Coding Challenge 125: Fourier Series

In this coding challenge, I visualize a Fourier series for a square wave in JavaScript with p5.js. Code: thecodingtrain.com/challenges...
🕹️ p5.js Web Editor Sketch: editor.p5js.org/codingtrain/s...
🎥 Previous video: • Coding Challenge #124:...
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🎥 All videos: • Coding Challenges
References:
🗄 Fourier Series: en.wikipedia.org/wiki/Fourier...
📄 Purrier Series (Meow) and Making Images Speak: bilimneguzellan.net/purrier-se...
📄 An Interactive Guide To The Fourier Transform by Better Explained: betterexplained.com/articles/...
Videos:
🎥 What is a Fourier Series?: • What is a Fourier Seri...
🎥 But what is the Fourier Transform? A visual introduction: • But what is the Fourie...
🚂 Polar Coordinates: • 3.4 Polar Coordinates ...
🔴 Coding Train Live 163: • Coding Train Live 163:...
Related Coding Challenges:
🚂 #61 Fractal Spirograph: • Coding Challenge #61: ...
🚂 #130 Drawing with Fourier Transform and Epicycles: • Coding Challenge #130....
Timestamps:
00:00 Welcome! Some resources on the Fourier Series
02:44 Explain! What is a Fourier Series?
07:00 Code! Create a dot spinning around a circle!
11:41 Code! Draw the wave path of the dot!
14:41 Oops! Invert the order of the wave!
16:16 Code! Add multiple circle waves!
23:50 Code! Draw the Fourier series!
25:30 Code! Add slider for number of circles!
27:39 Suggestions
Editing by Mathieu Blanchette
Animations by Jason Heglund
Music from Epidemic Sound
🚂 Website: thecodingtrain.com/
👾 Share Your Creation! thecodingtrain.com/guides/pas...
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💡 GitHub: github.com/CodingTrain
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🛒 Store: standard.tv/codingtrain
🖋️ Twitter: / thecodingtrain
📸 Instagram: / the.coding.train
🎥 Coding Challenges: • Coding Challenges
🎥 Intro to Programming: • Start learning here!
🔗 p5.js: p5js.org
🔗 p5.js Web Editor: editor.p5js.org/
🔗 Processing: processing.org
📄 Code of Conduct: github.com/CodingTrain/Code-o...
This description was auto-generated. If you see a problem, please open an issue: github.com/CodingTrain/thecod...
#fourier #maths #javascript #p5js

[@vigneshwarm]

3blue1brown recommended this video for his Fourier transform video

[@akremhadji7326]

I've just watched it, it was amazing !!!

[@FilthyManatee]

I just watched his video, then I tried coding my own Fourier series. Figured I would come on here and see what I did wrong.

[@akremhadji7326]

​@@FilthyManatee In this video the Fourier series is developed in JavaScript language to be run on a normal web browser. If you want more advanced tools to work with such series you can use mathematical software (Matlab, Maple, Octave ..) they have many dedicated methods to be implemented easily. If you want to do things the hard way ;) you can download the code of the presented script in this video and try to modify the coefficients or change other parameters.

[@FilthyManatee]

@@akremhadji7326 I wrote mine in the hard/fun way (javascript/canvas) already. I did it very differently than what was shown here, but was still able to learn a thing or two watching this video. It gave me a few things to think about and change in my code. I went right into the chain of alternating spinning vectors and drawing from the last point on the chain.

[@ejejej9200]

I came here from 3 Blue 1 Brown. And, I am so happy I did! This is a great channel! :)

[@oscard4801]

I'm 11 and I'm from Mexico, and have been programming for 3 years and Coding Train is my source of inspiration and learning.

