Summer of Math Exposition

Really nice write-up of turtle graphs! Maybe a little bit too long? Two concrete issues: The outgoing links should have target=“_blank” so that they open a new tab, though. And, of course, the vibe-coded widgets.

The interactive widgets are very fun!

Great graphs and very detailed math explanation！It’s good enough, maybe I think more math about square can be added (like Middle-square method ) so readers can feel the connection between different math branch.

Quite an interesting exploration into graphs of some simple rulesets. All the rules are explained quite well and derived, and as a result of the consequences of studying the properties of the equation.

I was slightly confused near the start by whether we would do regular shapes, or be moving towards the cumulative route, which was clarified by the table later. Maybe showing the table first, and then the interaction might help to make it easier for the reader to immediately latch onto the idea.

Clear, nice visuals.

For some reason this short “abstract” already is a great introduction to the subject. The only thing the user should know is the importance of chaos. Contrasting chaos to symmetry and you’ve got a very nice angle. I think the motivation is great for math enthusiasts. You could extend it though to bring it into a broader context. It mostly depends on your target audience.

Clarity is suprisinlgy good. It could be that you chose a rather simple mathematical subject to describe. However, I suspect it is rather the clarity at which you present the subject that makes it easy to understand.

The voice with which you write is very simple to understand. eventhough you do use jargon or tougher words they do not throw me off.

Never heard of the subject before nor have I seen turtle graphics, so new to me.

I would remember the subject and look deeper into it to find if it has more visuals hidden inside of it. The interactive examples do their job. rework the full interactive UI though, there is no good seperation of the elements and what they do. Having all controls in a single side menu is quite overwhelming.

Great topic and explanation, but doesn’t really keeps reader’s interest overtime

In the section “The Complex Case: gcd(S, 6) = 1”, your “special” set of primes appears to be primes congruent to ±1 mod 12. Of the 4 results on OEIS, 3 are the same up to starting terms, and the other includes composites, so you have effectively the one result, https://oeis.org/A097933 so prove that relation or find your counterexample

Cool visualizations, although I wish there was more text accompanying them (i.e. in the fourth section, explaining why the gcd tells us if the path will close or drift instead of just having a sentence in the viz about the gcd and not fully explaining everything in the following sections. I also think there could’ve been more exposition motivating the topic, even if just as a cool piece of math! Score averaged from the following: motivation 4, clarity 5, novelty 9, memorability 7.

Excellent. I would have liked to be able to enter my own S somewhere. Also, in the first interactive, the autoplay button doesn’t do anything if you’ve already looped around. This makes sense, but my first time using the interactive it felt like the button was broken since I had already manually looped around. Maybe have it go around one more loop in this case?

Also, consider setting the for the page!

Demos seemed to suggest that the Turtle has to perform a turn of some multiple of 360 / S degrees each time, and that it must perform some cyclic sequence of rotation (e.g. rotation of 60, then 120, then 360, when S = 3). Not entirely sure why it has to be cyclic.

Ah, it explains in the section below the demo what’s going on. Apologies!

I chuckled at the old-fashioned term “Drunkard’s walk”, which I thought was seen as dreadfully outdated now! :’)

Hmm, interesting, that cumulative direction formula looks suspiciously like the Triangular numbers formula?

I have it in mind that every squared number is either 0, 1, or 4 mod 8, so I guess the author’s getting something similar here with their mod 6.

Going by the examples under “Interactive — Closes or Drifts?”, drifting seems to happen when S = +/1 mod 6, which of course would both correspond to S^2 = 1 mod 6. Ah, no, can’t be quite that simple as S = 25 and 49 are both 1 mod 6…

Okay, here’s my overall feelings.

1. Really fun article - loved the interactive bits

2. I loved reading about the author’s research into these plots

3. The “E” is SoME is for Exposition, and does imply that the event is for Expository (Teaching) material. Did I learn things here? Absolutely! I really enjoyed learning about Turtle Graphics!

But the author is quite open about this being an ongoing research project, so I feel that this is arguably not an expository piece. That is the only reason I haven’t given the author a higher score, but I really did thoroughly enjoy reading about the author’s work. :)

Great job & I hope you continue this awesome project!

entertaining subject, well written

Pretty good work! I liked the exploratory nature of the argument - you see a phenomenon, ask questions about it, and then try to prove things about it. I also like the math typesetting where the math is rendered in a different color