Part 2 (featuring Pi) is here: kzitem.info/news/bejne/1aF5l3x-rqecapg
@user-dy9tf1ch1n
2 жыл бұрын
He's boring
@glg1969
2 жыл бұрын
Do you have a link to the Mathematica code for the turtle function, so I can show my son?
@TomRocksMaths
2 жыл бұрын
I could watch that machine draw all day… sooooooo satisfying
@shruggzdastr8-facedclown
2 жыл бұрын
Hey, you're the Navier-Stokes enthusiast! Seriously though, Tom, when's your next turn to guest host a Numberphile video?
@maestroeragon
2 жыл бұрын
Imagine if it could do tattoos! If you have any space left, I'm sure you'd have plenty of ideas for the machine haha
@mrphlip
2 жыл бұрын
The most impressive part of this whole video is taking the paper off the plotter mid-print, showing it off, and then putting it back on the plotter and being able to continue the print with everything still lined up properly...
@PhilBoswell
2 жыл бұрын
I'm guessing there's something analogous to "drawing pin holes" so that he can just attach the paper in the same fashion as before: I would be croggled if it actually uses old tech like drawing pins ;-)
@williamchamberlain2263
2 жыл бұрын
@@PhilBoswell doesn't it just use the _POWER OF HIS MIND?_
@MichaelOfRohan
2 жыл бұрын
Im sure the paper was bucked against jigs on a couple adjacent sides
@MichaelOfRohan
2 жыл бұрын
I still love you though
@unvergebeneid
2 жыл бұрын
haha, ikr!
@Rubrickety
2 жыл бұрын
Finally a Numberphile video with a plot. 😉
@lonestarr1490
2 жыл бұрын
ba dum tss
@Superphilipp
2 жыл бұрын
I definitely watch for the plot
@_rlb
2 жыл бұрын
You've got 42 likes which is the best number of likes.
@deltalima6703
2 жыл бұрын
Video is boring but the peanut gallery is on point! :))
@aurelia8028
2 жыл бұрын
lol
@grumpyrocker
2 жыл бұрын
I remember programming the Turtle at school in the 1980s. We had a physical Turtle robot and we could get it to draw big images on the large sheets of paper on the floor.
@Baconlessness
2 жыл бұрын
We had something similar that didn't draw anything. It looked like a small roomba that you could program with forwards, lefts and rights
@shruggzdastr8-facedclown
2 жыл бұрын
We had something similar to "Turtle" on our Apple II-Es when I took a basic/introductory computer skills workshop for a one-marking period elective back in eighth grade back in 1985/'86 where we would input some simple geometric instructions, and the cursor ("turtle") would draw triangles, squares, pentagons, hexagons, stars, etc.
@vigilantcosmicpenguin8721
2 жыл бұрын
Dang, guess I missed out on the cool Turtle lessons as a student in the 2010s. We just programmed Turtle using the Java Virtual Machine.
@tfofurn
2 жыл бұрын
I participated in a summer camp with the turtle robot. The instructor laid a course out on the floor and we each programmed our solution. One person thought the movement units were feet instead of inches, so on their attempt, the turtle barely moved. The teacher announced that the solution looked correct other than the scaling.
@danielstephenson7558
2 жыл бұрын
One of the most satisfying things I've ever printed is the Sierpinski Pyramid. Never had to take it's 'pen' off the paper the entire way up the object.
@davidgillies620
2 жыл бұрын
It's amazing what you can do with recursive formal grammars. Douglas Hofstadter goes into great detail in this vein in _Gödel, Escher, Bach_ .
@YerpyMoose
2 жыл бұрын
bloop, floop, gloop
@SquirrelASMR
2 жыл бұрын
I really like this guy's math visualization animations
@judychurley6623
2 жыл бұрын
The British artist Harold Cohen in the 70s had produced "Aaron" an expert system that produced important exhibitions (at the Tate Modern and elsewhere) producing large-scale artworks using a 'turtle' - but did not use pre-determined forms. Really interesting.
@SquirrelASMR
2 жыл бұрын
I wanna see these run forever
@goodboi650
2 жыл бұрын
I knew all those repressed LOGO memories would come in handy someday
@mrdrbernd
2 жыл бұрын
He seems to be using an AxiDraw (or clone). You can do these graphs in huge very easily with a polargraph (or makelangelo). Very simple to build and 1 m x 1 m size is easily achievable and very cheap to build. Had plenty of hours of fun so far with it.
