#visual math

[art-of-mathematics]

Today I drew the Deltoidal Icositetrahedron, which is the dual body of the Rhombicuboctahedron.

[obsidianandblacksatin]

Decoding Math’s Famed Fractal: The Mandelbrot Set

[knotty-et-al]

Visualization of the Rubik's cube

[xponentialdesign]

On my 37th birthday, I made a tool to trace orbital paths Realized later the source file was gone But a mistake saved me from the loss I had imported it into another project by accident That one was archived and I found it today So I'll play with it a little bit more DIGITAL ARCHIVE

[hizerain]

2025.05.05

A mess of notebooks and papers. I've taken to organizing them in multiple piles across my floor. Somewhere slowly functionality over aesthetics has taken over life. My various fragile and beautiful fountain pens swapped for a sturdy indestructible rotring 600 ballpoint. Beautifully kept notebooks exchanged for loose sheets of paper flouncing around. To some extent, I do miss the enforced slowness of the other tools. At the same time, I've always had an aesthetic obsession which has often been suffocating. It has been nice to let go.

[demaparbat-hp]

The Painted Lady turned around slowly, deliberately, and stared right through each ghost present in the room. Then, she raised her hands in a graceful arc, pointed loosely at the ceiling, and chanted, “Well, off you go.” She made a shoo, go away gesture, the spirits disappeared, and—wait. The spirits disappeared.

Izumi comes back in For the Spirits Chapter VI: Dream of You. Zuko has a mild panic attack and her upbeat attitude does not help him (or does it?).

Just what is she up to? And what is the meaning behind the blue eyes from Zuko's dream?

[vasira96]

the more time passes the more upset i am at the culmination of seasons 1 and 2 of arcane, like asdfghjkl what was even the point of any of the first season if that is how it all adds up????

[tremendouskoalachild]

how old can the Stranger conceivably be?

we don't know - and aren't supposed to know - at this point, possibly ever.

but with the recent-ish releases of The Visual Guide (reference book by Pablo Hidalgo) and Wayseeker (novel by Justina Ireland) we can narrow it down!

I: show-only extrapolation

the Stranger was Vernestra's student. at some point he left the Order in a way that made Vernestra assume him dead. he also has old scars matching Vernestra's signature weapon, suggesting a confrontation between the two.

Vernestra is pretty old. not only does she have a position of authority within the Order and with Republic leadership, we know she remembers middle-aged Sol as a shy youngling.

Osha came into the Jedi Order 16 years ago, and left 6 years ago, by the time of the show's present-day events. the Stranger very strongly suggests his departure was old news by the time she joined.

assuming he was at least a teenager when he left the jedi, and stretching Osha's unawareness of him to her not remembering the confusing drama around the time she joined as a little kid, he's at least in his 30s (with no real upper limit from the show itself).

II: taking into account the High Republic books

(i think the books can't be used to answer the show's mysteries, because the show is meant to stand on its own, both from a creative and economic standpoint; however, everything suggests the creative team is taking their lore into account and won't conflict with them.)

Vernestra is 16 years old at the start of the book series, which takes place 200 years before The Phantom Menace, and around 20-ish when they end (the exact chronology of the latest books and upcoming finale of the series is not firmly established yet).

the show doesn't clear up the exact year it's set in within its text ("one hundred years ago" referring to first THR book events in the flashbacks, "a hundred years before the rise of the Empire" in the opening text) but was described as set 100 years after the beginning of THR and 100 years before TPM prior to release. assuming very roughly a century since the books would make Vernestra around 116, let's say 100 to 125, during the show.

Vernestra's first Padawan, Imri Cantaros, reaches Knighthood around the time she is 19, towards the end of the book series (yes, the circumstances are special).

it isn't unheard of to take a student older than yourself (Grogu and all that), but we don't tend to see this scenario with human Padawans.

i'm gonna make this weird and say that with the THR books and show in mind it's conceivable the Stranger is around a hundred or even older. likely? fuck no. but the dark side is a pathway to many abilities some would consider unnatural.

