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But what is a Fourier series? From heat flow to drawing with circles | DE4

3Blue1Brown

8.7M subscribers • 42 videos on Hallway

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  • Recommended by 4 people: 4 on Hacker News.
  • A classic. People kept recommending it from 2020 to 2023.
  • Presented by Grant Sanderson, creator of 3Blue1Brown
  • Linked in the description3b1b/manimManimCommunity/manim3b1b/videos

Beginner. No background in the topic needed.

19M views7 years ago4 recommendations

Computer scienceGraphics and audioMath for programmersAlgorithms

Grant Sanderson provides a visual introduction to Fourier series, explaining how they decompose functions into sine waves and can draw arbitrary shapes.

Fourier series, from the heat equation epicycles. Help fund future projects: patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: 3b1b.co/de4thanks 12 minutes of pure Fourier series animations: youtu.be/-qgreAUpPwM Some viewers made apps that create circle animations for your own drawing. Check them out! reddit.com/r/3Blue1Brown/comments/cvpdn7/make_your_own_fouri… isaacvr.github.io/coding/fourier_transform/ Thanks to Stuart@Biocinematics for the one-line sketch of Fourier via Twitter. As it happens, he also has an educational YouTube channel: youtube.com/channel/UCKOiJd9YCbv7LeL2LFOGiLQ Small correction: at , all the exponents should have a pi^2 in them. If you're looking for more Fourier Series content online, including code to play with to create this kind of animation yourself, check out these posts: Mathologer youtu.be/qS4H6PEcCCA The Coding Train youtu.be/Mm2eYfj0SgA Jezmoon jezzamon.com/fourier/index.html For those of you into pure math looking to really dig into the analysis behind this topic, you might want to take a look at Stein Shakarchi's book "Fourier Analysis: An Introduction" Timestamps: - Drawing with circles - The heat equation - Interpreting infinite function sums - Trig in the complex plane - Summing complex exponentials - Example: The step function - Conclusion Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ These animations are largely made using a custom open-source python library, manim. See the FAQ comments here: 3blue1brown.com/faq#manim github.com/3b1b/manim github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: github.com/3b1b/videos/ Music by Vincent Rubinetti. Download the music on Bandcamp: vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe Various social media stuffs: Website: 3blue1brown.com Twitter: twitter.com/3blue1brown Reddit: reddit.com/r/3blue1brown Instagram: instagram.com/3blue1brown_animations/ Patreon: patreon.com/3blue1brown Facebook: facebook.com/3b

Why it's here

4 people recommend this

What people say. Highly recommended for its beautiful visual intuition of Fourier series and their applications.

kcoulon Hacker News • Recommends

On “A ‘Useless’ Perspective That Transformed Mathematics”

I wouldn’t call this 3blue1brown video a reference, but until I watched this (coming from an audio background), I didn’t quite grasp that a continuous stencil of any complex silhouette could be described in terms of a set of contributing vectors. Helped click that there is a perfect visual analogy to the deconstruction of complex audio to sine waves. link to this video
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bldavieson Hacker News • Recommends

On “Old blog of Matt Henderson, beautiful math animations”

3B1B is incredible. I loved his video ( link to this video ) using Fourier series to make epicycle animations. I worked through the details to make my own: link
View on Hacker News

maze-leon Hacker News • Recommends

On “Why Is Scientific Illiteracy So Acceptable?”

> It remains a badge of honor for many who like to describe themselves as highly cultured or artistic to describe themselves as mathematically challenged, or to say that their brains aren’t wired for mathematics. Because many of those they hold in high esteem have made similar claims, there is no real social penalty to them for doing so. For many scientific illiteracy is in the same category as mathematical illiteracy -- but the problem starts there already. Everybody should at least know what a Fourier transformation does -- it's not necessary to exercise it rigorously, but at least an idea... I think this video is enough to give even laymans an idea: link to this video
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teneon Hacker News • Recommends

On “Is the great neutrino puzzle pointing to multiple missing particles?”

…planet and the Sun sweeps out equal areas during equal intervals of time. 3) The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. In contrast, the epicycle models had 40-80 cycles with parameters tuned to match the observed data. I really like this video on how Fourier series work: link to this video…
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peter_d_shermanon Hacker News • Mentions

On “Spirograph”

Here are some interesting-looking Spirograph videos: Spirograph Designs Compilation: link Wild Gears: Triangle Gear 120 in Ring 210 with Birdsong link PDS: Speculation: There is a relationship between the Spirograph toy -- and Fourier Series: "But what is a Fourier series? From heat flow to circle drawings (3Blue1Brown)": link to this video PDS: Also, if I were to go for "full crackpot" (which I will, because I usually do! <g>) -- I'd speculate that fields, such as atomic, and subatomic fields (all particles -- because particles are basically all fields which act as particles) are "Spirographic"/Fourier Series in nature ... Yeah, I know... "You're a crackpot!" <g> (Oh, an even more crackpot conject…
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sargstuffon Hacker News • Mentions

On “Λ-2D: Exploration of Drawing as Programming Language, Ideas from Lambda Calculus”

…d recusion to perform assembly language instructions. Raster graphics without the yak ( link ) Feed back between tape & "traditional code" as neural network layer(s)! Flexiable code (via tessilations) without changing the actual imported source code! So, complete svg (tape interactions) web page as code source on how to interact with web page, ( link to this video ) what's displayed/played, documentation & usage manual included within code structure! Unicode permits implied piping rich kern font without all the tech fluff. Unicode fails because allows infinate multics and is there for k&r incomplete. But, this approach is way more dimensional/colorful than unicode/tech stuff. ?? can one's code uninte…
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lupireon Hacker News • Mentions

On “Fitting an elephant with four non-zero parameters”

IIUC: A real-parameter (r(theta) = sum(r_k cos(k theta))) Fourier series can only draw a "wiggly circle" figure with one point on each radial ray from the origin. A compex parameter (z(theta) = sum(e^(z_ theta))) can draw more squiggly figures (epicycles) -- the pen can backtrack as the drawing arm rotates, as each parameter can move a point somewhere on a small circle around the point computed from the previous parameter (and recursively). Obligatory 3B1B link to this video Since a complex parameter is 2 real parameters, we should compare the best 4-cosine curve to the best 2-complex-exponential curve.
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vismit2000on Hacker News • Mentions

On “Animals Made from 13 Circles (2016)”

Reminds of 'Drawing with circles' in 3b1b classic on Fourier series: link to this video So if we remove the condition of 13, everything is in fact made of circles only!
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u/Fit-Technologyin r/C_Programming • Mentions

On “Shapes with Fourier Series”

If you want a great explanation and a way to draw anything you want you should take a look at 3b1b on youtube
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