Terrific Toothpick Patterns - Numberphile

Fun with toothpicks. Featuring Neil Sloane.
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of the On-Line Encyclopedia of Integer Sequences: oeis.org
Play with the toothpick simulator: oeis.org/A139250/a139250.anim....
The Toothpick Sequence and Other Sequences from Cellular Automata by David Applegate, Omar E. Pol, and N. J. A. Sloane: arxiv.org/abs/1004.3036
Conway on Game of Life: • Does John Conway hate ...
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And support from Math For America - www.mathforamerica.org/
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[@SylvEdu]

I like how mathematicians solve things because they look fun and then later everyone is astounded that the solved problem has some amazing, unexpected, and useful real-life application, and the mathematicians are like, "yeah, neat..." but they are already working on their next puzzle just for fun.

[@Sciguy95]

@Dr Deuteron life is as lie. Lol

[@boaz2578]

Azzy that was a beautiful way of breaking down their dynamic.

[@cl4655]

mathematicians just think “hey it would probably be cool if i did this” then they do it and then later realize “hol up, this is actually useful!”

[@jayceonxander3413]

Instablaster

[@PC_Simo]

@Azariah My former high school’s maths teacher, Hannu Sinisalo, famously said: ”The less mathematics has to do with reality, the better. It’s not necessary to have anything to do with truth, anyway.”. 😅

[@blakef.8566]

"...and we don't understand this at all." When he says this, there is a childlike excitement in his voice. I guess that this goes to show that though it's exciting to understand things, it's can also be exciting not to.

[@annaliseoconner9266]

I caught that too. He was almost reverent when he said it, loving the challenge and mystery as much as the beautiful solutions. That was my favorite part of the entire video.

[@firebrain2991]

It's particularly exciting to *almost* understand things, even if you're actually nowhere near it

[@OrangeC7]

Waiting for Matt Parker to buy a space somewhere to start laying down as many toothpicks as possible in this configuration

[@keeperofthegood]

omg I first read that as Parker going to space... then had the image of the space station come to mind... all those square spaces and a Parker in them... woe betides the ISS

[@K-o-R]

A hojillion toothpicks in formation in low Earth orbit. What could possibly go wrong?

[@Jeremy0459]

Yes, but he'd probably mess up somewhere and then we would end up with a Parker square on one of the corners.

[@hirakmondal6174]

Then Parker toothpic is on its way..😂😂

[@pH7oslo]

If there's a way to approximate/calculate pi that way, he might just do that.

[@apocalypticbean]

Omar. Omar Poll .... yes 'yes' (whisper)

[@philadams9254]

Creepy

[@TheBlazeThrower]

Gollum

[@Invalid571]

3:52 😁

[@PaulMab9]

@@philadams9254 You could call it *passionate*

[@SimonCleric]

It kinda scared me a bit xD

[@jurrasicgrant2307]

The way he is talking lmao its seductive to be honest. Anyways, almost everyone on Numberphile is so passionate about their stuff, it's so amazing to see.

[@XenoghostTV]

Jurrasic Grant Exactly. You can literally hear these guys' passion in their voices.

[@JorgetePanete]

it's*

[@itthumyir4569]

@@JorgetePanete 👏👏👏👏👏👏

[@ngkenobi8376]

He's got numberphilia

[@carlchampagne941]

If this is how he talks in public, just imagine what he says to his mathematics in private.

[@Aciek25]

I like this professor. He is Numberphile's ASMR.

[@halberdier25]

Aciek25 he should narrate some bedtime stories.

[@aksela6912]

@@halberdier25 Yes (yes, hmm)

[@robertvralph]

He has an excitable wizard feel, that's for sure.

[@__gavin__]

He's like a soft-spoken professor Farnsworth

[@woopygoman]

Tadashi Tokieda has a great deep voice. IMO, he has the best ASMR voice on this channel.

[@andrewince8824]

Sloane was 79 at the time of this video's publication. Besides being an incredible mathematician he's an avid rockclimber. Seriously, Neil Sloane has managed to mathematically manipulate his age to stay so young.

[@samueldeandrade8535]

Is he still alive?

[@andrewince8824]

@@samueldeandrade8535 he's still going at 84 years young.

[@samueldeandrade8535]

@@andrewince8824 thanks Math. And thanks rock climbing. Hahaha.

[@PaulPaulPaulson]

Complexity emerging from simple rules and simple starting conditions is always fascinating!

