@itunes Back in the day I purchased a whole lot of dredg albums. I’ve noticed recently that I’m having a harder and harder time playing them. I keep getting popups asking me to subscribe to things, though with a great deal of work I can occasionally dismiss those popups and still listen. (1/2)

Hey Apple, why can’t I play albums I purchased a decade ago with Apple Music? I click on tracks I own and it brings up a full screen ad. I have no way to listen to the music I purchased from you.

Pluribus is literally just ‘reintegration’. The only reason it feels alien is because there didn’t happen to be a ‘severance’ that happened first.

I asked myself ‘what if bitmap textures could be circles instead of squares’. Then I did some math in desmos. With square textures you can easily bi-linearly sample between the pixels you know. In circle land, you additionally have to interpolate between the two ways to pick your local grid basis!

five men writing in fingers of gold #Tuesday #Fractals #FractalArt #DigitalArt

youtu.be/5CKuiuc5cJM?... ——- I think that to reason coherently about what ‘the AI’ ‘wants’, we really need to disentangle the ‘text prediction engine’ from the ‘helpful assistant character’. (1/4)

Turn Around

He’s a rescue.

Got to punch, right on target #Tuesday #Trippy #Fractal #DailyDose

Today I learned that “angle of incidence = angle of reflection” is an incomplete representation of what happens when light bounces. Turns out that the *polarization* of the light still refracts! That’s actually foundational for how ‘iridescence’ can be a thing.

New cool #math T-shirts! 🤯😍🤩😃👕 Get yours here: jcponcemath.secure-decoration.com/shop

These silver earrings in the Anemone family are a new design at Differential Geometry. The knotted band is a stylized representation of the complex 2/7-power function. www.diffgeom.com/product/anem... #MathSky #MathArt #Jewelry #3DPrinting

#Tuesday #Fractal #Fractals #FractalArt

Pattern block play with octagons! #21CenturyPB #iTeachMath

Some of this week’s math-y art.

This is a ‘vibe animation’! Produced 100% from fighting with chatGPT for 3 hours instead of spending the 90 minutes it might have taken to make it myself.

Radical moral philosophy idea inspired by physics: locality matters! People closer to you as measured through the fabric of space and time *should* be who you care more about! Not because some people matter more than others, but because jurisdiction and obligation must *necessarily* be distributed.

🧐🧐🧐

Islands of stability in the fractal landscape of double pendulums: youtu.be/dtjb2OhEQcU?...

Saw ‘blue noise’ beats ‘white noise’ for dithering. But it’s full of worms! Today I discovered: “blurred blue noise looks flat, blurred white noise has bumps”. This connects to fluid dynamics. If you make a fluid incompressible you force it to manifest a fractal fibration of turbulent streamlines!

AI is a mirror chatgpt.com/share/681ef9... I am certain that there must be a web of misconceptions lacing the questions I asked that require correction before the answers can be meaningful. But the AI is ready to help me write a research paper about my very rough ill informed intuitions.

I propose that traditional resume optimization serves an outdated model. Lots of people fitting their skills to compete for a small number of employers. What you know is at least twice as valuable if you teach it rather than employ it directly. (1/2)

#Wednesdsay #Wallpaper #WednesdayWallpaper #WallpaperWednesday

Unicode is pretty cool! But… Kind of a bummer it has a criminally deficient set of alpha-numeric characters that can be represented as subscripts. Apparently superscripts matter more. Also a bummer that all of the monospaced diagonals needed for general beveled box drawing are missing!

Noticed something funny about perspective. I was working to convert the position and radius of a sphere into the position and radius of a disc, billboarded to face the camera, which will exactly match the sphere boundary under perspective projection. 1/2

www.quantamagazine.org/catalytic-co... My main takeaway is that ‘reversible computation’ is more powerful than traditional computation because you can re-use memory that is storing long term results for storing short term intermediate results! 1/3

paulbutler.org/2025/smuggli... Use cases include: 1) Watermarking or cryptographically signing ‘plain text’ to detect piracy of creative or copy-writable content 2) Poisoning published content to protect it from ingestion by LLM training processes 3) General LLM prompt injection

www.rwgrayprojects.com/Universe/Dir... I had to rediscover it, but I’m pretty sure that this is the paper that inspired my spin animations.

@scrappapertiger.bsky.social made a modular origami buckyball! #truncatedIcosahedron #polyhedra

New fun with portals. youtu.be/1zgBwQVr-wI?... youtu.be/DTcfaHfDCEc?... youtu.be/3z3aC-1MGoE?...

Fan Dance #MathArt

Oasis, 250117

Knots made with @desmos.com for the 2024 Art Expo #desmos

Filigree #Friday #Fractal #FractalFriday #FridayFractals

This could be cleaned up and organized a bit better, but… www.desmos.com/calculator/9... Click the arrow to the left of ‘Q’ to move the red X to a random location. Click the arrow next to ‘P’ to see how my algorithm finds the nearest point on the golden spiral to the red X. 1/2

How did I miss this video for over a decade? Did YouTube somehow paradoxically get *better* at recommending videos about niche topics or care about? youtu.be/MFXRRW9goTs?... This shows the 120 cell construction in terms of two 60-cell chiral ‘tubes’ that fit together like a Clifford torus.

I just realized that the whole point of the modular group is to see the 2D structure of the rational numbers in terms of the integers. The first action increments the numerator, the second action exchanges the numerator and denominator. en.m.wikipedia.org/wiki/Modular... 1/4

I was prototyping a thing. It involved trying to figure out how many bits were needed in order to avoid visual banding artifacts in some lighting calculations. I provide it here as a pretty toy with incomplete documentation to play with. www.desmos.com/calculator/a... 1/2

#genuary4 prompt: Black on Black I went with color values below 50. We are traveling through a Polychoron in the 3Sphere sporting finite speed of light. #GENUARY #genuary2025

So say you want to map a value x from the range {-∞ < x < ∞} to the range {0 < x < ∞}. The ‘natural’ option is exp(x). But what if you want to avoid changing positive values very much while mainly constraining the negatives? Average a line with a hyperbola! www.desmos.com/calculator/5... 1/2