[@TheCodingTrain]

So nice to hear! Please feel free to share anything you make 🙂

[@GodofChookie]

it's awesome to have such a productive hobby you get enjoyment from and willingly invest your free time. especially at such a young age. keep it up

[@philippg6023]

Awesome keep it up

[@LongLe-nt8bv]

b0ss thats great for his age and its called a "comment", plus he just want to say thanks to Daniel

[@oscard4801]

​@@don1041 I learned Javascript, p5.js, HTML and CSS

[@jonnylinford]

So happy to see you and Destin interact. This is the intersection of all the best content on KZbin

[@blasttrash]

who is destin?

[@alexandermcclure6185]

@@blasttrash destin is the smarter every day dude

[@x-lightsfs5681]

That took me -1/12 lines of code

[@sujals7108]

Infinite lines is impossible.

[@x-lightsfs5681]

@@sujals7108 But what if i made a code that adds a line to the js file every frame?

[@sujals7108]

@@x-lightsfs5681 Then to make infinite lines, you would need an infinite number of frames, hence infinite time.

[@poopmaster9984]

@@sujals7108 how bout making more line each frame? Then you'll get to infinity in no time :v

[@PhoenixD]

@@x-lightsfs5681 cant go to infinity since memory is always limited :)

[@RoGeorgeRoGeorge]

@3:30 What you are calling "Amplitude" is in fact the "Peak to Peak" value. The "Amplitude" will be only half of that.

[@TheCodingTrain]

Indeed, thank you for the correction!

[@CJBurkey]

But the coefficient (often called amplitude) is the vertical peak to peak distance of the wave.

[@NoorquackerInd]

@@CJBurkey Peak-to-Peak value isn't the coefficient or the amplitude. Peak is the absolute distance from the average of a function to either the min or max and peak-to-peak is the absolute distance from min to max. The amplitude is the peak value, and on sinusoidal functions, the peak-to-peak value is double the amplitude or peak value. This is more of the electrical engineer view of it, though

[@sergey1519]

What are you calling "peak to peak value" is in fact sometimes called "peak to peak amplitude", and what you calling "amplitude" is sometimes called "semi-amplitude". It's kinda similar situation as with "Natural numbers" - the name is ambiguous and it's better to refer to it either as "Positive integers" or "Non-negative integers" depending on what exactly you mean.

[@sharphurt8753]

I'm Russian student and I want to express my huge thanks to The Coding Train channel! Thanks to you I have top marks in my school! The whole world loves you!!!

[@cassandradawn780]

Я думал русских ент

[@maximgasai1349]

Теперь это русский чат макс репост

[@TheCodingTrain]

Thank you!

[@sharphurt8753]

@@maximgasai1349 Русские везде Russians everywhere

[@user-xh9pu2wj6b]

@@sharphurt8753 у вас в школе преподают JS? Жестко.

[@ibuucoksiregar9024]

90% of my coding skill is from Coding Train. Everytime my friends ask me where i learned something, I always show them this channel. I love this channel so much❤️❤️

[@carlosmorasalguero]

Wow, smarter every day in the coding train... Avengers is no longer the most ambitious crossover in the history of the world

[@revimfadli4666]

Yeah who needs Rewind if they keep making quality crossovers like these

[@abhishektyagi4428]

Fuckavengers

[@AdamBechtol]

:p

[@USAwizeguy]

As an EET major looking back at studying how to code, I love this! We look at wave forms all day. I am going to recreate this and show my fellow electrical engineers at work.

[@SineEyed]

Did you do it? Were they impressed, or at least mildly entertained?..

[@alexandermcclure6185]

please we need an update

[@PatrickAnimator]

dude...I am obsessed. you are literally one of the best teachers Ive ever experienced.

[@sirecartier7881]

I am a high-school student from France and I am really happy to see how great and efficient code can be with people like you!!!