III: incorporating Wayseeker

(the book was written after the season was done but before and while it aired, and on a pretty hectic schedule, by Justina Ireland - Vernestra's creator. it was also written before the show got cancelled. there are allusions to Vernestra's last apprentice but nothing specific, and the timeline is pretty wishy-washy.)

we learn that the Stranger was the final one in a series of Vernestra's Padawans as of the book's timeline (presumably going on into the show - Mog is notably not her Padawan). however, this doesn't really narrow the timeline down at all; we only know she had at least three (though probably more) students over the decades. how long one stays a Padawan is highly individual, especially in newer media, not to mention frequent examples of a master dying or otherwise leaving and another Jedi concluding the Padawan's training.

Vernestra had a falling out with a colleague around or slightly over a decade before the book, and had recently marked "another" anniversary of her last student's death at that point. that suggests he has been presumed dead for at least 12 years during the book's events.

we don't get any significant hints at how long ago this might have been beyond that - the characters who discuss the possibility of Vernestra taking on another Padawan referencing her tragic experience are fairly old themselves, and don't give us any more context.

Indara is 26 at the start of the novel, and the plot of the book takes place over several weeks. while the show itself doesn't give us Indara's age, i think it's reasonable to say she might be in her 50s during the present-day events (Carrie-Anne Moss' age during filming), and several years older than Sol. let's go with very roughly 20-35 years between Wayseeker and Indara's death in the show.

Vernestra's age in Wayseeker is not specified beyond "nearly a century" in her own internal narration. the events of the book series, during which she was a teen, are also described as (nearly) a century ago several times. since i trust Vernestra's knowledge of her age over the historical precision of several characters, i'll say the oldest she can be in the book is 99 years old.

it has been at least 3 decades since the Stranger's presumed death as of the show's timeline, likely closer to 4 or more. continuing the reasoning that he was at the very least a teen at that point, the youngest he could be in the show would be in his late 40s (this approximation already contains several edge-case assumptions, so i'd say it's highly unlikely, but we're keeping our options open). keeping Vernestra's age as the upper boundary, the oldest the Stranger can be during Wayseeker is in his 90s - adding the 2-3 decades to get to the show, he could be well over a hundred years old.

IV: considering The Visual Guide

(material for the book was collected during the show's production and airing, and many minor pieces of information were clearly decided after the fact. the book incorporates information from the Kelnacca comic and Wayseeker for character biographies. it specifically omits information that Lucasfilm doesn't wish to reveal yet - or ever - including the Stranger's age, which is listed as "unknown".)

Indara's character page includes a timeline of her life, giving us a concrete way to anchor Wayseeker to the show: she was 26 during the book and 54 in the show's premiere. the book therefore takes place 28 years before the show's present-day events.

Kelnacca's page has a similar timeline of the last century of his life, giving us a way to relate show events to THR's chronology. we know he was 149 years old when assisting in the Starlight Beacon recovery mission (which occurred at the end of THR Phase I, around 2 years after the books start; Vernestra would be around 18 at that time, and it would be over a year later that she reconnected with her missing Padawan Imri and knighted him). Kelnacca was 248 at the time of his death in the show, and 231 during the Brendok mission (seemingly dating the show flashbacks 17 years earlier, though this is perfectly fine - the mission took months, and we don't know when his birthday is). the show is therefore set around 99 years after the Starlight Beacon's fall (which would also put it 99 years before TPM).

since some 28 years passed between Vernestra's Padawan being at minimum 12 years gone and the show, the Stranger could be at the very least in his late fifties, likely older. Vernestra is around 117 years old in the show, and there doesn't seem to be anything directly conflicting with the Stranger also being over 100, though it would be very unusual.

[colormush]

[art-of-mathematics]

I know I have drawn this shape so often already, but the process of drawing it is so soothing.

And for that, I have drawn a kind of step-by-step guide how to draw that shape in the top of this drawing:

(from left to right: ) [sorry in advance if I make it sound more complicated than it actually is. If you want to draw it, I would advice you to focus more on these illustrations rather than on my gibberish-text.]

