Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Show HN: Strange Attractors

blog.shashanktomar.com

Post reply on HN
Print view View original

51–60 of 83 posts

Re: Show HN: Strange Attractors

#51

Post by sorokod »

flatline wrote: post #29
cableclasper wrote: post #12

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?…

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, o…

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 ?

Re: Show HN: Strange Attractors

#52

Post by Libidinalecon »

Really visually wonderful. I tried to self learn about nonlinear dynamics after reading about Takens's theorem last year but I have to admit, I have no idea what an attractor is actually showing like this.

This might be inspiration to try to grasp these ideas again.

Rotating the Lorenz makes me think otherwise though because given the amount of time I put into this, I should understand that much more than I do.

Chance and Chaos by David Ruelle is a wonderful little book.

Re: Show HN: Strange Attractors

#54

Post by tliltocatl »

sorokod wrote: post #51
flatline wrote: post #29

Earlier quoted context omitted.

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, o…

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 ?

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).

Re: Show HN: Strange Attractors

#56

Post by lazide »

tliltocatl wrote: post #54
sorokod wrote: post #51

Earlier quoted context omitted.

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 ?

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).

Sure you do - waves only exist in 4D as they have a time vector (frequency).

Re: Show HN: Strange Attractors

#58

Post by Gooblebrai »

flatline wrote: post #29
cableclasper wrote: post #12

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?…

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, o…

I've been waiting for Miegakure for ages

Re: Show HN: Strange Attractors

#59

Post by Laremere »

flatline wrote: post #29
cableclasper wrote: post #12

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?…

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, o…

I've managed to visualize a Klein bottle in 4d. I easily visualize 3d objects. However I can't really do color - I startled myself recently when I briefly saw red. On that aphantasia test with an apple, I can hold it's 3d shape, but no surface texture or color.

People seem to have surprisingly different internal experiences. I don't know how common 4d visualization is, and I suspect even those capable require exposure to the concepts and practice. However I do think it possible.

Re: Show HN: Strange Attractors

#60

Post by atombender »

I bought "Strange Attractors: Creating Patterns in Chaos" (1993) by J. C. Sprott recently, which is a fun book about these kinds of attractors. The whole book can be downloaded online [1] from the author's web site [2].

It's such a typical object of its time. Garishly colored cover, comes with a floppy disk (!) and there are even 3D glasses to view some of the stereoscopic color plates (unfortunately these were missing from the used copy I got). I was surprised to find that most of the programs are in BASIC (maybe easier to do graphics on Windows back then?), though a small number of them are in C.

It's a nice book, and the author seems to have a lot of publications about chaotic systems. Anyone know him? He seems to still be teaching at the University of Wisconsin - Madison.

[1] https://sprott.physics.wisc.edu/fractals/booktext/SABOOK.PDF

[2] https://sprott.physics.wisc.edu/

Post reply on HN