[@callmetony1319]

emergence at its core.

[@Invalid571]

That was a wonderful video. His voice is mesmerising.

[@satyris410]

You need to listen to him with headphones. Wonderfully well spoken and passionate.

[@izuix5629]

it's called asmr

[@ashtonhoward5582]

"We're at a table. We have tooth picks. We notice that each tooth pick has two ends." Reminds me of when we rolled low on a perception check. Except not even then did we notice that the door has two sides.

[@OlbaidFractalium]

Every pattern is very beautiful. I also want to see 3D version.

[@richbuilds_com]

Just wait till someone releases a self replicating nanobot ai...

[@woodpecker_4255]

Well... I made one a while back.

[@woodpecker_4255]

The paturn I mean.

[@jimi02468]

If you did the same pattern with squares, (square is the 2D version of a toothpick) the squares would overlap and stuff and it would be a failure. So you can't have a 3D version.

[@totaltotalmonkey]

How is a square is the 2D version of a toothpick? The toothpick is already 2D, even if you consider the toothpick a one dimensional line (instead of a six sided shape) it is still being arrange on a 2D plane.

[@corncolonel9171]

Me in 2019: oh that's pretty neat Me in 2020: "how fast diseases spread" HA

[@gallium-gonzollium]

So basically everyone’s a toothpick?

[@aditya95sriram]

This is turning out to be a wonderful series. Neil Sloane himself giving us an inside peek of his marvelous encyclopedia entries. Keep em comin :)

[@ThePharphis]

best videos on this channel in years, tbh (but maybe I'm just too excited to learn about his database some more)

[@StupidLazyStupid]

Hello other Aditya

[@TriggerMeKaNiK]

“Good news everyone!”

[@matador1111]

„FARNSWORTH“

[@benjaminforman8901]

My sides!

[@888legends]

I felt kinda bad for laughing but he does have that charm. I love to hear him talk. "just a slice" 13:22

[@Inn1]

*They Form a Certain Shapes and “Copy/Replicate themselves ”* ; *We No*

[@Paul-yu4ep]

YES!

[@alan2here]

"And then when you look at 32 generations", it's suddenly a QR code.

[@Brontalo]

Oh my god. I can't even. I swear, i encountered the first pattern for myself via bored doodling back in school like 10 years ago and drew this pattern everywhere in notebooks cause it looked so pleasing. Thank you for showing it in an actual video.

[@Jehannum2000]

Me too. It's possibly how it all started.

[@mvmlego1212]

That sort of thing happened to me with Matt Parker’s video on pouring equal-strength cups of coffee from the same pot. I remember having OCD symptoms as a kid, (I’ve gotten them over them since then), so when I would tap one of my feet by accident, I would feel compelled to tap the other. But, since I tapped one first, let’s say my left one first for example, I would feel compelled to tap them both again, but with the right one first. But, because the _first_ first tap was with my left foot, I would have to do the same sequence of tapping, but flipped in order to even things out, and this would go on as long as I could keep track. Altogether, I ended up with a sequence going something like LRRLRLLRRLLRLRRL... The sequence was mentioned in one of Matt Parker’s video as the best way to “even out” things given certain conditions.

[@PhoenixD]

@@mvmlego1212 exactly like me. I ve gotten over it too, even if not completely. For example, when I'm programming, everything has to follow a certain order, similar constructs must be aligned, no memory leaks must be present or I can't leave my programming session and so on (which is not necessarily a bad thing, since i'm still in control). But when i was a kid, i had the same "tics" you described, plus many others, and "almost" couldn't resist them (almost because i didn't even try really). For example if i was going down a spiral staircase, i used to count how many times i rotated until I've come to the end, and rotate that many times in the opposite direction. When i noticed that things were starting to go out of control, like long sequences to balance everything out as you described, i said: I'm gonna provoke everything that i hate on purpose, and unbalance it as much as i can, let's see what happens. Nothing. Never had the strong need since then. Only difference with what you wrote is that my sequences were a little different. For example, i touch the wall with my right hand, using a force on a scale 1 to 10 of 5. I have to do the same with the left. I try, but hit with force 7. Now i have to do right 7 and left 5. I do left 5, but right 6, and so on.

[@dennisesters7163]

I also started bored doodling the drawing what they call the toothpick pattern for more than 15 years and maybe more than 20, and analyzing it to see if it contains anything useful. I have never cared how many lines there were a n-iterations (like this wonderful video). Until seeing this video today, I thought I was the only one.

