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.
This is so cool. Back in highschool during the Jurassic age I used ti play with attractors a lot. Unfortunately on a 486 it took 20-30 minutes to draw one even at low resolution. This renders in realtime and in 3D. Great work!
Still they've had a strong impact in how I see systems - orbits, instability, etc.
Lorenz Equations and Chua Circuits probed with an analog oscilloscope is mesmerizing! Great videos of a Chua Circuit being probed with an analog scope…
Also, plugging the circuit to a speaker via AUX port gives white noise ;)
I got really into fractals and attractors when I was also really into mushrooms, lsd, and dmt during my graduate studies.
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.
"IMSAI guy" created a Lorenz attractor circuit [1]. He talks more about it later [2]. I remember seeing the Lorenz attractor on some TV show about chaos.
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.
Author here, I have tried labeling the "More Information" sections as "AI Generated" where it was directly summarized from the wikipedia article, otherwise most of the post is written by me. I have taken help from AI to fact check and refine few things here and there, but boundaries are so blur now that am not sure if i should label the full post as AI Assisted.
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!
This is so cool. Back in highschool during the Jurassic age I used ti play with attractors a lot. Unfortunately on a 486 it took 20-30 minutes to draw one even at low resolution. This renders in realtime and in 3D. Great work!
Still they've had a strong impact in how I see systems - orbits, instability, etc.
Lorenz Equations and Chua Circuits probed with an analog oscilloscope is mesmerizing! Great videos of a Chua Circuit being probed with an analog scope… Also, plugging the circuit to a speaker via AUX port gives white noise ;)
This is absolutely stunning. Wonderful some function of the state of a point can give it colour.
Author here, there is a setting to pick colour mode. I implemented it after similar suggestion by someone on twitter. Give it a try.
I got really into fractals and attractors when I was also really into mushrooms, lsd, and dmt during my graduate studies.
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.
"IMSAI guy" created a Lorenz attractor circuit [1]. He talks more about it later [2]. I remember seeing the Lorenz attractor on some TV show about chaos.
[1] https://youtu.be/0wD2WbG7loU
[2] https://youtu.be/c14aXxlSxZk
Hobbyists hacking around and sharing their art, best part of the Internet!
Super cool visulitations.
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.
Author here, I have tried labeling the "More Information" sections as "AI Generated" where it was directly summarized from the wikipedia article, otherwise most of the post is written by me. I have taken help from AI to fact check and refine few things here and there, but boundaries are so blur now that am not sure if i should label the full post as AI Assisted.
too many of these vaguely look like what galaxies look like from earth
e.g. https://i.imgur.com/ZjiBF8f.png
just a coincidence?
Galaxies don't really look like that.
How can I code my own attractor?
Pick one and implement it. Find the equations to the lorentz attractor and use those if you need a suggestion.
Beautiful.
Thank you for sharing this on HN.
Very pleasant to watch!