How and why to take a logarithm of an image [video]

https://www.youtube.com/watch?v=ldxFjLJ3rVY

Comments

rappaticMar 27, 2026, 6:01 PM
Similarly, it's possible to take the derivative of a song. You can use a Fourier transform to express the song's waveform as a series of sin and cosine functions, then take the derivative.

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.

toxikMar 27, 2026, 6:48 PM
Well you get the frequency domain decisive. This is the same as scaling the time domain by a linear ramp. Not exactly hugely useful, unless you happen to be in radar.

You can take the finite difference with eg np.diff(waveform) though.

manudaroMar 27, 2026, 3:19 PM
I've been loking into how 3B1B builds their rendering pipeline, and it's honestly mind blowing. They use Python along with custom OpenGl shaders to handle most of geometric transformations, shich seems to be what creates those "brain breaking" visual effects.It's fascinating how our visual cortex tries to interpret overlapping geometric patterns and ends up producing such counterintuitive perceptions. Shat I still can't quite wrap my hand around is... to what extent are these effects caused by the rendering itself, and how much of it is just how our brain interprets the visual information?
john_strinlaiMar 27, 2026, 3:35 PM
there is at least one video, if not a series of videos, where he explains his process in detail, showing the coding process and everything. it is a collaboration with another person where, if i recall, he is teaching them.

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/

boriskourtMar 27, 2026, 1:21 PM
This video is an absolute tour de force of communicating a complex concept.
dmbcheMar 27, 2026, 1:29 PM
All of 3Blue1Brown is - hoghly highly recommend
boriskourtMar 27, 2026, 2:15 PM
I've seen most! Highlighting this one out of them all. Exemplary! : D
JKCalhounMar 27, 2026, 2:46 PM
Seems like you could apply the clever transforms to generate a displacement map (that then allows you to move it across any source image and quickly get the Droste effect).

(I still have not made it all the way to the end of the video though, perhaps that is where they end up.)

m-hodgesMar 27, 2026, 1:37 PM
The title I get when I click on this is, "How (and why) to take a logarithm of an image"
peesemMar 27, 2026, 1:43 PM
YouTube has A/B testing features that allow videos to have multiple titles and/or thumbnails.
m-hodgesMar 27, 2026, 1:46 PM
Right. So I thought it would be helpful to share the more-descriptive title that I got.
Modified3019Mar 27, 2026, 2:26 PM
This is what I use DeArrow for, crowdsourced titles and thumbnails (from the maker of SponsorBlock): https://github.com/ajayyy/DeArrow
dandanuaMar 27, 2026, 2:43 PM
I'm sorry, what? Can people now see different titles? Insanity, if true.
hidrotoMar 27, 2026, 3:44 PM
It has been that way for a while now. I see Veritasium video titles and thumbnails change quite often, it can be quite annoying as it sometimes gives the appearance of it being a whole new video.

A/B testing a title feels wrong to me, its almost as bad as A/B testing a UUID. Just pick a title and stick to it unless you need to fix a factual error.

zacmpsMar 27, 2026, 3:49 PM
Titles and thumbnails have a huge impact on video performance, and when it's your main income it seems reasonable to try to marginalise the impact.
throwaway290Mar 27, 2026, 5:33 PM
And video performance = ad revenue.
UltraSaneMar 27, 2026, 5:38 PM
Oh yes. Some channels cycle through many different ones as they test them. Veritasium is notorious for this.
sva_Mar 27, 2026, 1:47 PM
For me it is "Decoding Escher's most mind-bending piece"
close04Mar 27, 2026, 3:27 PM
> How (and why) to take a logarithm of an image

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.

3b1bMar 27, 2026, 3:53 PM
In case you're curious, when I ran that title/thumbnail AB test, the option "This picture broke my brain" did end up winning. I was a bit disappointed, because I didn't really _want_ it to win, but I did include it out of curiosity. Ultimately, I changed it to the other title, mostly because I like it better, and the margin was small.

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.

cromulent2Mar 27, 2026, 4:10 PM
That makes me wonder: do you see a difference in when viewers drop off between using a more math-y title versus a more accessible one?

The "broke my brain" title originally put me off from watching. I caved after a few days; I think the video is one of your best!

gowldMar 27, 2026, 6:44 PM
As annoying as those titles are, the work that you (and few others, like Veritasium) do makes it well worth the tradeoff. Just keep reminding everyone that the annoying title gets the video into the brain of thousands of other people who aren't subscribed yet. It's a tiny price to pay for astounding value.

Everyone who watches your videos loves them and wants everyone else to watch them.

john_strinlaiMar 27, 2026, 4:27 PM
perhaps a bit inappropriate of me to say so here as it is off-topic, but i am going to take the opportunity anyways:

big thanks for all of your work making math both enjoyable and accessible. my kids (and i) love your videos. your positive impact extends far and wide.

UltraSaneMar 27, 2026, 5:40 PM
You should be able to have different titles for different ages and education levels of users
john_strinlaiMar 27, 2026, 3:31 PM
i see "Decoding Escher's most mind-bending piece".

fascinating, and absurdly confusing, that there are multiple titles.

eblumeMar 27, 2026, 3:35 PM
It's a pretty common feature of youtube creator studio. https://www.theverge.com/news/840789/youtube-video-title-a-b...
john_strinlaiMar 27, 2026, 3:49 PM
i had no idea, thanks. at first glance it seems okay-ish for the creator, but only serves to be confusing for the users.
pierrecMar 27, 2026, 3:57 PM
This kind of technique can be used in 3D space as well! The analysis here represents Escher's techniques as conformal maps in the complex plane. Conformal maps are also possible, though more limited, in R^3. This is something that I explored some years ago and wrote an article about it, though it focuses more on graphics than math: https://www.osar.fr/notes/logspherical/
aprenticMar 27, 2026, 5:41 PM
Those videos are awesome! 3B1Bs visualizations finally made e^(pi*i) make sense.

