Amazing Graphs II (including Star Wars) - Numberphile

Full Amazing Graphs trilogy: bit.ly/Amazing_Graphs
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More links & stuff in full description below ↓↓↓
This video features Neil Sloane, creator of the OEIS: oeis.org
More videos with Neil: bit.ly/Sloane_Numberphile
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NUMBERPHILE
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Videos by Brady Haran
Editing and animation by Pete McPartlan
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[@numberphile]

Watch the full Amazing Graphs Trilogy (plus an extra bit): kzbin.info/aero/PLt5AfwLFPxWLkoPqhxvuA8183hh1rBnG

[@JamieJamez]

! Invalid parameters. Link is broken

[@jasondeng7677]

wait what? i guess not.

[@PraveenKumar-jp3ti]

In the first graph (base 3), it does look likes the triangular pattern i have seen seen somewhere else......maybe fractals.....can you make such similar pattern from similar kind of definition of (other)functions.....I would love to see a dedicated video on such functions giving rise to these pattern/fractals.

[@OG_CK2018]

17 likes? oh..18

[@ZachGatesHere]

So can we just have like fifty videos of these? Because wow they're satisfying.

[@CylonDorado]

Yeah, it might as well be a series. There’s probably a lot of them.

[@adammac.1342]

Can we just have more videos of Neil Sloane he has a lovely voice :)

[@SeaUrchinZone]

I would like an infinite sequence of Neil Sloane videos

[@TheBettinx96]

Yes please, more of these and more Neil 🙏🙏🙏

[@anarcho.pacifist]

There is an KZbin channel, called "Experimental mathematics", where Neil Sloane has some very interesting presentations on integer sequences. I highly recommend checking it out.

[@ImaginaryMdA]

"Allright then, this is brilliant." With all the excitement of someone being told to clean their room.

[@rq4740]

Aroight 😂

[@Roonasaur]

Came down to find exactly this comment, lol

[@Twigpi]

And yet, I paid more attention to this Brilliant promotion than any other one I've ever seen.

[@Triantalex]

false.

[@Chrnan6710]

_alright this is the sponsor today, let's get this stuff over with so i can get my money and all that, yep_

[@StarTheTripleDevil]

10:25 "The third and final one is coming very soon" "Pretty obviously, it's never gonna happen"

[@joshandrews8913]

Quality editing.

[@howardatkinson9789]

...If you look at the grafffff

[@Triantalex]

??.

[@Roonasaur]

"I can, therefore I must." ~Neil Sloane, 2019

[@TegukiSix]

"Are you sure?"

[@Triantalex]

??.

[@Spender604]

This is like watching Bob Ross. Very calming and satisfying.

[@xaostek]

Wait so is no one going to point out that that balanced ternary graph is a Sierpinski triangle???

[@v3spirit]

ITS THE TRIFORCE

[@gabrielkellar1935]

yes

[@anarcho.pacifist]

See also A213541.

[@user-vn7ce5ig1z]

It's all the more ironic since he specifically mentioned fractals later for the forest-fire series (but not for the wisteria series which also looked like a fractal).

[@kevina5337]

It's close but not quite (it's not a blacked out triangle in the center, more like a blacked out hexagon)

[@VibingMath]

These two episodes of amazing graphs just blow my mind away to the outer space. Great videos!

[@DekarNL]

The parallellograms right?

[@persereikanen6518]

Why? Minus one minus one minus one etc etc... boring.

[@alephii]

graphs are blow jobs!

[@bhavyakukkar]

Wait till you see the third one

[@jameleddinelassoued7228]

People to mathematicians: why do you do all this work that doesn't have any real applications? Mathematicians: I can and therefore I must.

[@frankupton5821]

Because mathematics is the only area of human enquiry where one can prove anything.

[@jameleddinelassoued7228]

@@frankupton5821 Actually I wouldn't give math that much credit, after all we have theorems like Gödel's incompleteness theorems

[@frankman2]

Mountain climber: "Because it's there"

[@frankupton5821]

We can't prove everything in maths, but we can prove (or disprove)most things, whereas in other subjects we cannot conclusively prove anything.

