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Terrific Toothpick Patterns - Numberphile 

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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/A13925...
The Toothpick Sequence and Other Sequences from Cellular Automata by David Applegate, Omar E. Pol, and N. J. A. Sloane: arxiv.org/abs/...
Conway on Game of Life: • Does John Conway hate ...
Monty Hall for dunmmies: • Monty Hall Problem (be...
Buffon's Matches: • Pi and Buffon's Matche...
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27 сен 2024

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Комментарии : 883   
@SylvEdu
@SylvEdu 5 лет назад
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
@Sciguy95 5 лет назад
@Dr Deuteron life is as lie. Lol
@boaz2578
@boaz2578 4 года назад
Azzy that was a beautiful way of breaking down their dynamic.
@cl4655
@cl4655 4 года назад
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
@jayceonxander3413 3 года назад
Instablaster
@PC_Simo
@PC_Simo 2 года назад
@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
@blakef.8566 5 лет назад
"...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
@annaliseoconner9266 5 лет назад
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
@firebrain2991 4 года назад
It's particularly exciting to *almost* understand things, even if you're actually nowhere near it
@OrangeC7
@OrangeC7 5 лет назад
Waiting for Matt Parker to buy a space somewhere to start laying down as many toothpicks as possible in this configuration
@keeperofthegood
@keeperofthegood 5 лет назад
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
@K-o-R 5 лет назад
A hojillion toothpicks in formation in low Earth orbit. What could possibly go wrong?
@Jeremy0459
@Jeremy0459 5 лет назад
Yes, but he'd probably mess up somewhere and then we would end up with a Parker square on one of the corners.
@hirakmondal6174
@hirakmondal6174 5 лет назад
Then Parker toothpic is on its way..😂😂
@pH7oslo
@pH7oslo 5 лет назад
If there's a way to approximate/calculate pi that way, he might just do that.
@PaulPaulPaulson
@PaulPaulPaulson 5 лет назад
Complexity emerging from simple rules and simple starting conditions is always fascinating!
@Aciek25
@Aciek25 5 лет назад
I like this professor. He is Numberphile's ASMR.
@halberdier25
@halberdier25 5 лет назад
Aciek25 he should narrate some bedtime stories.
@aksela6912
@aksela6912 5 лет назад
@@halberdier25 Yes (yes, hmm)
@robertvralph
@robertvralph 5 лет назад
He has an excitable wizard feel, that's for sure.
@__gavin__
@__gavin__ 5 лет назад
He's like a soft-spoken professor Farnsworth
@woopygoman
@woopygoman 5 лет назад
Tadashi Tokieda has a great deep voice. IMO, he has the best ASMR voice on this channel.
@andrewince8824
@andrewince8824 4 года назад
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
@samueldeandrade8535 10 месяцев назад
Is he still alive?
@andrewince8824
@andrewince8824 10 месяцев назад
@@samueldeandrade8535 he's still going at 84 years young.
@samueldeandrade8535
@samueldeandrade8535 10 месяцев назад
@@andrewince8824 thanks Math. And thanks rock climbing. Hahaha.
@Invalid571
@Invalid571 5 лет назад
That was a wonderful video. His voice is mesmerising.
@satyris410
@satyris410 5 лет назад
You need to listen to him with headphones. Wonderfully well spoken and passionate.
@izuix5629
@izuix5629 5 лет назад
it's called asmr
@apocalypticbean
@apocalypticbean 5 лет назад
Omar. Omar Poll .... yes 'yes' (whisper)
@philadams9254
@philadams9254 5 лет назад
Creepy
@TheBlazeThrower
@TheBlazeThrower 5 лет назад
Gollum
@Invalid571
@Invalid571 5 лет назад
3:52 😁
@PaulMab9
@PaulMab9 5 лет назад
@@philadams9254 You could call it *passionate*
@SimonCleric
@SimonCleric 5 лет назад
It kinda scared me a bit xD
@Brontalo
@Brontalo 5 лет назад
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
@Jehannum2000 5 лет назад
Me too. It's possibly how it all started.
@mvmlego1212
@mvmlego1212 5 лет назад
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
@PhoenixD 5 лет назад
@@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
@dennisesters7163 4 года назад
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
@717UT 4 года назад
@@mvmlego1212 you should have taken up drums in band
@InviDoll
@InviDoll 5 лет назад
Love everything about this guy. His knowledge, his wallpaper, his t-shirt.
@Ashbakhaaz
@Ashbakhaaz 5 лет назад
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
@BigDBrian
@BigDBrian 5 лет назад
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
@f_f_f_8142 5 лет назад
It is basically modular arithmatic. It works as long as the neighborhod is symmetrical so hexagonal, triangular, exctended Neumann neighborhood ... all work.