[@sobanudlz]

*Procrastinating intensifies*

[@AntonySimkin]

Underrated comment lol

[@TheFishKing64]

hah, yeah

[@unlikelysalmon786]

hell, there are worst ways to distract yourself. programming fourier transformations is a decent way to waste your time (though time spent learning isn't wasted, I'm told)

[@snacksy7754]

28:28 I love that ending. *Has a good moral:* If you stumble over your words instead of trying to solve the confusion just give up, blow your flute, and say goodbye :D

[@ianprado1488]

I need to more consciously appreciate the amazing, high quality content on KZbin. We are living in a beautiful time in history

[@iVideo1011]

Just stumbled across your channel. This is the best KZbin channel I've ever seen. So many high quality videos and such great teaching and enthusiasm. I'm just speechless!

[@dianewilliams5830]

Thank you. As always, you make learning so much fun. I've never been able to visualize how Fourier creates a square wave or any wave until now.

[@MrSonny6155]

After visualising this in the full complex form, it becomes pretty clear how higher frequencies enhance the "precision" of the wave position. I love how the whip rolls up into a tight ball with each rotation and each addition of epicycles.

[@shashik962]

My favourite channel... This is really great...

[@oblivionronin]

An interesting thing that was done i think in 3blue1brown was to assign random or non-regular growing or shriking radius to the circles. Theses Fourrier series create really unique and interesting patterns, some of them event ressembing famous man made paintings.

[@RicardoOliveiraRGB]

It's the first video of yours i've seen, and damn! I wish my brain could think that fast for programming crazy math stuff lol. Congrats man, you got a new fan here

[@zackd41]

LOVE The Crossover with Smarter everyday, Been getting into coding because of you, thanks!

[@shannonadamj]

Yoooo nice plugging smartereveryday. I love that channel.

[@AliParlakci]

1:21 Website's name actually means "science is so beautiful"

[@ferhatakan5056]

dafgjkdfjaglh

[@Abhishek-hy8xe]

I love this channel and this guy and all the videos. Thank you .

[@POPO-od8jb]

Isn't it so satisfying to witness that sine waves are making rectangular wave , that ending of this video made my whole 2019 yr , and a good start of 2020 , thanks for this awesome video 🌷

[@HeerdyesMahapatro]

Fantabulous! This needs to be taught in every DSP course!

[@myetis1990]

You can translate Bilimneguzellan= Bilim+ne+ guzel +lan = Science+ what+ beautiful +guy = hey guy Science is what a beautiful thing ! for pronounciation, go to google translate, select turkish , type the "Bilim ne güzel lan" and tap the voice button :)

[@muhtesemtavasap6411]

Oh be gördüm rahatladım. Yoksa ben yazacaktım.

[@eminmerden1072]

Iyi yetiştin

[@amorphsilicon938]

Adamsın, adam sitenin ismini okurken bunaldım...

[@ataberkaslan2235]

djfsdfsjdfjdfljdfg çok iyi okumadı mı dfghjkdfghjdfghjhjdfgkdfg

[@sonik382]

Awesome, interesting and instructing. Thank you for all the effort you put in the channel!

[@FM-kl7oc]

27:18 Kinda cool illustration of aliasing that happens when the sampling rate is not a perfect multiple of the signal frequency being sampled. After increasing it to 100, sometimes you get a big spike at the corners on the square wave, sometimes not -- this is the aliasing. Sometimes you're "lucky" to sample (draw) when the tip of the pendulums are at the very top or bottom of the corner, and you get a spike. Sometimes you're "unlucky" to sample (draw) when the tip of the pendulums are not near the top or bottom, and you get a more traditional "90 degrees corner" without the spike.

[@tmendoza6]

this is so freaking fantastic! I could do this all day

[@siddhantrai7529]

I love the way the best and the brightest youtube channels are inspired and motivated by each other...that is a really positive environment.... Siraj,you,smarterEveryday,3 blue 1 brown..... You guys really help me and many others as well . Thank you.

[@deez_gainz]

That refactoring song though ahah! We need 10 hour version for productive coding work!