[@717UT]

@@mvmlego1212 you should have taken up drums in band

[@InviDoll]

Love everything about this guy. His knowledge, his wallpaper, his t-shirt.

[@BenjiSzucs]

Me during the day: Omg I’m so tired, I’m going to bed early today. Ma at 3am: *Terrific toothpick patterns*

[@madumlao]

I love how he was incredulously like "who would ever design a gull toothpi..." and he just answered "Mark Pol" without skipping a beat.

[@JJ-kl7eq]

Most Numberphile videos are ver good. This one is better, I dare say an excellent ...pick.

[@toropazzoide]

I'd say terrific, even

[@julijanmartincevic1856]

@@toropazzoide terriPick

[@JorgetePanete]

very*

[@tristrumandrewsfisho339]

This comment and every reply except this one now has a power of 2 likes. You're welcome.

[@tristrumandrewsfisho339]

never mind i can like my own comment

[@Ashbakhaaz]

One of the best videos on the channel, imo! Very interesting, very mathematic AND aesthetic, simple yet complicated, and not arbitrary... I want moar of this! :D

[@dcsignal5241]

I smiled when I saw his large piece of paper. I have books and books of this kind of stuff from a phase I went through in the 90's. Complexity from simple rules is absolutely fascinating.

[@Artifexian]

Looks like Piet Mondrian's work! Very cool.

[@scottanderson8167]

Artifexian love you, love your videos

[@robertvralph]

This was exactly my first thought. I immediately thought of taking these patterns and applying color to them.

[@vtron9832]

Didn't expect to find you here!

[@wouterzandsteeg412]

Jeej, a dutch artist

[@pmcpartlan]

Are you aware of an artist called A Michael Noll? He made some of the earliest computer art, one of which was a series of versions of a Mondrian painting

[@FerousFolly]

It's like Attenborough but with numbers.

[@jivejunior8753]

The resemblance is there, despite that he's not British.

[@Sacklar]

@@jivejunior8753 He is. He's British-American. Born in Wales

[@felix4093]

everytime he says "we do this forever" its gives me chills

[@bailey125]

Always thought Sloane's voice is oddly soothing and satisfying.

[@CalvinHikes]

For sure

[@zacharieetienne5784]

asmr

[@LuisAlonzoRivero]

The Bob Ross of power of 2 patterns

[@rickskinner4424]

Creepy!

[@ottovonbaden6353]

@@LuisAlonzoRivero That is the weirdest descriptor that I can remember agreeing 100% with.

[@codebitcookie8053]

This was one of my favorite Numberphile videos. It was absolutely flabbergasting to see the patterns unfold like that. When he brought out the hexagonal cellular automaton analysis paper, it really showed his passion.

[@BigDBrian]

how the heck does the replicator work? it seems like magic. I drew a smiley face and an arbitrary picture, and both got replicated perfectly. In the simulator I was using, the field was limited, and interestingly, when it hit the corners it actually produced a mirrored version of the original. Even more interestingly is that the simulator didn't consider the diagonals, only the direct neighbours.

[@f_f_f_8142]

It is basically modular arithmatic. It works as long as the neighborhod is symmetrical so hexagonal, triangular, exctended Neumann neighborhood ... all work.

[@IRanOutOfPhrases]

Was this the simulator linked to in the video or a different one? I'd like to give that a spin!

[@lfteri]

I have never loved even a person as much as he loves mathematics, I feel jealous :(

[@tiberiu_nicolae]

The Parker Love

[@EinChris75]

Awesome... just recently I looked up a sequence on OEIS. Then I wanted to know who made that database. And I found out, it was him. And now we have him explaining cool stuff here. Almost as amazing as replicating pixels.

[@malcolmgruber8165]

I love the hex, because the pattern is so much more complex. You get repeating bits, but slowly those bits grow into larger patterns as you get more growing hexes! So beautiful! And lots of triangles in its shape as well.

[@lithostheory]

I'm so happy that people can work on things like this, humanity is doing some things right...

[@andygup1585]

this is one of my favourite numberphile videos!!!!

[@flamencoprof]

Brings back memories. Back in the Eighties, I read an article in Scientific American on cellular automata which led to a fruitful period of learning to program my new Commodore 64, first in Basic and then when that was too slow, with opcodes, reading, processing and then writing directly to the screen memory, one pixel at a time. You can now find websites with such wee programs you can play with.

