(I still have not made it all the way to the end of the video though, perhaps that is where they end up.)
I see what you did there.
Imagine, for the sake of simplicity, you could express the song's waveform with the function 13 * sin(41x).
The derivative of this function is 533 * cos(41x).
Cosine, of course, is just a phase shifted sine, and the constant coefficient inside the function stays the same. So you're not changing anything about the shape of the wave, just stretching it vertically.
This has the effect of mimicking a "high pass filter," amplifying the volume of the highs.
You can take the finite difference with eg np.diff(waveform) though.
I watched it a few days ago and this descriptive title was part of the reason I clicked. I generally trust 3B1B anyway but normally a title like "This picture broke my brain" would put me off.
I was genuinely torn about how to title this, because one of my aims is that it stands to be enjoyed by people outside the usual online-math-viewing circles, especially the first 12 minutes, and leaning into the idea of a complex log risks alienating some of those.
fascinating, and absurdly confusing, that there are multiple titles.
Or could you walk around in such a world? That would be a very cool concept for a game.
Well, the 3D structure just needs to be sufficiently "holey" for the effect to become apparent. For example a cage-like structure, or a house with no roof (when seen from above).
His videos on Euler's formula inspired me to make a silly toy so I could play with it myself.
[0] https://en.wikipedia.org/wiki/Print_Gallery_(M._C._Escher)
[0] https://pub.math.leidenuniv.nl/~smitbde/papers/2003-de_smit-...
But, as with all jokes, the punchline isn't funny at all without the setup.
This kind of risks obscuring what's actually going on.
Also curious what happens if you take Escher's painting and undo the effect. Probably not great since it wasn't in the video.
What a cool video.
i will see if i can find it.
edit: "How I animate 3Blue1Brown | A Manim demo with Ben Sparks" https://www.youtube.com/watch?v=rbu7Zu5X1zI
more on workflow: https://github.com/3b1b/videos?tab=readme-ov-file#workflow
code for videos: https://github.com/3b1b/videos
manim: https://github.com/3b1b/manim
manim community edition: https://github.com/ManimCommunity/manim/
EDIT: seems like dang or team took care of it, thanks!
It’s a drawing of a guy looking at a picture of a town with himself standing in the town, but it’s all twirled and twisted so it’s self repetition isn’t obvious.
This would be an excellent title :)