@matthewwilson8292
2 жыл бұрын
Andy Murray’s secret second brother ;) - amazing video!
@naathcousins4658
2 жыл бұрын
When I was young we had a turtle robot that drew on paper on the floor, it was cool
@AdamArcherPigeons
2 жыл бұрын
Reminds me of Langton's Ant.
@mossy8419
2 жыл бұрын
I’d like to see a simulation where theta is set to 361/360 and subsequently 129601/129600; I think that the former will make a spiral of spirals and the latter will make a spiral of spirals of spirals
@MelindaGreen
2 жыл бұрын
The big triangles don't contain exact copies of the smaller ones. They are slightly different in the corners where they attach to other copies.
@MariusSc
2 жыл бұрын
That’s cool! Going to try this out myself :)
@nosuchthing8
2 жыл бұрын
Now I need some hyperbolic parabaloids
@bfuatrophyxtissues
5 ай бұрын
I was watching this and i was like turtle drawing things using coding? Ive read a comic book series on that before!
@Frownlandia
2 жыл бұрын
Is there a way to construct a fractal Euler-spiral-of-Euler-spirals and derive a theta value from that?
@vigilantcosmicpenguin8721
2 жыл бұрын
Ah, this video confirms a truth I hold close to my heart: when you have a robot, you can do awesome things.
@MrPeterFranc
2 жыл бұрын
it's incredible how it looks like some kind of protein or something
@Veptis
2 жыл бұрын
The turtle graphics is an (eso)lang called LOGO
@ZeDlinG67
2 жыл бұрын
I had the fortune to learn Comenius Logo in elementary school, now I'm a lead developer.
@RickSanchez78-d2v
2 жыл бұрын
Ok, now have your machine give me a tattoo of that
@asi.izzygizmic
2 жыл бұрын
The last figure is very viharty
@FanTazTiCxD
2 жыл бұрын
I know this is unrelated, but can anyone solve this math problem I have always puzzled over? I call it the copy/paste problem: Suppose you want to make a comment with a lot of the same letters repeated over and over, such as "NOOOOOOOOOOOOOOOOOOOOOO". You want to put in at least 1000 O's. Of course, you could type it all, which would require an N and 1000 "moves" of typing an O. But you want to save time, so instead, you type 10 O's, then copy those 10 O's and paste 100 times. Now that equals to 10 moves (for typing 10 O's) + 100 moves (for pasting 100 times. Copying does not count as a move). In total, you made only 110 moves instead of 1000 because you were smart and copy/pasted. Now what would be the best copy/paste strategy to type at least 1000 O's in the least amount of moves? Eventually, the question I want answered is: What is the perfect strategy, to type at least N amount of a letter, in the least amount of moves? Remember that it's at least. Ending up with more than your aim is fine too. Typing the letter counts as a move Pasting what you copied counts as a move But copying doesn't count as a move What's the solution? Like my comment if you have a solution, since replies don't notify me. Then I'll check back
@Robinson8491
2 жыл бұрын
What would you need algorithmically to get the Bernouilli solution to the brachystochrone curve? It would be possible to draw with this robotpen, and thus there should be a program. I need this in my research Edit: preferably based on the transcendental number e so the curvature gradient equals the value on the vertical axis
@wallywutsizface6346
2 жыл бұрын
Would the picture be less jagged, but the same spiral I’d you halves the angle, but also halved the step size?
@Foxxorz
2 жыл бұрын
Looks like those twisted atoms that were just discovered.
@naringrass
2 жыл бұрын
draw a hilbert curve!
@vsm1456
2 жыл бұрын
6:05 This figure for 1.0456 looks like a pattern. I wonder where does it come from? In the form of fraction that number would be 1307/1250, doesn't look particularly interesting...
@sperenity5883
2 жыл бұрын
Reminds me of the Julia Set, but I'm sure it's coincidental.
@ixian98
2 жыл бұрын
is there a python equivalent for "SubstitutionSystem ?" thank you
@GourangaPL
Жыл бұрын
You could've filled the paper with Hilbert's Curve
@bighammer3464
2 жыл бұрын
Plotting it with the machine is absolutely against the numberphile rules.
@maximilianosotomayorga4977
2 жыл бұрын
tim burton vibes math teacher
@AMGUESSING
2 жыл бұрын
How does lotto function
@nimmira
2 жыл бұрын
beautiful can we find specific patterns of such equations when working with tessellations?