[@izzy31337]

you always release coding challenges just when im studying a specific topic

[@marcinkienast1134]

Yeah, I'm supposed to study algorithms and time complexity proving. So... I guess I will fail the test, but I will know a bit more about FS. Totally worth it xD

[@marcus_w0]

Right? I was recently looking into graph plotting and stumbled upon this, too. And within a week there this video. Hee's tracking my browser history.... I have to go.

[@maxteer2800]

I really appreciate the goofs and slight logic mistakes on this one, it was almost more enlightening than if he had just done the thing

[@gloubiboulgazeblob]

awesome !!! The movement of all those circles radii looks so "biologic", fascinating !

[@jonathanwalther]

Best analogy ever. Very smooth.

[@HisMajesty99]

This was amazing, thanks for doing a video on this

[@jerryplayz101]

4:12 - To play a musical note, the sine wave is made of multiple sine waves. You have the note you want, but you also have some overtones.

[@xnick_uy]

The end result looks like a fantastic whip. WT-TSH!!

[@abhijithnair3078]

It's wappah

[@MACHINEBUILDER]

Wow awesome job it's super satisfying! :)

[@michael-gary-scott]

I’m actually so excited for this video

[@kavinbharathi]

the slider part at the end is even more interesting as it gives even chaotic curve which when condensed give non continuous sine waves of different frequencies......*wow*

[@jegant8216]

This is a good example of coding Fourier series, thanks.

[@Wolf-gt3kd]

This was really fun to watch that i didn't notice the video's lengh was 30min. Nice work really :D

[@BonsayCow]

Fun fact at 27:20 you can see spikes on the corners of the function and this is called the Gibbs phenomenon and you can never get rid of it, due to the discontinuity of the function that you are trying to approximate.

[@jonathangodar4239]

I searched on how to get the x and y values on something that had been rotated for hours. I knew that it would be something having to do with the angle and the hypotenuse, but I never found what I was looking for. I finally got the answer by some guy on Reddit this morning. Why couldn’t I have watched this video when I really needed it?

[@HardusHavenga]

Dude, you are my new hero.

[@JenishJain6]

What a coincidence the video was suggested to me just when I was about to start Fourier series for my exam prep.👻

[@kindpotato]

I'm glad after a couple years of thinking about the fourier transform, I made something like what he talked about with the homer simpson being drawn,

[@askquestionstrythings]

I was anticipating your video since you mentioned doing this in the smarter everyday video comments.

[@Apocalypsee07]

I like these Coding Challange videos :) trying to replicate these in python makes learning so much fun and also easier. Thank yyou!

[@Brenzle]

What do you use to draw in python? Turtle?

[@iqbaltrojan]

27:38 - 27:40 there is a time where the line is near horizontal facing right! pause and use the , (comma) and . (period/full stop) to go back/forward by 1 frame edit: press 27:38 then wait for it to go right edit 2: 27:55 also edit 3: also at 27:54 it's at a very high point (right side)

[@SreenikethanI]

hehe yeah even I noticed that, when all the circles are extended to the right, it essentially cuts the wave!!!

[@anandprakash4995]

This video inspired me to learn p5.js .Will be my new resolution to learn p5.js !!!

[@matthewvicendese1896]

You can make y = negative radius sin(time) ..... because y is upside in computer land.

[@sidim.aourid9958]

The amplitude is from axis x to max or to min. Example if, s(t) = a sin(t), a is the amplitude. Thank you for all your videos, they are instructive and well done.

[@TheCodingTrain]

Thanks for the correction!

[@mefuri_k]

You have a great taste on youtube channels you watch

[@yusufberkaygirgin9694]

page's name is "bilim ne guzel lan" and it means in english "science is what a sweet thing buddy" :D

[@djtygre]

my most favorite to date

[@AlGhifari7]

Hey, go to 3Blue1Browns Channel for a new video about Fourier Series!!

