

[@neodavinci9770]

This is probably the most interesting Numberphile video I've seen so far. At least, it's up top in the list

[@bolerie]

This is why I love math

[@athul1193]

Oh my ! This is profound and spectacular ! I have been trying this out on matlab and its wonderful ! Thanks guys !

[@lyanbv]

I am more surprised that Derek of veritasium does not watch your channel at all

[@hanzyfranzy]

I like how they just casually mention that it's part of the Mandelbrot set at the end there. That's deserving of its own video!

[@thej3799]

Because the emergent image is sequential calculations of an equation tat gets either o4. Inside or out. In other words what is essential to the fractal what isn't. Primes are what's essential to integers

[@whozz]

What happens between periods less than a year?

[@AidenOcelot]

WHoZ the world blows up

[@proto9053]

WHoZ Why don't you try some stuff in an attempt to figure it out?

[@whozz]

+Aiden Ocelot I have no idea how to do it. The index of a sequence term must be a natural number :/

[@DrGerbils]

That depends on what you're trying to model. As noted, biological systems are often seasonally dependent so a single equation is unlikely to be useful for periods of less than a year. If you modeling the number of customers at a restaurant each step might be 1 week instead of 1 year.

[@HopUpOutDaBed]

the reason it's yearly is because most animals have yearly breeding cycles and ecosystems tend to naturally follow a yearly pattern of growth/decay. If they have longer/shorter breeding cycles the math doesn't necessarily change, just replace the word year with "x years" or "x months". What's important is that you capture a full cycle with each iteration, not that it's literally a year.

[@SomeoneCommenting]

I love the plots that come out of this thing. Really interesting.