@Epinardscaramel
2 жыл бұрын
I want to buy an AxiDraw but they've been out of stock since 2021 😩
@justinhsu3253
2 жыл бұрын
The spiral of spirals is definitely genius. I wonder what if we let the theta respond to the movement smoothly rather than stepwise.
@vaxjoaberg
2 жыл бұрын
@numberphile, the "part 2" link at the end of the video isn't working.
@numberphile
2 жыл бұрын
It will tomorrow.
@spot1401
2 жыл бұрын
Who else is shopping for plotters in the middle of the night?
@piripow8930
2 жыл бұрын
Was I the only one shocked that I couldn't find part 2? 😂
@TheLoafOfBreadOG
2 жыл бұрын
F 4 T 67° F 1 pen ⬆️
@talideon
2 жыл бұрын
For those without Mathematica, Python has a built-in turtle graphics module.
@BrianBlock
2 жыл бұрын
Yeah, you can basically find a turtle library/function for any language these days, this is a classic :)
@DeclanMBrennan
2 жыл бұрын
@@BrianBlock Thanks Seymour Papert. You gave generations of kids some serious fun while they were learning through osmosis with the Logo Turtle and Language.
@flyingphysics9664
2 жыл бұрын
Mathematica comes free on the Raspberry Pi...
@odraz0101
2 жыл бұрын
@@flyingphysics9664 is it fully functional Mathematica or is there limitations? Does it have access to knowledge base?
@gregwochlik9233
2 жыл бұрын
I used that Python turtle module myself. I got it to draw the Sierpiński triangle myself. I picked up a recursive code on line.
@DqwertyC
2 жыл бұрын
This is kind of amusing. I make Minecraft datapacks, usually based on fun math concepts. One of my main inspirations is this channel, and sometimes I'll try to recreate the processes in Numberphile videos in Minecraft. But this time, I posted a datapack about a topic just before you! My latest video was the Sierpinski Arrowhead Curve, which was generated with the same replacement method, and I'm working on a larger video about Lindenmayer (replacement) systems.
@alexelliott9733
2 жыл бұрын
1:41 - "a can of hyperbolic paraboloids" - that brought me back to my calculus class where my professor kept referring to that shape as a pringle
@rhoddryice5412
2 жыл бұрын
Videos with Henderson are always great. Looking forward to part II.
@QuantumHistorian
2 жыл бұрын
Ok, but why does the substitution trick work? I can kind of see that it replicates the nested symmetry of the shape, but it would be really nice to see a proof of it. Numberphile has recently been stopping _just_ short of the proper maths itself, which is a bit of a shame.
@ideallyyours
2 жыл бұрын
It's not a trick so much as it's a rule. It's an example of Lindenmeyer systems (L-systems) that use rules like these to generate structures with some self-similarity or of a recursive nature. In addition to Forward and Turn (+/-) rules, there are also Scale (multiply/divide length), Scale (multiply/divide angle), Push/Pop (for generating branches), Trim (ends a branch), and in 3D you also have additional rules to deal with line thickness. The rules in this example are specifically designed to create self-similarity, which is not a guaranteed result of any combination of L-system rules.
@RichardHolmesSyr
2 жыл бұрын
Takes me back to the early 1970s when I was an undergraduate, tying up the (admittedly not much used) Hewlett-Packard XY plotter on a timesharing DECSystem 10 drawing dragon curves...
@JimC
2 жыл бұрын
I plotted dragon curves around the same time! On the plotter we used, you had to issue each drawing command twice to get perfect corners. That was because the pen decelerated at the very end of a command and that was easier than coming to an abrupt stop. I used just one command for each segment of dragon curves because perfect corners made it look like an incomplete grid, not a curve. I also drew a 31-gon and all its diagonals.
@DeclanMBrennan
2 жыл бұрын
Next step up: for the turtle: an automated combine harvester let loose in a very large corn field to produce a Sierpinski triangle - that would certainly upstage the usual crop circle. :-)
@shruggzdastr8-facedclown
2 жыл бұрын
I imagine that such a field would have to be super flat as I'd think any irregularities in the topography would likely throw off the combine-plotter
@DeclanMBrennan
2 жыл бұрын
@@shruggzdastr8-facedclown Some of the modern combines have impressive technology for very accurately locating themselves in real time. Makes for a very expensive turtle though. :-)
@DickHolman
2 жыл бұрын
@@shruggzdastr8-facedclown As long as the slopes are within the machines' physical limits, no problem. GPS, especially with local transponders & on-board physical sensors in the control-loop, are centimetre-accurate. And, you can remote-input driving instruction into the really expensive ones. :) Can anyone hack a combine?