[@eda-un8zr]

I'm native Turkish and i like how you pronounce the name of the website :D and great video, thank you

[@xnick_uy]

In case you are wondering, although a Fourier Series and a Fourier Transform are not the same, it is possible to devise a framework in which you can formally treat them on equal footing if you want to (you might need to look into Dirac combs and intervals of ever-increasing length). And more importantly: within the realm of numeric computation you are pretty much forced to use the *Discrete* Fourier Transform instead of the "bare" (continuous) Fourier Transform, which turns out to be essentially the same as the Fourier Series. (I'm assuming you don't make a distinction about using either trigonometric functions or complex exponential).

[@TheCodingTrain]

Thanks for this clarification! I'm hoping to do a video on DFT next!

[@alajlan2012]

this is EPIC , would you please continue uploading like this content? especially on fourier drwaing visuals?

[@TheCodingTrain]

yes, i'm planning to!

[@joecamroberon9322]

You deserve so much more attention.

[@aeswere]

I took a small hiatus from this channel but came back as I was bored, decided to follow this video (I usually watch). I changed the slider into an input box so you could input whatever number you'd like, and the circles would be added. I'm not sure if this is the best way to use an input box in this scenario but it does work. function setup() { createCanvas(960, 350); input = createInput(); input.position(5, 325); } function draw() { frameRate(30) background(0); translate(200, 200); let x = 0; let y = 0; let circles = 0; if (input.value() == 0) { circles = 1; } else { circles = input.value(); } for (let i = 0; i < circles; i++) { let prevx = x; let prevy = y; let n = i * 2 + 1; let radius = 50 * (4 / (n * PI)); x += radius * cos(n * time); y += radius * sin(n * time); stroke(255, 100); noFill(); ellipse(prevx, prevy, radius * 2); //fill(255); stroke(255); line(prevx, prevy, x, y); //ellipse(x, y, 8); }

[@tomasvenegas6062]

How did you make the html document or how did you see the code in Chrome?

[@matthewvicendese1896]

I am so excited !!

[@luisaisat]

thanks, yesterday i was trying this

[@BillyBustamante]

Primer video que veo. Adoro!

[@shamilcarela1699]

Great video, loved it.

[@bertronixtv]

Amazing. Thank you for sharing your awesome skills.

[@clementlebeau484]

I’d love to see a part 2!

[@AmirAdzim]

Just to correct you there on the definition of amplitude at about 3:45 the amplitude is the height difference between the very top and the middle part of the wave (position of equilibrium) :) overall very nice video!

[@TheCodingTrain]

Yes indeed, thank you for pointing this out!

[@AmirAdzim]

@@TheCodingTrain thank you as well for providing very educational (and interesting) content!

[@rahulbansode1537]

What do you mean the middle part or position of equilibrium Sorry I don't understand

[@AmirAdzim]

@@rahulbansode1537 the point that is right in between the highest peak and the lowest peak of the sine wave is called the equilibrium position. Say you have a child on a swing. The equilibrium position is the position of the child when the swing is at rest. When the child starts swinging, the highest peak (and this is relative) is when the child is on the highest position in front (positive) of the equilibrium position and the lowest peak is when the child is on the highest position behind (negative) the equilibrium position. So the amplitude (or in this case the maximum height at which the child is swinging at) is the height difference from the position of equilibrium (not swinging) to any of the maximums (either behind or in front of the swing). Sorry if this analogy is too complicated im not really good at explaining stuff.

[@rahulbansode1537]

@@AmirAdzim that was a great explanation thank you!

[@bobbymcdingdong]

Brother, dude, friend Daniel, thank you!

[@vladimirshitov2160]

Damn, I love Python and wanna use it for work. But I don't know yet how to do all these cool stuffs in Python so I learn JS because of this channel :D Thank you, that is great!