1. draw a 2-dimensional Cartesian plane - or, in other words: just draw a cross like depicted

1.1. mark 2 points on the y-axis/vertical line with same distance to the coordinate origin, then mark 2 points on the x-axis/horizontal line with the same distance to the coordinate origin. (The markings on the y-axis need to be farther away from the origin than the markings of the x-axis)

2. connect the 4 marked points like depicted above. This is a function plot of a tractrix. (it has two mirror symmetry axes. )

3. draw an ellipse and connect the two markings on the x-axis. This becomes a kind of "belt" for the pseudosphere (4th picture)

4. part the ellipse into whatever-amount-you-want of partings (like you would cut a cake) and slightly mark these.

5. now imagine you cut that shape horizontally on the outer surface. (In the 5th picture I depicted that with red-ish pen across the pseudosphere. ) -

6. then the cut shape needs to be "(shape) shifted". For that we use a set of marked points we did in step 4). Furtherly, we "cut" the ellipse open, and push one end of it to the top, and the other end to the bottom. (depicted in picture 6 )

7. Then we connect the rest to get that shape:

[obsidianandblacksatin]

✨ Explore the Mandelbrot Zoom ✨

Get ready to dive into one of the coolest experiences where math meets art—the mesmerizing Mandelbrot set! This fractal is a wild ride of infinite patterns and shapes, and zooming in feels like uncovering a hidden universe of beauty.

🌌 Named after mathematician Benoît B. Mandelbrot, this set comes from a simple formula but creates stunning, self-repeating structures. The deeper you zoom, the more intricate and mind-blowing the patterns get.

🔍 If you’re into Mandelbrot sets like I am, you know how addictive it is to explore the endless details. Every zoom feels like discovering something brand new, reminding you just how infinite this world is.

✨ Whether you’re into math, art, or just love a good dose of cosmic wonder, the Mandelbrot zoom is pure inspiration.

Let’s celebrate the beauty of math and all the endless surprises it has to offer!

[knotty-et-al]

Pseudosphere and dini surface

^ Visualization about the transformation of a pseudosphere into a dini surface.

v Pseudosphere

[xponentialdesign]

Reverse Orb Bits

[gilearstimboards]

---

Gunthrie "Gunnie" Miggles-Rashbax Stimboard

The ball is stratospheric at this point.

Credits: x x x | x x x | x x x

[bensboards]

Hello, could you make a graham burns stimboard please? (If not it's ok)

Graham Burns [RB] Themed Stimboard 👓 ๋࣭⭑ with engineering / math / tech themes and green colored gifs

💾|👓|💾 📝| ★ |📝 💾|👓|💾 ★: divider center gif made by me :3 source: transformers rescue bots season 3 episode 7 graham is my favorite of the burns family :D

[eriquin]

Making weekly progress graphs

All it took was one (1) person asking about it and I decided to make a post for how to make my progress graphs. Maybe I've done this before. I don't know. I'm doing it now.

For what I do, I use a spreadsheet. It's google docs right now, but I assume you can use anything because I'm not using anything unique to google docs.

You need at least 2 tabs. I have more than that, but let's start here.

Tab 1: Wordcounts

My first tab is called "WIP Progress". Here's what it looks like:

That's one line per WIP per day, if I work on it.

Month and Week are columns derived from the Date column using formulas.

Want the actual formulas? Month is "=concatenate(year(C2), ", ", month(C2))" and Week is "=concatenate(year(C2),", ", text(weeknum(C2-1), "00"))", at least in row 2.

Date column is the day you worked on it, hand entered.

Fic is a title per WIP. You should keep the title the same for each WIP because this will be used to track progress in graphs.

Detail is a note column, doesn't have to be unique. I use it to figure out working ideas and track parts of things. Like, parts 1 and 2 of the Prophetic D&D game are under the same Fic name with the actual title in the Detail column

Start wc is the number of words on that WIP at the start of the day

End wc is the number of words on that WIP at the end of the day

Total is a math formula that does the difference between Start wc and End wc. Literally just "=G2-F2"

And then every day, I add as many lines as things I'm working on and copy the formulas from a previous row and adjust them. So, for today, it looks like this:

Insert rows, copy, paste, change the dates, copy End wc to Start wc, and I'm ready to go.

