Summer of Math Exposition

The first major part of the video, the blur -sharpen explanation and the reaction-diffusion equation, are excellent. Would rate it a 9 if I could.

However, there are some topics that are discussed in the last few minutes: computational complexity and using fft to speed up convolution, which don’t fit in with the core premise of the video, and don’t have a clear motivation. Having these as two separate videos would have been better.

Two mechanisms for turing patterns are explained, one is computational/digital and the other is a more chemical / biophysics one. However, neither of these directly apply to the yogurt lid, which is a homogenous material.

Everything is too bouncy/squishy. To a degree where it actually distracts from the explanation. And the sound frequency examples are badly mixed; mostly too loud compared to your voice.

This was a really good video. I love the applications and a wide variety of real world connections. I feel like there is much more to learn about here. I would be interested in connections with chaos theory as that seems to be where this is going. Also it seems like there might be connections with AI. Overall this video made me think and is one of the better ones I have seen in SOME. I think you did a good job of covering a lot of material in the 20 minutes.

A couple of things, I’m still not sure how a yogurt lid is related in anyway, other than through chemical reactions? And a similar pattern? The zebra, lion analogy didn’t seem to add anything, I kind of missed the connection.

Thanks for the great video.

The intro was memorable and amusing. The one-dimensional sequence of pixels-to-audio-frequencies mapping was somewhat jarring, but weirdly will probably be the number one thing I remember from this video in a year. Tigers and zebras was not a very strong analogy. It sort of reads like image convolution with extra steps. The explanation of how the FFT leads to checkerboard patterns was mind-blowing despite very much not being the point of the video. I still don’t understand why these patterns occur in physical space, especially why they would occur both in emergent properties like zebra stripes and in manufactured products like a yogurt lid.

You build up the intuition very well, and the examples are all helpful.

Two details I think are missing: Why is that what the band-pass of an image looks like? And how does the predator-prey model connect back to the yogurt? You’ve done the hard work building the models, you just need to connect them back to the problem we started with.

The video talked about Turing patterns which are really cool. I like how he showed the relationship of convolution to diffusion and sound frequencies. I like how he showed the sounds in the video. Some math videos help you understand a problem but this one reminds me of 3b1b.

I really liked the idea and its execution!

Motivation: 6 / 9 – the yoghurt lid motivation was very intriguing and lovely, but you didn’t give the full explanation why does Turing pattern appear on it. I’ve seen your reply in comments, and I understand you were short on time, but it doesn’t justify it not being in the video. The whole thing seems incomplete because of it, so that’s my only concern here

Clarity: 8 / 9 – generally you explanation of stuff was brilliant, especially the grey-scott model. The only things I want to pick on are: 1. Fourier transform not explained at the end of the video – for me it was a crucial part of the explanation and I would love to see it, just for a few minutes; 2. I kinda got lost around 6-10 minute mark when you were talking about the relation between images and fequences and all those passes – it might be just me, but I felt like more explanation, maybe like screen on definitions would be better.

Novelty: 9 / 9 – for me, the idea for this video was brilliant and the way you contained so much mathematics in it was inspiring. Absolutely great job on that

Memorability: 8 / 9 – the video was beautifully done, but there were a few flaws in the audio and video desing, only a few. Also, if I would need to pick on something – the thumbnail looks kind of generic and not very mathematical. Maybe working on that would help with the reach this video gains.

Overall: 7.75 – this is one of my fav videos of this edition of SoME and I think you did a great job with only a few minor issues. Good luck in the contest!

Very informative and engaging video. Especially appreciate that every explanation is intuitive. Also, some humor and overall structure of the video is very well done.

My feedback got deleted several times :( generally it was more positive than what you’ll read below but presume that i’m mostly giving you feedback on what you could improve. There are a lot of things you are doing correctly and the one thing that jumps out is the connection you make between you, the viewer and the real world around them. Your video makes Turing patterns tangible.

Motivation was great you combined history, real life examples and transitioned into the morphological operators seamlessly.

Visual clarity was good. Be careful with animating everything though, for instance, the kernel operations became distracting since you are repeating the same animation multiple times. Also the object could be slightly larger think as if you are looking at it from a very small screen or far away in a lecture hall.

The number of concepts you are introducing is too much:

Laplace operator, Convolution, Reaction-diffusion, Gaussian, Gradient, Grey-Scott model, Low band pass, Convolution theorem, and many many more concepts.

Take a look at how 3b1b divides up his series, those are ofcourse deep dives while you are combining the different techniques under the same turing pattern umbrella. But you would win in clarity simply by cutting some content and staying with the morphological operation -> turing patterns -> chemical model beats.

The idea you are working on is not novel. But the edge that you bring is your real world examples.

The lid pattern, the glasses, ferrofluid in milk and generally your personality make the video memorable and engaging.

Het mag er wezen!

This is a very nice video, very clear and funny. It is very easy to watch, the equations are made so easy to understand with a nice analogy. The animations and text constantly falling down might get a tiny bit distracting after a time, and the sound demonstrations are just a bit too loud (ow my ears), but those are just details. I did not expect to see a link between gaussian blurs and frequency filters, and I was delighted to learn about it.

I’ve never seen such good intuition for why the reaction diffusion system makes these patterns. Very well made video with good humor and music and great explanations, I can tell you put a lot of thought into every detail.

Good video production.

Some terminology introduced without explanation (Laplacian). Jumped around from topic to topic a bit too frequently. Conceit of the video (why do these patterns appear in yoghurt?) is never explained. Some sound effects were jarring.

