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

123 points

by jgwil2

4 days ago

| past

| 9 comments

| youtube.com

| HN

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manudaro

1 hour ago

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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?

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john_strinlai

1 hour ago

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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/

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boriskourt

3 hours ago

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This video is an absolute tour de force of communicating a complex concept.

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JKCalhoun

2 hours ago

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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.)

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dmbche

3 hours ago

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All of 3Blue1Brown is - hoghly highly recommend

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boriskourt

2 hours ago

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I've seen most! Highlighting this one out of them all. Exemplary! : D

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m-hodges

3 hours ago

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The title I get when I click on this is, "How (and why) to take a logarithm of an image"

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peesem

3 hours ago

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YouTube has A/B testing features that allow videos to have multiple titles and/or thumbnails.

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m-hodges

3 hours ago

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Right. So I thought it would be helpful to share the more-descriptive title that I got.

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Modified3019

2 hours ago

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This is what I use DeArrow for, crowdsourced titles and thumbnails (from the maker of SponsorBlock): https://github.com/ajayyy/DeArrow

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dandanua

2 hours ago

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I'm sorry, what? Can people now see different titles? Insanity, if true.

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hidroto

1 hour ago

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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.

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zacmps

1 hour ago

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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.

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sva_

3 hours ago

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For me it is "Decoding Escher's most mind-bending piece"

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close04

1 hour ago

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> 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.

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3b1b

1 hour ago

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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.

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cromulent2

1 hour ago

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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!

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john_strinlai

43 minutes ago

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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.

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john_strinlai

1 hour ago

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i see "Decoding Escher's most mind-bending piece".

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

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eblume

1 hour ago

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It's a pretty common feature of youtube creator studio. https://www.theverge.com/news/840789/youtube-video-title-a-b...

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john_strinlai

1 hour ago

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i had no idea, thanks. at first glance it seems okay-ish for the creator, but only serves to be confusing for the users.

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pierrec

1 hour ago

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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/

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qoez

37 minutes ago

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Makes me wonder how this would look/feel interactively if a game world was rendered like this

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marginalia_nu

2 minutes ago

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Manifold Garden isn't far off.

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OscarCunningham

2 hours ago

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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.

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amelius

3 hours ago

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Clickbait title broke my brain.

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Jeff_Brown

3 hours ago

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I love 3B1B but generally don't have time to watch long videos. Can anyone sum up the punchline?

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ahns

3 hours ago

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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)

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rcxdude

2 hours ago

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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.

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pdpi

2 hours ago

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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.

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yread

2 hours ago

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The print gallery is just Aw^c in the complex plane

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griffzhowl

28 minutes ago

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Answers that are only comprehensible to those who already know the answer:

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marginalia_nu

1 minute ago

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Well he wanted video boiled down to the punchline. Ask a silly question, get a silly answer.

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rcxdude

2 hours ago

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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.

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oulipo2

2 hours ago

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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?

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Lerc

1 hour ago

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Awᶜ

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

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coldpie

3 hours ago

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Clickbait title could use another pass. What is this about?

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jgwil2

2 hours ago

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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!

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wodenokoto

3 hours ago

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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.

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nticompass

3 hours ago

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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".

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hnuser123456

3 hours ago

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It's about examining the mathematical methods MC Escher used in one of his recursive drawings.

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rcxdude

2 hours ago

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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.

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coldpie

3 hours ago

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> Examining the mathematical methods MC Escher used in one of his recursive drawings

This would be an excellent title :)

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SirMaster

3 hours ago

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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.

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c-hendricks

2 hours ago

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That's great for YouTube, but HN has some guidelines:

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