How long have I been doing this? ...

A while.

More formula and some graphs behind the cut.

Tab 4: Last Week Progress

Let's skip to tab 4 because that's where my graphs come from. Tab 2 is "Progress by Day" and Tab 3 is "Progress by Week" but we'll come back to those if anyone is interested.

Okay, so the general idea is that it looks back 7 days and does a count of how many words, the average (ignoring 0s), and the counts per work per day. Then it graphs them. So how does this work?

Well, the top row is my constants:

Formula in F2: "=averageif($D3:$N10,"<>0")"

Formula in H2: "=MINIFs($D3:$N10, $D3:$N10, "<>0")"

Formula in J2: "=MAXIFS($D3:$N10, $D3:$N10, "<>0")"

The words "Word Documents" is in L2 because I use it in my unique filter. I used to keep track of my work writing but I didn't want it in this graph, so it's filtered out.

Rows 2 through 10 are my data rows. Here's what they look like:

A3: "=TODAY()", A4: "=A3-1", A5: "=A4-1". Follow that pattern as far back as you want to look.

B3: "=sumif('WIP Progress'!C:C,A3,'WIP Progress'!H:H)". Copy that down the column as far as you put down dates. That's give you your daily wordcount.

C3-C10: "=$F$1". Literally that's it. Just inserting the calculated average so that I can graph it nicey.

Tricky bit! D2 is a complicated formula. It looks like: "=transpose(sort(unique(filter('WIP Progress'!D:D, 'WIP Progress'!C:C>=today()-8,ARRAYFORMULA(if(not(exact('WIP Progress'!D:D, 'WIP Progress'!$D$1))*not(exact('WIP Progress'!D:D, $L$1)), True, false))))))"

EDIT! There's a better way that doesn't use ARRAYFORMULA. It's still a monster, but ARRAYFORMULA only works in google sheets. See my reblog of this post for an update:

... Yeah, that's a monster. What it's doing is taking the rows in my WIP Progress tab and filtering out anything that's not within the last 8 days. If you go back more than a week, change the number in the part that says ">=today()-8" to something higher. Then it also removed anything that matches my header row in WIP Progress, and also anything that matches my filter field ("Work Documents"). And then it takes all the unique values of what it finds, sorts them into alphabetical order, and transposes them so that they go in as column headers. This means the column headers change if I add more things to my daily wordcounts, and they stick around for the week.

Anyway, that's what determines the column headers for columns D through M. I've never written on more than 10 WIP in a week, so I've never needed more than that.

For cell D3, I have this formula: "=sumifs('WIP Progress'!$H$1:$H, 'WIP Progress'!$D$1:$D, D$2, 'WIP Progress'!$C$1:$C, $A3)". That is then copied and pasted into the rectangle of numbers there. Everything that needs to change will change, and everything that doesn't won't.

What's it do? Well, it matches the header of the column (D$2, E$2, F$2...) to the date on the lefthand side ($A3, $A4, $A5...) and then does a sum of the values for wordcount that match that column and that date. So if for some reason I have two entries for a WIP on the same date, it'll add them up.

Why would I have this? Sometimes I move stuff to a different document and start a new line with new start wc and end wc. It happens.

Okay, all the formulas are in! Now I have a bunch of numbers. How do I make a graph? This is easier through screenshots:

Go to Edit chart. Again, this is the googs, so if you're in Excel you'll have to look up how to do it differently.

In Setup, this is a Smooth line chart. The data range has the columns from my table above, with a little extra because I think maybe I started with 2 weeks worth. Whatever, extra is fine.

X-axis is Days, which is the first column. Then the series that get plotted are basically one of each column, except for Words because it threw things off.

Series view:

All the blank ones are on here because they don't show up if they've got no data. Well, technically they do but they're all at the 0 line so it just looks darker.

Also helpful:

Next, Customize the chart:

Mostly boring defaults, but here's the place to set the title.

And that's how the chart gets made. I have more charts than this, though...

So many more charts...

I'm willing to write more about them or help with formulas if anyone wants to know more.