@IRanOutOfPhrases
@IRanOutOfPhrases 5 лет назад
Was this the simulator linked to in the video or a different one? I'd like to give that a spin!
@alan2here
@alan2here 5 лет назад
"And then when you look at 32 generations", it's suddenly a QR code.
@TriggerMeKaNiK
@TriggerMeKaNiK 5 лет назад
“Good news everyone!”
@matador1111
@matador1111 5 лет назад
„FARNSWORTH“
@benjaminforman8901
@benjaminforman8901 5 лет назад
My sides!
@888legends
@888legends 5 лет назад
I felt kinda bad for laughing but he does have that charm. I love to hear him talk. "just a slice" 13:22
@Inn1
@Inn1 5 лет назад
*They Form a Certain Shapes and “Copy/Replicate themselves ”* ; *We No*
@Paul-yu4ep
@Paul-yu4ep 5 лет назад
YES!
@dcsignal5241
@dcsignal5241 5 лет назад
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.
@codebitcookie8053
@codebitcookie8053 2 года назад
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.
@EinChris75
@EinChris75 5 лет назад
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.
@Artifexian
@Artifexian 5 лет назад
Looks like Piet Mondrian's work! Very cool.
@scottanderson8167
@scottanderson8167 5 лет назад
Artifexian love you, love your videos
@robertvralph
@robertvralph 5 лет назад
This was exactly my first thought. I immediately thought of taking these patterns and applying color to them.
@vtron9832
@vtron9832 5 лет назад
Didn't expect to find you here!
@wouterzandsteeg412
@wouterzandsteeg412 5 лет назад
Jeej, a dutch artist
@pmcpartlan
@pmcpartlan 5 лет назад
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
@bailey125
@bailey125 5 лет назад
Always thought Sloane's voice is oddly soothing and satisfying.
@CalvinHikes
@CalvinHikes 5 лет назад
For sure
@zacharieetienne5784
@zacharieetienne5784 5 лет назад
asmr
@LuisAlonzoRivero
@LuisAlonzoRivero 5 лет назад
The Bob Ross of power of 2 patterns
@rickskinner4424
@rickskinner4424 5 лет назад
Creepy!
@ottovonbaden6353
@ottovonbaden6353 3 года назад
@@LuisAlonzoRivero That is the weirdest descriptor that I can remember agreeing 100% with.
@malcolmgruber8165
@malcolmgruber8165 5 лет назад
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.
@FerousFolly
@FerousFolly 5 лет назад
It's like Attenborough but with numbers.
@jivejunior8753
@jivejunior8753 5 лет назад
The resemblance is there, despite that he's not British.
@Sacklar
@Sacklar 5 лет назад
@@jivejunior8753 He is. He's British-American. Born in Wales
@flamencoprof
@flamencoprof 5 лет назад
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.
@BenjiSzucs
@BenjiSzucs Год назад
Me during the day: Omg I’m so tired, I’m going to bed early today. Ma at 3am: *Terrific toothpick patterns*
@lithostheory
@lithostheory 5 лет назад
I'm so happy that people can work on things like this, humanity is doing some things right...
@dhidavidhuys8487
@dhidavidhuys8487 4 года назад
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
@photinodecay
@photinodecay 5 лет назад
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
@ErikOosterwal
@ErikOosterwal 5 лет назад
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.
@andrewince8824
@andrewince8824 4 года назад
Some people have voices just perfect for explaining abstract and incredible mathematical concepts.
@lfteri
@lfteri 5 лет назад
I have never loved even a person as much as he loves mathematics, I feel jealous :(
@tiberiu_nicolae
@tiberiu_nicolae 5 лет назад
The Parker Love
@jasertio
@jasertio 5 лет назад
Brady, you said that I was going to enjoy this video, and you were right! Lovely video, thank you!
@numberphile
@numberphile 5 лет назад
hooray - we got there in the end!
@Brayden.1P
@Brayden.1P 5 лет назад
I love Neil Sloane's passion! Thank you!
@GladionD.Pierce
@GladionD.Pierce Месяц назад
His voice seeks into my brain and and whispers int oits very depths. . .
@JamesSpeiser
@JamesSpeiser 3 года назад
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.
@Bronco541
@Bronco541 2 года назад
his excitement about toothpicks is infectious
@StefanReich
@StefanReich 5 лет назад
I believe everything you say, Professor Farnsworth
@Ben.....