[@devious5348]

python has p5 too

[@wesleycantarino4464]

this video made me study Fourier series again

[@OonHan]

I needed this

[@smanzoli]

Interesting to see the fractal tree branches being produced here by the circles radiuses 23:50

[@bamkparto]

4:56 - Fourier Serier is like a smothie, like a video in premiere, like a song in FL, like a 3d scenerey in Blender,like a lego model, 7:53 - 10:09 - VS autocomplete feature 3:45 - Amplitude is the height difference between the very top and the middle part of the wave (position of equilibrium) :) overall very nice video! ​​@irAdzimm by @K When you went to 100 iterations for the square wave, the overshoot spike would jump from the top of the wave to the bottom after it was already drawn. Look around @ and pay close attention to the top and bottom of the wave after they're drawn, as they move across the screen. *Related* *Projects* kzbin.info/www/bejne/eZupg2emZrKqpsk @t

[@anjardwisaputra1671]

AMAZING!!

[@RegisMichelLeclerc]

Cool! In generating sound samples, it means I can represent anything by a series of function modifiers, amount depending of the level of precision I need. Now, how can I do the opposite, i.e. transform an arbitrary sample to a series of modifiers? IIRC, Mathologer did something like that with his Homer Simpson drawing using a similar mechanism, (epicycles) but he used Mathematica to figure the functions, not very practical. Is there a way to do that with JS instead?

[@diemirarr4728]

Amazing!

[@johnvonhorn2942]

This guy is the smartest guy in the neighborhood - the Mr Rogers of code.

[@stuartyellow1679]

Do you know about the Gibbs phenomenon? It dosent matter how hard you (your computer) try you will have those "peaks" at discontinuities. Only if you add up infint waves it is theroretically converging to the rectangular function. I hope my explantion makes sense :)

[@johnphilmore7269]

Hey man! Found your channel today And I really love it! I do want to just correct a little error. There’s a difference between the Fourier TRANSFORM and the Fourier SERIES. The transform is indeed unsmoothying a smoothie so to say, but that has to do with infinity integrals in the complex plane (don’t ask). The series on the other hand takes a periodic function and approximates it with an infinite series of simple sines and cosines. Kinda like a Taylor series for periodic waves. There may be a connection between the two, I don’t deal with them a lot in my life, but just wanted to let ya know 😊 Edit: ah I see u addressed it. Thank you!

[@TheCodingTrain]

Thanks for the feedback!

[@johnphilmore7269]

The Coding Train my pleasure! I really enjoy the channel! Will be staying glued to ur work for a good long while As a coding challenge, why not try Runge Kutta approximations of differential systems? Something very similar to what you did with Lorenz System, but much more accurate. Just maybe something to tickle your fancy

[@user-co5ob1fv1m]

Very very useful. Thank you so much Dan

[@johnnyserup5500]

I like your approach to explanation - really interesting - cool video

[@fatehaligolani7751]

Thank you so much man

[@alonh.4968]

OMG, I like this channel a lot! thank you and, btw, how did you cancel the auto-fill? 😂

[@germandavidmurillasmondrag4004]

very nice code, ofcourse would be nice other slider for time this is the function that I made for this timeslider = createSlider(0.001, 0.05,0.001,0.001); and then where it is time u put timeslider, the variables for this are (min,max,default,setpbystep)

[@buddhanag4987]

Just awesome

[@The.Jaynish]

You are the best man

[@oxydol3456]

Thanks!

[@TheCodingTrain]

Thank you for the support!

[@easyunderstandbanglatv7080]

Brother me Bangladeshi your good tips my head very easy work thank you so much brother

[@jamesstreets5176]

good video :)

[@morphyngames]

Thanks for making the video

[@gwawrz1]

I'm curious, what's that song "I will refactor this later"? :D

[@rafaelamaral7756]

this guy is so funny i love it

[@cainespade514]

What I see is "The Professor" is teaching us the Fourier

[@Moccar]

Shoutout to 3blue1brown! His videos are really good as well as yours Dan!

[@harrysvensson2610]

28:20 Eyyy that would be based on quaternions. Fun.

[@Forced2]

Is it just me or is this pattern of circles rotating around eachother looking like a whip when it reaches a hundred. Maybe this is how a whip delivers such a fatal blow.