[@dielfonelletab8711]

I sense a Coding Train video coming out of this...

[@zitronenwasser]

It's here

[@Brayden.1P]

I love Neil Sloane's passion! Thank you!

[@dudewaldo4]

Thank you for the work you put into the description! It is nice to know that relevant links will always be there :) checking out the toothpick simulator now

[@StefanReich]

I believe everything you say, Professor Farnsworth

[@dhidavidhuys8487]

for somebody totaly sucking at math my whole life , yet not able to resist not subscribing to this channel , i just think i wish i had this man as my math teacher... i just got high watching this its amazing

[@jasertio]

Brady, you said that I was going to enjoy this video, and you were right! Lovely video, thank you!

[@numberphile]

hooray - we got there in the end!

[@EnglishTeacherBerlin]

I don't understand maths but I am touched by the compassion and dedication of this wonderful man to his subject. Just beautiful!

[@cubethesquid3919]

Neil Sloane is the David Attenborough of mathematics

[@Skyefaux]

I love how much that guy loves math

[@christopherperez6126]

I love this channel and I love how enthusiastic mathematician are on here

[@legendhero-eu1lc]

Thank you for the video! All of you are super awesome!

[@camelapodo]

Absolutely loved this one

[@LunarcomplexMain]

This mans voice is delightful. I would love to hear more of it!

[@asmrtingletime4611]

I love this old mans passion!

[@up4life108]

This video is absolutely outstanding. I love cellular atomata and (without knowing mathmaticians think about it) i always draw those toothpicker patterns in class.

[@baconology3065]

this is the best video on the channel i have come across, great work on the logo and graphic effects. this guy really loves what he does, and i relate to that, he hasn't given up!

[@nofka77]

Amazing patterns! Love them so much!

[@ErikOosterwal]

On the hexagonal pattern, the inner pattern spawns four replicas of itself after reaching a power of two. In the replicas that grow in a more outwardly direction from the center it's easy to see the replicated pattern, but the replicas that fill the empty space between the points of the hexagon start interfering with each other to create a slightly new pattern in the middle of the new triangle.

[@nickcorrado5105]

This is a wonderful one! Would love to see more content with Neil Sloane.

[@callumstewart5891]

I would listen to anything he said for hours. His voice is wonderful.

[@TreniFS_]

The most beautiful thing I've ever seen people do with toothpicks

[@JamesSpeiser]

I love when you see a magnification of a fractal pattern that diffraction type patterns come and go. I swear after so many decades of studying it....it seems like it communicates something sometimes that way...a higher order of the pattern revealing itself. Trippy.

[@dragoncurveenthusiast]

His enthusiasm is so contagious!

[@gamerwizard69]

i love this video because the second the concept was introduced my first thought was different shapes so i was filled with glee when the other options were shown in the video!

[@Z_Inspector]

Watching this actually caused me to stop what I was doing and play around with the simulations. Amazing content!

[@KatzRool]

Thank you Mr. Sloane, very cool!

[@CptPatch]

The replicator of the hearts in the outro is amazing. Thank you.

[@reillystevens9448]

i love videos like this... they honestly have to be my favorite. proofs are neat but i love being able to really visually see these patterns. especially after watching several of your videos you start to see patterns in the patterns in the patterns and realize that it's all just math. everything. lol. thanks brady

[@SquirrelASMR]

God I love this niel Sloane guy he's so relaxing and happy and always has interesting topics to me

[@ianbeach5861]

Played around with this stuff in golly, it's super cool to see some of the math behind it.

[@yosoyjose]

i really really like this kind of videos, about patterns and about fractals

[@LeoStaley]

More of stuff like this please.

[@_infinitedomain]

What a brilliant video, loved this one

[@macedindu829]

That's so beautiful. Amazing.

[@lemonlordminecraft]

Cliff and Neil are two sides of the same math-loving coin. One with a chaotic and excitable approach and the other with an equally powerful ordered and serious approach. Both seem to have the exact same passion for the field and I think it's beautiful.

[@roros2512]

This is like the 10 time that I listen this video, I really like the content and in general the content of numberphile, but the voice of this gentleman is really warming and calming, it relaxes me -_-

[@717UT]

I would have loved having this fellow as a professor. Passionate people make learning easy.