His videos on Euler's formula inspired me to make a silly toy so I could play with it myself.

https://gitlab.com/aprentic/complex-viz/

OscarCunninghamMar 27, 2026, 2:47 PM
I've been wondering if you could do a similar thing for a Droste effect image containing two copies of itself. Packs of Laughing Cow cheese show a cow with two earrings, each of which is a pack of the cheese.
Jeff_BrownMar 27, 2026, 1:38 PM
I love 3B1B but generally don't have time to watch long videos. Can anyone sum up the punchline?
ahnsMar 27, 2026, 1:47 PM
One of Dutch artist M.C. Escher's works is a man is admiring a piece of art that itself depicts the building the (very same) man is in [0]. Escher left out the middle bit of the painting, probably since it's fairly complicated, putting his signature there instead. The video itself is about the complex analysis used to fill in that missing middle, based on a paper ~20 years ago.

[0] https://en.wikipedia.org/wiki/Print_Gallery_(M._C._Escher)

rcxdudeMar 27, 2026, 2:33 PM
I think the gap also has a compositional purpose: the viewer's eye is meant to travel around the image in a circle, and the gap helps anchor that in a way that the filled-in version might not.
ahnsMar 27, 2026, 5:21 PM
Hm, since I can't edit my comment: link to paper [0]

[0] https://pub.math.leidenuniv.nl/~smitbde/papers/2003-de_smit-...

daedrdevMar 27, 2026, 5:39 PM
HN only allows editing comments for a short time
pdpiMar 27, 2026, 2:23 PM
The punchline is that you can fill in the centre of Escher's piece by using complex analysis, and it produces a very satisfying, "obviously correct", solution.

But, as with all jokes, the punchline isn't funny at all without the setup.

yreadMar 27, 2026, 2:19 PM
The print gallery is just Aw^c in the complex plane
griffzhowlMar 27, 2026, 4:42 PM
Answers that are only comprehensible to those who already know the answer:
marginalia_nuMar 27, 2026, 5:09 PM
Well he wanted video boiled down to the punchline. Ask a silly question, get a silly answer.
griffzhowlMar 27, 2026, 5:59 PM
Well, maybe, but that seems like a deliberately uncharitable interpretation of the question, which I interpreted more as "Can you summarize the video in ~1 line?" - or at least closer to that than "Can you give me the answer the video comes to without specifying the question it asks?"

Even in those terms the answer given isn't really an answer because it just gives an expression with undefined variables.

rcxdudeMar 27, 2026, 2:36 PM
The image is essentially a self-similar 'droste-effect' image in disguise. The warping of that image shifts that self- similarity into a visual loop, but the warped image still has a droste-style self-similarity in the center as well.
oulipo2Mar 27, 2026, 2:14 PM
The whole point is the explanation... it's a bit like someone telling you to take a 2 week holidays somewhere and you'd just say: it's too long, can't someone just get me a plane ticket there and back the same day so I can compress the stay?
LercMar 27, 2026, 3:50 PM
Awᶜ

This kind of risks obscuring what's actually going on.

qoezMar 27, 2026, 4:33 PM
Makes me wonder how this would look/feel interactively if a game world was rendered like this
marginalia_nuMar 27, 2026, 5:08 PM
Manifold Garden isn't far off.
ameliusMar 27, 2026, 2:05 PM
Clickbait title broke my brain.
coldpieMar 27, 2026, 1:31 PM
Clickbait title could use another pass. What is this about?
jgwil2Mar 27, 2026, 2:46 PM
This was the title used when I came across the video. Apparently YouTube uses many different titles for A/B testing but this is the one I got. Can't edit it now, unfortunately.

EDIT: seems like dang or team took care of it, thanks!

wodenokotoMar 27, 2026, 1:40 PM
It makes more sense when seen on YouTube where you get the thumbnail of one of M. C. Eschers famous drawings is shown.

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.

nticompassMar 27, 2026, 1:37 PM
I clicked on the link and the video title is "Decoding Escher's most mind-bending piece", which is a lot better. I also had no idea what "3B1B video" meant, apparently it's a channel called "3Blue1Brown".
hnuser123456Mar 27, 2026, 1:40 PM
It's about examining the mathematical methods MC Escher used in one of his recursive drawings.
rcxdudeMar 27, 2026, 2:38 PM
Probably he didn't use these techniques explicity: the video mentions but doesn't emphasise that he probably sketched out the map by feel instead of analytically, which is probably one reason why he didn't fill in the center.
coldpieMar 27, 2026, 1:46 PM
> Examining the mathematical methods MC Escher used in one of his recursive drawings

This would be an excellent title :)

SirMasterMar 27, 2026, 1:48 PM
Depends how you define excellent. If the goal is to get more views then it's not all that great, and views are kind of the point of YouTube for many, especially if they are trying to make a living from it.
c-hendricksMar 27, 2026, 2:12 PM
That's great for YouTube, but HN has some guidelines:

> please use the original title, unless it is misleading or linkbait