Summer of Math Exposition

Nice video and nicely animated. Easy to follow until the repeating cycles part. I also miss a conclusion, intuition or a why do we care or are doing this. What is the takeaway of this video. Without any questions, proofs, attempts or potential paths to proofs it more feels like a showcase

Found It very interesting, A brief explanation at the end as to why the centre is so Hard to find with respect to lack of a period would be interesting. The animations looked very nice. The financial incentive to understand the problem I think helps to hook the watcher. Thanks

This video is fantastic, you’re exciting toned and polished animation all make this interesting topic even more attractive.

I think you need to do more to grab and hold interest. At the beginning I thought it was a mildly interesting self-generating rule based game, but as we got into the minutia I started losing interest. Maybe more discussion about determinism and the arrow of time?

That was fascinating and easy to understand! I did not think I would care about those automata, but the enthusiasm of the narration is contagious. The animations are very natural and help greatly.

I think I would have preferred if you haven’t shifted the diagonals. And in the context of SoME I must critise that there is very little motivation for why you care about this topic. But overall, another fantastic Eric Rowland video.

I enjoyed the part about the right boundary, the left boundary was a bit less interesting and maybe could have been cut? I understand that you want to say what you know about it though.

• Animations are clean
• Explanations are great, but they are a bit fast and dense at some points - I had to re-watch “diagonal periodicity” through “local nested structure” a second time before I got what they were saying - there are long periods with no animations and just narration, which makes it a bit hard to follow. The explanation is there, but sometimes it’s easier to digest as a written script than as a narration.
• As an example, when you talk about “local nested structure”, it would be helpful to travel down in time until you get to a large triangle that “looks like” the infinite black triangle at the initial state, so that it’s easier to see what you’re talking about.
• When you are showing why the periods are powers of two, you shift the $2^{n+1}$ diagonal over to the left a bit (I assume for visual clarity), but it makes it seem like it was two diagonals left of the $2^n$ diagonal, and not one over to the left. So I was confused until I went back and saw the shift happen.
• Another example is that during the multiverse discussion, I didn’t realize you had changed the framing to “what if we changed the initial state” until I went back and rewatched - so I was confused why the pattern was suddenly branching.
• Excellent choice of topic, I love the enthusiasm for research questions like these and partway through I forgot I was supposed to be taking notes for review because I just got lost in it.

Really cool video, and the visuals helped a ton to understand the material.

Nice video! I liked that this was an interesting extension of where cellular automate could go and the interesting patterns that might go from alternate rulesets. It was quite clear about the consequences of the rulesets and how interesting it can turn out to be even though we don’t understand oto much on it.

I think having a quick simple of cellular automata (maybe something like Game of Life) might help to get a few more viewers acquainted with the subject more.

This is a really great video! You clearly put a lot of time and energy into making it. The visuals using Manim are excellent. That narration was also very good, and it’s a math topic that few people (including myself) are/were aware of. The idea of reconstructing the past of this particular “universe” as well as going back in “time” before the initial conditions was also fascinating.

There were some places I got a bit lost in the details. This is probably unavoidable, though, as it requires quite a bit of time (longer than is available in single video) to really understand what’s going on. The video gives you just enough of a taste of the subject to want to learn more about the subject.

Overall, an excellent video!

A very unique topic—the speaker’s enthusiasm is palpable, and I found myself getting carried away!

Great visuals and buildup and simulations. Really helps to understand about the automaton and its mathematical significance. I just think a few parts were a bit too complex, but further reading definitely helped understanding the video. Well done

I was not super familiar with this, but I had heard about this before from a professor. I had been wanting to review cellular automata and Rule 30, so thank you for that!

Thanks you your video I have had a good refresh on what cellular automata are and how they work, along with a lot of neat info about rule 30 that I didn’t know.

That being said, my ability to retain all this new info and keep following the video drastically waned right after your elegant explanation of two consecutive diagonals repeating every 2^n. After that, I found that my working memory was stack-overflowing. I think that adding a tiny bit more silence at some spots and also a couple of refreshers or recaps for where we are and what we’ve learned up until that point in the video would really help me understand the last third.

In terms of Motivation, I can’t quite remember what you said for this part, which I think means it could use a bit more work. Perhaps just a few more sentences throughout could help ground this more to stuff that more tangible in an everyday sense.

Excellent and interesting! And the visuals were very nice!

Awesome stuff! I hope your computer didn’t melt to bring us those pretty pictures :)

I really liked this video! Thank you so much for making it. It was really interesting to see a lot of the questions I had from looking at the initial picture addressed throughout the video.

I don’t know if this video was necessarily the place for it, but I would love to see some more analysis of how rule 30 fits in with the rest of the 2^8 evolution rules, especially since part of what makes it so interesting is that many of the other rules don’t do much at all.

