I love turning basic Math concepts into art. This is a Riemann sphere driven by a moving rational function R(z) = ∏(z-aⱼ) / ∏(z-bₖ) The glowing roots and poles orbit across S² while log|R| and Φ = arg R continuously reshape the surface. The small particles ride the phase... gradient ∇Φ.show more

You are the Bob Ross of mathematical visualization. I stop and stare because I understand the math. I miss the ignorant bliss, honestly. I hope @elonmusk helps you compensate into this as a full time endeavor.

@elonmusk Thank you!🫡

Fascinating. Cyclical variation of parameters can lead to fascinating results. I did myself some fractal animations some time ago that went beyond zooming in but instead changed the parameter space of complex functions.

Ilysm

This is way better than art

And thank You again! We love the geometry

@ProofofMaro I do like these 🙂

How do you approach designing each visualization? Very curious about your process. Your art is lovely!

It starts from the 2D plot of the ration function on a unit circle. It's just imagination here. I decided to bring out the four main components of a rational function i.e., the landscape it carves, distinctly marking the roots and poles as well as having some particles ride the phase gradient so we can see how deep/shallow the landscape is all over the plot. So, I guess there's a little bit of an artistic element that comes in here...and I love art😊. Taking it to 3D is something that's influenced by what you see in 2D you're just wondering how can I take this to 3D? Everything else is about iteratively improving the aesthetics... for instance I'm thinking right now about how I marked the roots and poles... maybe I should probably embed the roots inside the surface and just let them pop out slightly from the surface like little pearls that's what I'm gonna do in the next post 😅

May I ask what program you use to produce such beautiful animations?

Python with matplotlib but sometimes I use VTK if I want to avoid occlusion

Incredible stuff 🎼👏🏼

The boundary between potential and actual.

It’s beautiful

死んだ後は宇宙でこうしたさまざまなアートが観られるんだろうな♪（戯言ですw）

😅

This is peak math art, where rigorous concepts become genuinely mesmerizing visuals.

"basic math" and then it's this

😅

Fascinating

I always enjoy your work, thank you ✨

Thank you!🫶

What if you slowly remove the roots while the particles are still flowing? Seeing whether the phase gradient survives after its sources are gone would hit hard visually.

I’ve got one for you. A framework that has a saturation condition: C(φ) = αV₀φ²e^(-kφ) / 3π = 1 which resolves through the two real branches of Lambert W: φ = -(2/k) W₀,₋₁[-(k/2)√(3π/αV₀)] I’d love to see the two branches rendered as a moving saturation geometry, with C → 1 as the glowing boundary and a tiny irreducible polar asymmetry ε ≠ 0 preventing perfect closure, forcing bifurcation and structural reorganization at saturation. I suspect it would look pretty insane.

math is art and art is math your just making function match forum which is devine not just art

@imagine mk

Do you mind to tell how it can be used for something to be produced?

let's say some cosmic cataclysm happened and only one of those orbs survived,.... ×^/what would that look like?

Me too! My exploration of glyphermathographic representation includes quantic and sextic "non math nonliteraly conceptual" relational geometry through which I can cocreate beautiful glyphermathographic images from base textual glyphermathograph inputs 👌🙌🌬

@FFPPod Care to explain?

Makes for a good sea creature

Awesome

Super cool 😎

I like the "zone" this thing dances in. It rides a fence where you can't decide if it's evil, or benevolent.