[@JamesSpeiser]

I've seen quite a few videos with this gentleman speaking and he is easy to listen to and interesting to relate to.

[@Ben.....]

I happy guys like this exist to ask and answer questions i would have never even conceived of

[@eac-ox2ly]

The passion this guy has is formidable

[@trexpaddock]

Such a wonderful thing. Thank you.

[@Luminous.A.Glory_VitaNostra]

I love how excited he is!!!

[@altejoh]

My favourite part of these videos is looking at these kinds of activities, and seeing how they can be applied to other areas of life and science. For example, immediately this makes me think of crystal growth, with each of the "toothpicks" being a different tiny crystal domain, a set of regular crystal lattices, forming into small crystals that then themselves form on specific sites of other crystals, and then continue to grow into a massive, chaotic, and yet still periodic, superstructure.

[@christianp7200]

close your eyes and enjoy 3:54

[@mdfogarty]

Gosh, what a delightful, gentle soul Neil is.

[@tdbla98]

I love math for reasons like this. Makes me so happy, something so small(yet large) is so entertaining to me. I'm thinking about going back to college to get into physics or some type of science/maths heavy field. KZbinrs like you and 3 blue 1 brown, Matt Parker, etc. You guys really make maths fun

[@sparhopper]

One of my favorites

[@anthonyblot828]

I used to replicate the first toothpick pattern with cards to build a squared base for many houses of cards. It's a pretty strong structure, and now I can know exactly how many cards is needed depending on the size of the base. Thanks.

[@jyrinx]

I would LOVE to see more working notes from mathematicians! Exciting to see what's on the horizon like that, and to glimpse at how they approach problems.

[@MostlyIC]

Dr Sloane is one of my heroes, thanks for interviewing him :-) !!!

[@FriendlyIndex]

Keep up the good work Brady! love it!

[@SaveSoilSaveSoil]

Very beautiful patterns!

[@natejack2292]

1. Excellent video. This kind of video shows the innate beauty of mathematics in a way that makes me want to pick up a pencil and start drawing iterations. One can only imagine how these sequences are related to others found in nature. 2. This would be an awesome screensaver.

[@andrewince8824]

Some people have voices just perfect for explaining abstract and incredible mathematical concepts.

[@Bronco541]

his excitement about toothpicks is infectious

[@hoseja]

Math Bob Ross.

[@AnkhAnanku]

First one looks like a frank-lloyd-wright window-screen. Reminded me of the guy who did the “dragon’s curve” as a tiled wall decoration...

[@jburtson]

I was trying to code my own cellular automata once and with a test rules system I ran into the same patterns as this video! Fascinating. My ruleset was in the next iteration a cell is filled in with a value according to the number of neighbors that had the value “1”. Other than some fancy extra colors, it looks like I stumbled upon the Ulam Warburton Cellular Automata!

[@caio-jl6qw]

Amo este canal!

[@milkosek]

Really wise words in this interesting problem! And the Hendrix shirt on the man... I love that!

[@VibratorDefibrilator]

15 years ago I've been playing with Conway's Game of Life, in fact playing with the rules of the game, and found (after many trials and errors) that very beautiful and intricate patterns could appear with this set of rules: 1. Cell turns ON if it has 1, 3, 5 or 7 neighbours. 2. Cell stays turned ON only if it has no neighbours; otherwise it turns OFF. It behaves very much like that Fredkin replicator, because... now I see that it has pretty much the same rules. The variety of patterns of course depends on the starting position. Curious patterns and trends appear when we change the concept of the neighbouring cell - for example: besides the "classical" neighbours (which have common side or vertex with our cell) we will include the neighbours of the neighbours. There is plenty of this to observe and explore. Very nice and informative video, by the way.

[@woutervanr]

Niceeee, an other Neil video just like I wanted!

[@ethanalexander7957]

so it becomes a square at every power of two, better call computerphile!

[@drewdurant3835]

Love you guys!!! Thank you 🙏❤️ y’all be dat 🔥

[@photinodecay]

It looks like a really cool city design. Big boulevards down the center and then smaller boulevards crossing the quadrants and then breaking down into neighborhoods on side roads that are not through streets

[@SomP0]

THIS IS CRAZY! I can assure yall I have never heard of this problem but this was my tactic to dealing with anxiety in a class by doodling this exact problem. I thought I was a genius to come up with this but thanks for shattering my ego. Still cool to see!