[@jonathanberliner288]

@@jameleddinelassoued7228 actually, Gödel's incompleteness theorem say we can't prove EVERYTHING, not anything. We certainly can (and do) prove many statements.

[@osmeridium]

I can't believe Neil Sloane is 80 years old

[@JobvanderZwan]

More proof that exercising your brain keeps you sharp into old age

[@LouisOnAir]

I never want the Neil Sloane videos to stop, he is just the best.

[@kevinemery2750]

He's a legend

[@pafnutiytheartist]

Cool thing i found (probably was already found but i did it anyway): You can do the first sequence with any base if you replace all non-zero even digits(d) with -1*d+1 It gives you the same fractals but with any length of 'arms' on a V shape.

[@pafnutiytheartist]

@jj zun It kinda does. It will still produce a feactal shape. But with my method you get a nice V shape. With other rules you will have an asymmetrical (but still repeating as a fractal) shape.

[@matthewweitzner8956]

You should go to OEIS and submit that sequence

[@pafnutiytheartist]

@@matthewweitzner8956 which one? There's an infinite number of them (one for each value of d).

[@matthewweitzner8956]

@@pafnutiytheartist Choose your favorites, and list any number of terms in a row

[@KatzRool]

These Neil vids sure aren't Sloane down!

[@heyandy889]

👉😎👉

[@AndrewWHeff]

I always enjoy Numberphile, but WOW!! These videos are amazing. Looking forward to third in the series. 😀😀

[@DyllonStejGaming]

The first thing I noticed with the Balanced Ternary Graph is how it looks like an infinite fractal of Triforces.

[@iveharzing]

look up Sierpinski Triangle, I think you'll enjoy it

[@oledakaajel]

@@iveharzing Infinite Triforces within Triforces

[@kaitudhope9122]

go back to breaking brawl with mods

[@GravelLeft]

"It's well defined, it's unique, and it's crazy." Yeah me too, Neil, me too.

[@casperg3rl789]

My thoughts exactly. :P

[@timotheuspeter734]

Laughed hard at that point xD

[@Triantalex]

false.

[@scottclowe]

1:13 It should be noted that the column labelled Balanced Ternary isn't actually Balanced Ternary. The Balanced Ternary (where T conventionally denotes -1) for decimal numbers is as follows: 1 is 1 (= 1*1) 2 is 1T (= 1*3 + 1*-1) 3 is 10 (= 1*3 + 0) 4 is 11 (= 1*3 + 1*1) 5 is 1TT (= 9-3-1) 6 is 1T0 (= 9-3+0) 7 is 1T1 (= 9-3+1) 8 is 10T (= 9 + 0*3 -1) etc Similar to using Roman numerals, you write 2 as "three less one". What is described in the video is a mapping in which numbers are written in ternary, partially "bit-flipped" with 2s turning into -1s, and then rewritten in decimal. It's a perfectly fine thing to consider and explore, but it isn't Balanced Ternary.

[@williamhautekiet9061]

Shouldn't 5 be 1TT in balanced ternary? It makes more sense to me to only allow the symbols T, 0 and 1. Then 6 is 1T0 7 is 1T1 8 is 10T etc.

[@scottclowe]

@@williamhautekiet9061 That's what I put! I wrote it incorrectly at first and then corrected it immediately afterwards to be as you say, 5: 1TT. Are you still seeing my original, incorrect version?

[@williamhautekiet9061]

@@scottclowe Now I see your correct version, I don't know why I couldn't see it at first :)

[@androidwalle4932]

Thanks for that, I didn't get that part in the video at all.

[@Anya-B.]

OH! Thanks a lot! As someone who use balanced ternary quite often, I was really sad to see he's not talking about the real balanced ternary here, without even saying that that's not the real one! Thanks for bringing some precision here

[@joshandrews8913]

Neil episodes are probably my favorite. The animations of Neil are a nice touch.

