Still they've had a strong impact in how I see systems - orbits, instability, etc.

Thank you for sharing this on HN.

[1] https://youtu.be/0wD2WbG7loU

[2] https://youtu.be/c14aXxlSxZk

It actually shaped my post doc work quite a bit and shifted my focus from individual classroom education to strategic systems analysis of entire university and k-12 institutions. Somewhere along the way, a switch flipped and allowed me to view complicated hierarchies like college systems as 2-d fractal geometry in my mind. I can't really explain it, but now that I consult, I can feel when a department is broken before I can prove it with data. It's like they don't fit or reflect the main structure of the institution.

I would not suggest taking this route though. Maybe just take some graduate courses or something.

Fun fact, though, defending your dissertation to a room of around 200 people while still feeling the effects of dmt is a really good way to induce a panic attack. Source: it's me. I'm source material.

e.g. https://i.imgur.com/ZjiBF8f.png

just a coincidence?

Side note: Did anyone else know it was AI before reading the post? Mathematicians would be argent enough to assume the name was enough, displaying the algo when clicking the name was the give away.

(I wonder if there are slick ways to visualise the >3D case. Like, we can view 3D cross sections surely.

Or maybe could we follow a Lagrangian particle and have it change colour according to the D (or combination of D) it is traversing? And do this for lots of particles? And plot their distributions to get a feeling for how much of phase space is being traversed?)

This visualization also reminds me of the early debates in the history of statistical mechanics: How Boltzmann, Gibbs, Ehrenfest, Loschmidt and that entire conference of Geniuses must have all grappled with phase space and how macroscopic systems reach equilibrium.

Great work Shashank!

There isn't always "a" correct extension into higher dimensions. There may be many, there may be none, and either way something "close enough" may well be interesting in its own right.

If you'd like something concrete to poke at you can try searching around for people's adventures in trying to make a 3D Mandelbrot. I've seen a couple of good write-ups on those adventures. I don't know if anyone has ever landed on a "correct" solution, it's been years since I last looked, but certainly some very interesting possibilities have been found.

It reminded me of one of my (cranky) musings from back in college about galaxy formation and whether they were more like tossed pizzas (i.e. spreading out) than like whirlpools getting sucked in.

https://github.com/gradientwolf/fractals_SFML

Your post gives me so much joy. These tiny little things take me back to teenage years, simpler times & when interests were different. (I put a little note as "why" in my GH repo readme)