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Show HN: Strange Attractors

(blog.shashanktomar.com)
763 points shashanktomar | 1 comments | 31 Oct 25 23:23 UTC | HN request time: 0.207s | source

I went down the rabbit hole on a side project and ended up building this: Strange Attractors(https://blog.shashanktomar.com/posts/strange-attractors). It’s built with three.js.

Working on it reminded me of the little "maths for fun" exercises I used to do while learning programming in early days. Just trying things out, getting fascinated and geeky, and being surprised by the results. I spent way too much time on this, but it was extreme fun.

My favorite part: someone pointed me to the Simone Attractor on Threads. It is a 2D attractor and I asked GPT to extrapolate it to 3D, not sure if it’s mathematically correct, but it’s the coolest by far. I have left all the params configurable, so give it a try. I called it Simone (Maybe).

If you like math-art experiments, check it out. Would love feedback, especially from folks who know more about the math side.

Show context
cableclasper ◴[01 Nov 25 00:50 UTC] No.45778311[source]▶
Visualizations like this truly highlight how much there is to be gained from viewing the 3D phase space, but also how much richness we miss in >3D!

(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!

replies(1): >>45779257 #
flatline ◴[01 Nov 25 04:31 UTC] No.45779257[source]▶
The conclusion I’ve come to from works like Flatland, 4D toys, etc., is that we simply don’t have the neural circuitry to grasp anything beyond three dimensions. We can reason about them, we can make inferences about the whole from partial understanding, but we cannot truly grasp more than three, or perhaps only for an instant of forced conceptualization using heuristics like you mentioned. Even three is a stretch, our minds have adapted to build a three dimensional realm from something like a 2.5 dimensional field of combined visual, tactile, and auditory stimuli. I suspect 3D reasoning itself is a huge adaptive trait compared to most other animals.
replies(4): >>45779561 #>>45780567 #>>45781132 #>>45781143 #
sorokod ◴[01 Nov 25 10:19 UTC] No.45780567[source]▶
At least for 4D, would you not consider 3D-over-time as a four dimensional model? Doesn't watching the evolution as seen here allows for building up an intuition ?
replies(1): >>45780920 #
tliltocatl ◴[01 Nov 25 11:46 UTC] No.45780920[source]▶
Well, what's interesting about 4D is that's not just an extra dimension slapped on top, it's extra rotational degrees of freedom. You can't really get that with time (at least not until you get relativistic, and it still would be hyperbolic rotation, not euclidean).
replies(1): >>45781046 #
lazide ◴[01 Nov 25 12:12 UTC] No.45781046[source]▶
Sure you do - waves only exist in 4D as they have a time vector (frequency).
replies(1): >>45782597 #
1. tliltocatl ◴[01 Nov 25 15:47 UTC] No.45782597[source]▶
What I'm talking about is something like this: https://en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euc...

You can either sweep a cutting hyperplane through time or rotate a fixed projection or cut through time, but not both simultaneously.