[@DekarNL]

These graphs are so cool. Please make more of these! I might just hang one as a poster in the study room :D

[@yoyoyogames9527]

"It's well defined, it's unique, and it's crazy" im definately using this haha

[@Tytoalba777]

I always like listening to the graphs on OEIS. There's some of the craziest horror/ boss music stuff you'll hear.

[@argentinephenomenologist]

What a coooool few graphs those all are! Please more videos with this man! He's amazing and seems so passionate about what he's explaining. I remember when I read about his work in the book Alex's Adventures in Numberland, SO cool!

[@Rob9]

I would love to see a continuing series of these. Please don't stop at 3! The graphs and the professor are amazing

[@LaGuerre19]

I could watch Professor Sloane make graphs all day. Art with numbers. These are great. More, please and thank you.

[@Luminous.A.Glory_VitaNostra]

I don't understand the math, but I love to listen to him explain things!! Very satisfying. And he usually looks so happy =)!!!

[@user-ph5wf5ko6x]

Thx for using my piece for A123456

[@lindhe]

Can't get enough of these graphs!

[@miachen2635]

Over the past few weeks, I've actually been playing with the "Forest Fire" sequence and have come up with a few related sequences I might submit to OEIS. Instead of limiting to positive integers, you can specify that instead of picking the lowest number that doesn't create arithmetic progressions, you pick the lowest absolute value, with positive numbers before their inverses. The graph is pretty cool, more like sand dunes. You can also start with this sequence and define another sequence that's based on running partial sums. As expected, there's a strong positive bias, but there's quasi-periodic behavior, and it seems possible to me that there will be an infinite number of negative partial sums. I'm also playing with a different "greedy" algorithm. Instead of computing values of the sequence incrementally, if you have with some N that's the size of the sequence you want to compute, you can go all the way up to N filling in 1s whereever possible, and leaving blanks where it's not possible. Then, fill in the blanks with 2s whereever possible, etc. That sequence looks like a series of horizontal bands with gaps in between them. One question that can be asked is whether the gaps between bands extend to infinity. I haven't worked it out yet, but it seems like it shouldn't be difficult (and is perhaps trivial for an actual mathematician) to show that there can never be a 3 in the sequence. However, it seems like there's a gap between around 750 and 950 but there's no clear boundary. I suppose the same extension to non-positive integers could be applied to this algorithm too, but I haven't looked at that yet!

[@josebonilla5493]

My variation is that the minimum is how many terms back you saw the last term.

[@Dudleymiddleton]

Utterly fascinating! Looking forward to the next video. Brilliant! :)

[@joelstock94]

I love this type of video :) the patterns that arise are fascinating!

[@BenjaminGoldberg1]

Could you please include links to OEIS for these sequences in the description? Thanks!

[@Henrix1998]

We need like 10 more parts

[@nickpaarlberg73]

These are so cool. Can this be a series on here? I could look at these awesome graphs all day.

[@hammadusmani7950]

these videos are some of the best in this channel

[@tyhayter5022]

0:01 Balanced Ternary 1:50 Wisteria 3:37 Forest Fire 7:42 Artificial Sequences

[@gigglysamentz2021]

All of these graphs blow my mind!

[@danhoenn]

LOVE the videos with Neil!

[@jacobkenning5926]

love this guy, we need more of him!!!

[@tommykarrick9130]

I want to see a million of these kinds of videos, it’s so interesting and it’s all stuff nobodies ever heard of

[@raphaelneubacher6614]

Never seen such a convincing brilliant advertisment and I have seen many of them ^^

[@limbridk]

Fantastic videos. Keep going with these please.

[@GodlessPhilosopher]

These are amazing! More graphs please.

[@Yoshiyosh]

These are very satisfying. I would love more.

[@roverknight2502]

It's the Man the Myth the Legend ASMR Maths Teacher

[@Project_Kritical]

RoverKnight it’s Scott Sterling

[@Nossairito]

Aight Brady congrats on getting me hooked on this, now please give me more before I go mad

[@deanwinchest3906]

This has been your most inspirational video✌️π Thank you so much~

[@felipevasconcelos6736]

I love how the first frame of the video is the name of my favorite additive number system.