@ideallyyours
2 жыл бұрын
I would recommend using a Hilbert Curve ruleset instead, since fields tend to be made up of parallel rows and more closely resemble a square (or rectangle, which can be thought of as a series of (overlapping) squares.)
@Philip_J
2 жыл бұрын
Don't think I've been this early to a video before.
@chinobambino5252
2 жыл бұрын
Amazing at 7:47 - very similar to the way DNA packs itself when condensing "coils of coils". Even the little ball-ish nodes look like the histone proteins that it coils around.
@Mathaveld
2 жыл бұрын
Like a fractal, nature loves fractals :)
@matdex
2 жыл бұрын
I thought the same! Wonder if there's a connection.
@carvoloco4229
2 жыл бұрын
Yeah! It brought the same idea to my mind!
@chinobambino5252
2 жыл бұрын
@@matdex connection is probably just an optimal packing formation - every (human) cell has around 6 feet of DNA that it needs to store inside a tiny nucleus. Fun fact: with ~10 trillion cells in your body, thats 10 billion miles of DNA you're carrying right now.
@xenorac
2 жыл бұрын
@@chinobambino5252 No wonder I weigh so much...
@awandererfromys1680
2 жыл бұрын
Man, I remember Turtle from computer class waaay back in 1989. Then last year I discovered Python comes with a simple Turtle implementation. So now I guess I only have to build a plotter lol! Really cool this program is still around.
@antonmiserez934
2 жыл бұрын
Did he just call Pringles hyperbolic paraboloids at 1:42? I'm gonna use that...
@rosiefay7283
2 жыл бұрын
Those spirals of spirals are beautiful! They remind me of how the continued fraction expantion of some real number x can be used to give more and more accurate rational approximations to x.
@Brontalo
2 жыл бұрын
Would be cool to expand on lindenmayer systems a lot more and show how they can mimic treelike fractals. An L-system i found is A -> - C++A B -> B - - C+ C -> D D -> AB you start with AB and + & - is a 45° turn.
@ideallyyours
2 жыл бұрын
C -> D seems like a redundant step, you could replace it with C -> AB
@DaedalusYoung
2 жыл бұрын
@@ideallyyours Try it, see if there's a difference skipping the D.
@RibusPQR
2 жыл бұрын
Don't skip D-day.
@Brontalo
2 жыл бұрын
I think in the limit they look the same with or without the D. But with D it's much easier to draw by hand on squared paper. On that the diagonal lines are longer by sqrt 2, but that doesn't change the original scaling much.
@ideallyyours
2 жыл бұрын
@@Brontalo Maybe you found an elegant way to "time" when rules are applied by adding a holding step C -> D, so that different instances of C/D are substituted which could give a more organic and less layered look.
@same9643
2 жыл бұрын
Matt Henderson Numberphiles are definitely my new favourite Numberphiles
@numberphile
2 жыл бұрын
You'll love the second part of this one!
@Zveebo
2 жыл бұрын
I agree - great topics and very interesting. Plus his accent is very relaxing to listen to ☺️
@Челленджер-х5ж
2 жыл бұрын
@@numberphile second part?) That's awesome!
@effingineffable685
2 жыл бұрын
Yay pretty maths drawings!
@bogdanfokin1913
2 жыл бұрын
Ou, fractal euler spiral
@WAMTAT
2 жыл бұрын
beautiful mathematics
@zionklinger2264
2 жыл бұрын
Love it when I see my area of research in a numberphile video! Lindenmeyer systems which are what the guest used to generate a sierpinski triangle! Personally I'm using them to generate 3D trees!!
@AppleoTexza
2 жыл бұрын
It is not a case of chaos....if we repeat it enough times and zoom out enough we can see that it essentially will be the Euler spiral nested on itself. we need theta to be an irrational number for a chaotic patterns with different degrees of chaos maximum being with the golden ratio i think
@PushyPawn
2 жыл бұрын
If he'd made the turtle a rabbit, that printer would have been much faster.