@Ben..... 5 лет назад
I happy guys like this exist to ask and answer questions i would have never even conceived of
@TreniFS_
@TreniFS_ 5 лет назад
The most beautiful thing I've ever seen people do with toothpicks
@asmrtingletime4611
@asmrtingletime4611 5 лет назад
I love this old mans passion!
@altejoh
@altejoh 5 лет назад
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.
@MostlyIC
@MostlyIC Год назад
Dr Sloane is one of my heroes, thanks for interviewing him :-) !!!
@SquirrelASMR
@SquirrelASMR 2 года назад
God I love this niel Sloane guy he's so relaxing and happy and always has interesting topics to me
@up4life108
@up4life108 5 лет назад
This video is absolutely outstanding. I love cellular atomata and (without knowing mathmaticians think about it) i always draw those toothpicker patterns in class.
@lemonlordminecraft
@lemonlordminecraft 5 лет назад
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.
@christianp7200
@christianp7200 5 лет назад
close your eyes and enjoy 3:54
@maximeansell7372
@maximeansell7372 3 года назад
Love the Hendrix t-shirt feels very appropriate for this kind of fractal maths
@JamesSpeiser
@JamesSpeiser 3 года назад
I've seen quite a few videos with this gentleman speaking and he is easy to listen to and interesting to relate to.
@VibratorDefibrilator
@VibratorDefibrilator 5 лет назад
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.
@dudewaldo4
@dudewaldo4 5 лет назад
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
@dragoncurveenthusiast
@dragoncurveenthusiast 5 лет назад
His enthusiasm is so contagious!
@jyrinx
@jyrinx 5 лет назад
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.
@Z_Inspector
@Z_Inspector Год назад
Watching this actually caused me to stop what I was doing and play around with the simulations. Amazing content!
@roros2512
@roros2512 5 лет назад
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 -_-
@venkatbabu186
@venkatbabu186 4 года назад
Division is the one rule of partitioning. Numbers are junctions of partitions. Patterns vary every time you hit prime.
@deepslates
@deepslates 2 года назад
I did this on my notebooks in school. When u get big full page patterns it’s just a big square with the same 4 ends as the start, and that’s square gets bigger by powers of 2.
@mdfogarty
@mdfogarty 5 лет назад
Gosh, what a delightful, gentle soul Neil is.
@natejack2292
@natejack2292 5 лет назад
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.
@dejremi8190
@dejremi8190 4 года назад
My favourite numberphile mathematician by far!
@SomP0
@SomP0 3 года назад
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!
@ceruchi2084
@ceruchi2084 5 лет назад
This video is the perfect response to all the haters saying this new guest has "ruined" Numberphile. Brilliant, beautiful video. More Sloane!
@KatzRool
@KatzRool 5 лет назад
Thank you Mr. Sloane, very cool!
@baconology3065
@baconology3065 5 лет назад
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!
@rocksparadox
@rocksparadox 5 лет назад
These are great examples that deviate from the rules in Conway's Game of Life.
@ethanalexander7957
@ethanalexander7957 5 лет назад
so it becomes a square at every power of two, better call computerphile!
@tdbla98
@tdbla98 2 года назад
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. RU-vidrs like you and 3 blue 1 brown, Matt Parker, etc. You guys really make maths fun
@shruggzdastr8-facedclown
@shruggzdastr8-facedclown 4 года назад
This Neil Sloane has a very pleasing voice!
@Czeckie
@Czeckie 5 лет назад
ok, I didn't particularly enjoy the previous two videos with prof Sloane, but this one is amazing. I wan't toothpick design on my walls
@nullanon5716
@nullanon5716 5 лет назад
I actually independently discovered something like this, but the child nodes and the parent node were 120 degrees apart forming a triangular shape
@gamerwizard69
@gamerwizard69 5 лет назад
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!
@Dae-Ying-Kim12345
@Dae-Ying-Kim12345 2 года назад
CRAZYLY BEAUTIFUL.
@Luminous.A.Glory_VitaNostra
@Luminous.A.Glory_VitaNostra 5 лет назад
I love how excited he is!!!
@CptPatch
@CptPatch 5 лет назад
The replicator of the hearts in the outro is amazing. Thank you.
@Morgiliath
@Morgiliath 5 лет назад
Played around with this stuff in golly, it's super cool to see some of the math behind it.
@yosoyjose
@yosoyjose 5 лет назад
i really really like this kind of videos, about patterns and about fractals
@jordansandoval7097
@jordansandoval7097 4 года назад
Idk if this is very significant, but you can simulate the original toothpick machine using a grid and cells. You just need cells to survive with 1-5 neighbors (if you change the survival states, you can get variations of the same image, and I find them all rather delightfully pretty) and to be born with 1 neighbor (diagonals included for both) I noticed the toothpicks greatly resembled a simulation I created in an app meant to replicate conway's game of life, but where you can alter the rules if you please. Cells born from single neighbors naturally reflect this corner-centric style of growth.