[@samueldeandrade8535]

Let's all be honest: Neil Sloane is the absolute BEST we had in Numberphile!!!!

[@pahom2]

On this thumbnail Sloane is even more similar to Homer Simpson

[@siyavash65]

The moment that he reveals the grAph! so satisfying!

[@TheNextFool]

It makes sense that any rules you use to generate numbers show some kind of regularity unless you pick something specifically that would not be regular, like first appearance of a given integer in the digits of pi. Even the primes show some nice regularity in Ulam spirals (I'm sure there is a numberphile video on that). Other regular rules give random (or pseudo random) numbers. The generalisation and categorisation of what types of rules generate which is surely a fascinating study!

[@hannah-uf7id]

this is amazing great guy. his passion for what he does is obvious

[@benjaminbaron3209]

Lovin the crazy unknown properties of those graphs!

[@Mabndo]

This was a really fun video!

[@chelsea4twsb]

Please keep making these videos

[@sb-hf7tw]

Master of sequences... Hattsoff off to you NumBerpHile👍 BRILLIANT NUMBERPHILE...

[@FLS96]

About the smoke pattern, maybe you could find a new constant by comparing the sizes of the fractal parts, like in the bifurcation diagram :D these are interesting, keep them coming!

[@riteshj]

More... More... These are fantastic

[@vistabuntuu]

Amazing that the Sierpinski triangle emerges from graphing the balanced ternary sequence, while also covering all integers exactly once

[@Bronco541]

this is amazing work;

[@WaffleAbuser]

Neil's videos are so damn interesting!!!

[@Mrhollerr]

MORE GRAPHS AND MORE SLOANE... please.

[@7177YT]

thank you! more pls! (:

[@DontMockMySmock]

*graph makes sierpinski's triangle* now what nerdy franchise does that remind me of? neil: star wars me: *facepalm*

[@falpsdsqglthnsac]

Thank you! I had hoped I wasn't the only one.

[@TykoBrian7]

What

[@falpsdsqglthnsac]

@@TykoBrian7 Legend of Zelda.

[@owencosgrove8347]

Although it does look more like a massive fleet of star destroyers

[@TheGreatIndoors1979]

Starcom's Shadow Force emblem.

[@theblinkingbrownie4654]

Make a series of this!

[@gigglysamentz2021]

2:52 Literally loled at how sick this is :')

[@blergblergblerg1343]

There should be an entire channel for this

[@atlasxatlas]

Please more amazing graphs!

[@gradf8678]

Add some more I am enjoying it

[@atome-ro9yj]

For the graph at 7:00 If you do it at a point n and find the n + 1 point, if you make a central symmetry with this new point as center and from a previous point, the result is a white space, and if you do it with all previous points with the new point as center then you get the central simetrie of the previous graph in white space.

[@frognik79]

Dude, when you were saying those 2's and 3's at the end it sounded like the old Buck Bumble intro song on the n64.

[@PeterVC]

More of this! :)

[@squatking77]

I want you to know that I fall asleep to almost all of these videos.

[@odefinierad]

@8:33 "yeah right..." always so polite

[@latneyb]

Brady you have a gift for asking questions.

[@lukaszkonsek7940]

I'm addicted to this after two dose. Give me episode III

[@shruggzdastr8-facedclown]

That Star Wars-y graph at the beginning also resembles an array of Sierpinski triangles with one corner extremely stretched-out.

[@behnamasid]

These video series are amazing, it's like being on LSD without taking LSD

[@pyromen321]

This guy is the best!