This is a nice introduction to the complicated behavior arising from cellular automata. As someone who’s seen a fair bit on the topic (but has never studied it with any seriousness) I did appreciate your restraint to not over-philosophize about emergent behavior.

I have no major technical complaints about the video. The animations were decent, the script was reasonably organized, and the narration was mostly smooth, with a few points of emphasis. Still, I’m not inclined to describe this as “better than most” math explainers, although it’s difficult for me to put my finger on why.

My best guess: I wasn’t entirely sure what this video wanted from me. This point was most clearly illustrated in the time symmetry section. On one hand, the argument for why there is no pre-period on the right diagonals was quite satisfying. It was conceptual with no crunchy computational step, and so ran the risk of feeling a bit wishy-washy, but I thought this explanation navigated it well. I was a little less convinced by the argument for why it implies large black triangles eventually appear. I was able to figure it out, but only after pausing the video. I think the intention is not to think so carefully about justifying the claims being made in this section since it’s prefaced by a “one more amazing thing!” kind of introduction.

The impression that I had gotten at that moment was that I should “not listen for the details, listen for the music”. If that was the intention, it could be clearer. However, I also this feeling for most of the section on left diagonals, where a similar signpost seemed lacking.

It’s really hard to get interested in these wolframisms, even though I do appreciate your exposition style.

Interesting topic. Animations are well crafted. There are some nice ideas such as putting diagonals to columns which help understanding the phenomenon and see the patterns in a different perspective.

On the down side, visual “proofs” of the reason of some patterns are too verbose for my taste. Maybe it should be that way, but most of the time, I got lost through the way. Seems like they need more elegant proofs that is easier to follow. Video is also on the long side, would be better if it was shorter.

There’s a ton of great information in this video, but I wish it was ordered in a slightly different way. What I love most about 3b1b videos is their therefore structure. Where a simple concept is introduced and then expanded on until its consequences are shown to be so fundamental as to be obvious. This is what leads to the moments of revelation. I think this topic can be done similarly: begin with the basic cellular rules, walk through the different integer iterations, linger on them a little so we can think through which might create structure, then show how they propagate, pause on rule 30 “hmmm, this one is interesting! patterns on the left, none on the right, what’s going on!”.

Good audio quality; good speaking voice. Very well made animiations, but as a piece of feedback: in a number of places it was not ideal to have black be one of the colors, on a black background. I was watching on a small screen, and the border around black squares was too subtle. Maybe you do actually want the “black” squares to be background-colored, so the shapes and patterns in the other color are more prominent and it looks like they live in an infinite world (aha! there was more!) – but when you were explicitly showing cutouts of patterns (and the rules themselves), it is relevant where the border is. At very first glance, it looked to me like the rules were 3x2 rectangles, not the 3+1 T shape. (Still: very well animated of course!)

Great video, an excellent introduction to a topic I knew nothing about!

Great job on completing your SoME5 entry. Cellular automata are interesting puzzles to consider. My feedback is mainly around the Motivation and Clarity aspects.

First off is the motivation. I would like to know where we’re going in the video right from the start. I did not know this so I was just following along and didn’t know the destination. After I finished watching I said to myself “OK, so the video was about proving some periodicity behaviours on the left and right edges of the rule 30 cellular automaton.” But I didn’t know that at the start. The topic of cellular automata is so broad. Even in the video you were able to go on some tangents about time reversal, how it’s locally nested, etc. From the perspective of someone like me who’s just watching this video with no context, I have no clue which rabbit hole you were going to jump into. So mentioning this up front would have been great.

For clarity, I found myself having to do a lot of heavy thinking on my own to reorganize the ideas and flesh out the proof steps.

Specific example. This was my live reaction as I watched your video:

Right diagonal periodicity.
10:28 I wanted to know why those diagonals repeat periodically, not just be told that they do.
11:25 “The period lengths seem to be powers of 2.” Again why is that? Why can’t we have periods of non powers of 2?
11:48 OK so the explanation for the repeating diagonals starts here…
12:31 So I worked out the right most 2 columns on my own, but then I’m told that “the same idea works for every diagonal”
12:41 “If the previous 2 diagonals are periodic, then from that point on, the 3rd diagonal proceeds the exact same way.” I see, so there’s an inductive argument going on here.

18:00 All right, so 5 minutes later, now the explanation for the power of 2 period starts.
19:30 I see… so it’s another inductive argument. I guess it works but I would’ve really liked to see the key aha moment clearly highlighted.

etc.

This goes back to my comment about Motivation. In my live reactions, you were eventually able to answer the open questions I had in my head, but if the destination was clear from the beginning, and if you presented the aha moments clearly when they arise, it would’ve been a more enjoyable video for me.

Very clear and simple to follow, the visuals were very helpful and the topic interesting.

Awesome video, my favorite this year so far, almost everything is explained well