@HolyG-sus
@HolyG-sus 3 года назад
I like how he said "u can do it on ur computer at ur home" assuming that his computer has better aspects but still lags
@nix207
@nix207 4 года назад
I had this in the background while doing homework and I jumped when he started mentioning how things spread and how this might be useful for people studying epidemics. Kinda makes sense why RU-vid decided to recommend this one
@multilevelintelligence
@multilevelintelligence 4 года назад
Sometimes he sounds like Mr freeze turning on buttons in Batman and robin....lol....Great work guys
@briangonigal3974
@briangonigal3974 5 лет назад
I stumbled upon the toothpick pattern myself as a kid, in my case it was with playing cards, building a sort of one-story "house of cards" by propping up a playing card standing on its side by crossing it with two other cards, one on each end, then crossing the two ends of those two cards with other cards etc. The pattern very quickly grew unwieldy yet interesting enough to switch to graph paper, and I soon filled much of a graph paper notebook with lined patterns, and on the other side of each page lists of numbers keeping track of how many "cards" were added to each generation, fruitlessly trying to find a pattern in the numbers. Being a ten year old or so kid who would not ultimately be drawn to a career in mathematics that's as far as it went, but it's cool to see some actual competent mathematicians picking up where I left off
@entropysalamander
@entropysalamander 5 лет назад
Absolutely loved this one
@no_handle_required
@no_handle_required 5 лет назад
At first I thought, so what? Then the fractal toothpick took over and hypnotized me into just thinking.....wow.
@reillystevens9448
@reillystevens9448 5 лет назад
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
@LeoStaley
@LeoStaley 5 лет назад
More of stuff like this please.
@macedindu829
@macedindu829 5 лет назад
That's so beautiful. Amazing.
@radielkill
@radielkill 5 лет назад
as a chemical engineer i can se how some of this sequences can be used in different models to predict a catalytic reaction, a really impressive work, great video ¡¡¡¡
@idvarhurd7804
@idvarhurd7804 5 лет назад
10:00 Stanisław Ulam was Polish Mathematician from Lwów who developed in Los Alamos together with Hungarian Physicist Edvard Teller igniting mechanism for H-Bomb. Just for context.
@WillBinge
@WillBinge 4 месяца назад
I remember coming across this pattern while messing about in Minecraft. I never went into the maths of it, but it is cool.
@hiimapop7755
@hiimapop7755 5 лет назад
One of the most simple but interesting fractals, I've seen.
@solsystem1342
@solsystem1342 2 года назад
I actually stumbled into the same construction as the automaton from a different direction. Specifically, I was trying to fill as much of a infinite grid as possible with the similar placement rules. You can only fill in a tile that has 1 or 0 filled in neighbors. You can tile the board with a 1st step version of this (5 squares in each star). I later figured out that you could repeat the process forever and tiled the board with a single infinity step star. I iterated on them by creating 4 copies of the last step and then coloring the space in the middle. This design can always be made with these placement rules and gives you a larger portion of the board colored in then anything else I could find.
@Ny0s
@Ny0s 3 года назад
The e animation is so beautiful.
@SaveSoilSaveSoil
@SaveSoilSaveSoil 4 года назад
Very beautiful patterns!
@Youngy
@Youngy 3 года назад
2:05 How Super Paper Mario draws their levels when you enter the door for the first time.
@kieronwelman4954
@kieronwelman4954 4 года назад
I play this every night and I sleep like a baby now. A masterpiece
@huntermunts9660
@huntermunts9660 5 лет назад
I wonder if there are any crystal structures that look like this
@paceyplodder5911
@paceyplodder5911 5 лет назад
Looks like a Borg ship regenerating.
@failgracefully7911
@failgracefully7911 5 лет назад
Neil Sloane has the best job
@guyspy21
@guyspy21 5 лет назад
I was playing around with the simulator and If we go the ulam-warbaton rule and select "outward corner" we get the sierpinski triangle mirrored! That just blew my mind!
@milkosek
@milkosek 5 лет назад
Really wise words in this interesting problem! And the Hendrix shirt on the man... I love that!
@MuzikBike
@MuzikBike 4 года назад
At every step which is a power of two the amount of toothpicks is also roughly a third of a power of 2
@maxchatterji5866
@maxchatterji5866 5 лет назад
How funny. I just had an interview with Neil Sloan for my Oxford maths application process.
@thomazmarra5437
@thomazmarra5437 5 лет назад
Nice Hendrix shirt, man
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