[@VibratorDefibrilator]

After I watched this video, as I was playing with that good old generalisation technique, I came up with this - "Not average" sequence: 1. a(1)=1; a(2)=1 2. For every a(n) all possible sums of type s(n, i) = a(n - i) + a(n - 2*i) are calculated { i < [n / 2] }. 3. If s(n, i) is even, we have v(n, i, 1) = v(n, i, 2) = s(n, i) / 2 4. If s(n, i) is odd, we have v(n, i, 1) = (s(n, i) - 1) / 2 and v(n, i, 2) = (s(n, i) + 1) / 2 5. We seek the smallest natural number that do not appear within the arrays of numbers v(n, i, 1) and v(n, i, 2). This is the next member of the sequence, a(n). 6. Repeat points 2. - 5. for a(n+1). The sequence is like: 1, 1, 2, 3, 4, 1, 1, 4, 4, 5, 6, 7, 2, 1, 7, 1, 1, 2, 8, 7, 9, 7, 1, 6, 9, 9, 6, 9, 10, 3, 10, 11, 3, 11, 12, 1, 1, 13, 3, 2, 1, 13, 3, 13, 13, 10, 1, 1, 3, 1, 9, 11, 14, 3, 14, 13, 15, 15, 10, 15, 16, 1, 16, 4, 17, 4, 12, 11, 9, 17, 16, 15, 17, 17, 18, 15, 19, 18, 11, 5, 19, 19, 20, 21, 1, 4, 21, 20, 22, 22, 4, 22, 23, 24, 25, 1, 25, 2, 2, 26, 4, 16, 1, 1, 27, 24, 4, 3, 5, 22, 25, ... and at first glance has most erratic and peculiar behaviour. If you look at these numbers, scattered on the plane, a fractal structures do appear... which is not that strange, because the sequence writes onto itself. The big question is how to know (or prove) that these structures will go on to infinity or there is some kind of loop that dramatically will change the behaviour of the sequence (like the Langton's ant or that sequence showed to us here recently - I forgot its name). "Nobody knows", my favourite quote of Mr. Sloane, meaning "Let's find out", of course. I don't know, there must be some theory lurking in these questions. You know what beautiful mathematics appear from the thin air, when one explores the prime numbers, for example... and they belong to sequence that also writes onto itself, by definition. So, who knows what mathematical wonders await us in these sequences?!

[@chilledvibes99]

this guy is a legend

[@chloepeifly]

“it’s well defined, it’s unique, and it’s CRAZY” 6:40

[@REL1C]

Those are some nice 2s

[@johnchessant3012]

Very nice!

[@5Zacc]

6:50 When Thanos snapped, this graph was made

[@nymalous3428]

It's amazing what you can find when you just start compiling numbers and shifting them into graphs. Of course, sometimes what you find is just a rather beautiful set of numbers...

[@sauna-man3024]

I envy people that get paid to think about these things

[@rebrandedidiot]

I love numberphile videos!!! They are always so good at teaching. Numberphile is actually what caused me to want to study maths.

[@skeletonrowdie1768]

That sponsor question was so funny

[@Maniclout]

Why does it look like a Sierpinski's triangle?

[@bengineer8]

Looks more like what happens if you try to generate one with chaos game, but use something less than 1/2 for the rule.

[@aldobernaltvbernal8745]

@@bengineer8 specifically 1/3

[@BorisJensen]

@@japanada11 That is an amazing explanation, thanks :)

[@AlanKey86]

1:28 Legend of Zelda!

[@pcfilho425]

Neil Sloane is a math hero!!

[@Foxxey]

Could you do a video about Mandelbox? I'm very interested in fractals like this and want to know about the mathematical background about it.

[@blumousey]

Numberphile already has a couple of videos on Julia sets and the Mandelbrot set :)

[@Foxxey]

@@blumousey I mean the Mandel*box*

[@visvakrtram610]

One more video!!!

[@happypiano4810]

I love typing sequences into the OEIS search to see if they have it. I weirdly love when it doesn’t match anything in the OEIS,.

[@chigginheadD]

more please

[@larsn0va]

6:48 I don't feel so good, Mr. Sloane

[@Drachenbauer]

The "Starwars"-graph looks actually like a modifyed version of that triangular fractal(1.divide a big triangle into four smaller equal shaped and sized triangles 2. divide each of the three corner triangles like step 1 3. repeat step 2 on all smaller and smaller corner-triangles of next bigger triangles).

[@bruinflight1]

MORE!!!!!!

[@drainbamage2542]

keep making these graph videos...