@PhilBoswell
2 жыл бұрын
I want a pen plotter that doesn't cost an arm or a leg, is that even possible nowadays? We used to have an HP plotter (I want to say something like 7475?) but I don't know where that went and I'll bet USB won't touch it :-(
@telotawa
2 жыл бұрын
oh hey! i remember doing stuff like this in Scratch lol
@SoleaGalilei
2 жыл бұрын
The spirals of spirals reminded me of how if you zoom out far enough in space, you see that galaxies are grouped into clusters and superclusters of galaxies.
@stefanf922
2 жыл бұрын
Would be cool to see a dragon curve made from Euler spirals.
@SquirrelASMR
2 жыл бұрын
This guy refers to Pringles as hyperbolic parabaloids 🤓 haha
@mebamme
2 жыл бұрын
After a past video that called it "yooler spiral", this is the long-awaited redemption video.
@GladionD.Pierce
Ай бұрын
im gonna show you some interensting curves to draw Me: ill draw ur curves
@victorfromheart
2 жыл бұрын
Honestly, this kind of video is the core reason I like this channel
@user255
2 жыл бұрын
Please post the spirals source code! 5:08 I want to see animation, where theta is increased very slowly (n being constant).
@laurilehtiaho9618
2 жыл бұрын
When I was in high school, I used to waste my French classes plotting the Dragon Curve on a paper like this. I would have pages of L's and R's marking left and right turns. Turns out I am both retaking French classes, and bumping to fractal drawings again - almost 20 years later. Now I am focusing a bit more on my French, though.
@yashrawat9409
2 жыл бұрын
Is that a V7 pilot pen ? Where is the part 2 coming by the way :)?
@_modiX
2 жыл бұрын
6:05 1.0456 is beautiful
@scottmuck
2 жыл бұрын
You’ve created some very valuable brown paper, if they’re for sale!
@stephengraves9370
2 жыл бұрын
My favorite part of this video is the Pilot pen that the machine draws with
@dedwarmo
2 жыл бұрын
Has Part 2 been posted yet?
@tomoki-v6o
2 жыл бұрын
euler spiral used in transportation engineer .like highway and road design
@drenz1523
2 жыл бұрын
Remembered something like this years ago, i think it was the square squigle fractal vid.
@KurtSchwind
2 жыл бұрын
@11:32 "It's within the rules of Numberphile". Then again, so is the Parker's Square.😀
@vgoj
2 жыл бұрын
Brady, do you still sell the brown papers on ebay ?
@MysliusLT
2 жыл бұрын
Matt was amazing in this video. The articulation, the body language, the work. More videos please.😊
@SquirrelASMR
2 жыл бұрын
Ah yes a turtle with a pen up it's 🐢🍑✏️
@davidhutchins8144
2 жыл бұрын
I absolutely love this and all of Matt's videos. Cheers!
@didiermuller5797
2 жыл бұрын
Thank you Numberphile! After seeing this video I made a version of it on Scratch. Pretty fun to show how it works to my little student and how math can be beautiful without being useful.
@SaveSoilSaveSoil
2 жыл бұрын
Love the spiral of spirals!!! For Sierpinski, what happens when you do other angle pairs except +/- pi/3?
@jackwisniewski3859
2 жыл бұрын
turtle graphics is my favorite python module, i love it a lot, its so very simple, powerful and fun i even have a yt video i made using it that im actually pretty proud of
@rujon288
2 жыл бұрын
Watching these videos is so relaxing
@denny141196
2 жыл бұрын
Is it just me or do the Euler spirals look like they could have come from the Mandelbrot set?
@tracy9610
2 жыл бұрын
That was my first thought when I saw the thumbnail.
@gh0stdog89
2 жыл бұрын
The turtle gave me a great sense of nostalgia
@1.4142
2 жыл бұрын
What if you used the golden angle?
@SatisfyingWhirlpools
2 жыл бұрын
is there an angle that makes a spiral, then a spiral of spirals, then a spiral of spirals of spirals, then a spiral of spirals of spirals of spirals, etc...?
@CrowArchLane
2 жыл бұрын
So this is what Brady's been plotting...
@epimaths
2 жыл бұрын
Hình ảnh bản đồ
@misteragb7558
2 жыл бұрын
To me, this is pure art and I really mean that, especially what he shows in part 2
@juansalvemini9270
2 жыл бұрын
Really appreciate when you don´t just show the pretty picture, but take the time to build up to it from the basic rules. All that complexity from two simple statements!
@bloomp7999
2 жыл бұрын
The turtle pattern reproducing itself in high iterations is amazing I Wonder what it looks like in billions of iterations
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