Funny and interesting if you know the concepts. Idk how much I’d have gotten from this video had I not know what convolutions, Fourier transforms, etc are

Really loved the video, you managed to start from a yogurt lid to explain many different topics.

Really good video, however I have to be real, the audio clips you played are kinda horrific haha. But for real, great video! I’d have liked a bit more detail about certain aspects, like how the laplacian works in the discrete world, or what happens to the edges during a convolution, or even how the 2D fourier transform works! Regardless, it was a great video, keep it up!

Really great video. Especially liked when practical examples were shown.

When it went to 3d and made a brain that was awesome

Great video!

…but the audio samples were quite loud and annoying.

The graph at 18:28 is amazing. The video was clear and interesting, though I’ve seen similar videos on the same topic.

Interesting video, but the title and intro do not give a good idea of what the rest of the video is going to be about. It would be nice to see in the introduction some sort of outline of the rest of the video.

Waouh !

Impressively educational. The animation is superb when it needs to be, and clear and fun when it’s useful. The length is perfect, too, and the pacing is spot-on. The sound quality is excellent. I’ll bet 100 euros (with myself. If I win, I celebrate; if I lose, I keep the money for next year) that this will be the winner of the season.

Un grand merci.

I enjoyed the humour in the video, but it ended up being quite educational as well. I enjoyed seeing the connection between the simple methodology to generate a Turing pattern compared to its biological/chemical counterpart which did give a sense of why something would work the way that it should. I think probably it’d be also interesting to understand more about what studies arose from the Turing pattern in more detail. Also, would appreciate some of the audio warnings as some of the sounds were quite loud.

Very cool!

I like that you investigated one idea from so many different angles, and at the end expanded to other domains (audio and 3D)

Visuals were great, humor was great

I wonder if there could have been a little more explanation for the “why” of how the pattern appears from this process

Really cool video. I was hooked right away, and needed to know more. I thought your explanations were fantastic, though I did get to a point where I was losing track of the details and not seeing the big picture. I think there needs to some attention to why this all matters - not just the yogurt pattern but what all the blur patterns do, or why they might be useful, .such as in AI image detection or generation. Still I thought did a good job holding interest, and the animations were wonderful. Easily one of the best submissions I’ve seen so far.

The best video I watched so far.

OMG this video was amazing, one of the best math videos I’ve ever seen. The hook at the beginning made this video unskippable. I loved the way that even without fully knowing the FFT, I was still able to understand at the surface level what was going on because of the visuals and explanations. The Grey-Scott model equations were also explained in such an easy-to-follow way that I really appreciated. Your combination of image processing, chemistry, and humor made this incredibly engaging and fun to watch; I had to stop myself from laughing multiple times in the library.

That being said, I was confused on what exactly was being demonstrated at ~18:28 with the parameter space graph. What did the color at each point represent? I also think some arrows at the 19:28 section would have helped illustrate more clearly what was being subtracted from what, since right now it looks a bit like the DoG is being subtracted from the original image cascade.

The examples at the beginning were very good motivational tools. Explaining Box & Gaussian blurs helped root viewers’ experience with image editing software. Convolution algorithms explained reasonably for intended audience. DO NOT LIKE audio patterns given at 4:10-4:40, 7:10-8:20, 23:20-23:50. These hurt my ears, please make them quieter than other items in the video. Some textual items were overlapping the caption “safe-zone”, but it was less noticeable than in other videos, largely due to important information and attention being located / directed elsewhere. Difference / Laplacian of Gaussians were interesting topics and had strong connections to the high- & low-pass filters. The expansion of the Turing Pattern into empty space may have been related to bacterial growth in a growth medium (agar plate). There could be an interesting discussion of extensions of the topic, here. (or a different extension that actually exists) Animation style with the animals bouncing around the boxes using physics was a nice touch. Relating the predator-prey model to diffusion was a memorable and interesting addition.

Great hook - very curious to learn more. Loved the humor and transition to the beautiful macro shot of the lid. Nice choice of music and aesthetic choices. 28 seconds in and I feel I’m in for a great video.

I like that you juxtaposed real mathematical content throughout (e.g. equations like Grey-Scott model, connection to the heat equation, associativity rule, etc), but more importantly, allowed the viewer to directly experience the various filters, via both image and audio.

Beautiful animations throughout, e.g. at 1:00 building the Turing Pattern out of image editing operations. Great music choices as well. Very aesthetic, and the ending experiencing the yogurt lid is hilarious.

Some of the audio at 4:12 is unsettling on higher-volume earbuds, I feel it could have been turned down a bit, especially the high frequency signal. But the visualization of the soundwave and frequency is excellent.

Beautiful visual shots and transitions to the ferrofluid at 11:46 and wine glasses at 12:16 (great audio splash here too).

Great music pairings throughout - especially delightful at the tone shift of 13:21 to zebras and leopards.

Loved the video throughout and don’t have anything critical to say. Bravo! Great use of YouTube as a medium to communicate math.

Very interesting video overall. The convolution <-> frequency/filter connection was very insightful. Same with the connection to chemistry/population dynamics. I walked away from the video with many questions/directions to keep learning (in a good way)!

This is such a cool topic and exceptionally well executed. I like that the creator gave concrete examples of Turing patterns arising as emergent behaviour (like the ferrofluid, yogurt lid and fingerprints) - it complements and grounds the theoretical explanations very well.

All around good video, nothing I can really think of that needs improving here.

Fantastic video! Great explanations and great use of animations. Maybe why the pattern is present on yogurt lids should be explained a bit more. Still, very good video. Keep up the great work!