[HN Gopher] Show HN: Strange Attractors
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Show HN: Strange Attractors
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.
Author : shashanktomar
Score : 734 points
Date : 2025-10-31 23:23 UTC (23 hours ago)
(HTM) web link (blog.shashanktomar.com)
(TXT) w3m dump (blog.shashanktomar.com)
| Grosvenor wrote:
| 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.
| anjel wrote:
| Fractint4life https://fractint.org/
| cs702 wrote:
| _Beautiful._
|
| Thank you for sharing this on HN.
| JKCalhoun wrote:
| "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
| Loughla wrote:
| 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.
| orzig wrote:
| Hobbyists hacking around and sharing their art, best part of the
| Internet!
| hshdhdhehd wrote:
| Very pleasant to watch!
| adtac wrote:
| too many of these vaguely look like what galaxies look like from
| earth
|
| e.g. https://i.imgur.com/ZjiBF8f.png
|
| just a coincidence?
| layer8 wrote:
| Galaxies don't really look like that.
| HeliumHydride wrote:
| How can I code my own attractor?
| dmbche wrote:
| Pick one and implement it. Find the equations to the lorentz
| attractor and use those if you need a suggestion.
| vis_lover wrote:
| 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.
| shashanktomar wrote:
| 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.
| cableclasper wrote:
| 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!
| flatline wrote:
| 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.
| cantor_S_drug wrote:
| Do you think an AI can learn this intuition by training it in
| similar environment?
| vincnetas wrote:
| Can we train our neurons? Like the experiment where human
| vision adapted to upside down image, could our brains
| somehow adapt to understanding 4D data from VR headset?
| gf000 wrote:
| I'm sure some form of training is possible where you get
| a better understanding of a 4D universe with some limited
| inference abilities, but with a bad analogy, this would
| all be "software emulated" with no hardware acceleration
| - we only have the latter for 3D and we can't update it
| without a hardware change.
| logicchains wrote:
| With future improvements in brain-computer interfaces it
| might well be possible to send a 4D visual signal into
| the brain.
| lioeters wrote:
| Yes, I believe it's possible to train our brains and
| learn to perceive better in higher dimensions. There's a
| great description in the science-fiction book Neverness,
| where pilots meld their minds with the spaceship computer
| to visualize and navigate hyperspace.
| apples_oranges wrote:
| Good point, why not? Communicating it back to us could be a
| problem. Hmm.. what if future ais hide data from us in
| dimensions we can't wrap our heads around?
| sorokod wrote:
| 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 ?
| tliltocatl wrote:
| 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).
| lazide wrote:
| Sure you do - waves only exist in 4D as they have a time
| vector (frequency).
| tliltocatl wrote:
| 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.
| Gooblebrai wrote:
| I've been waiting for Miegakure for ages
| Laremere wrote:
| 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.
| d_tr wrote:
| For me, being able to visualize 4D would imply that I can
| picture four mutually perpendicular axes, something which I
| find completely impossible for me to do. And I thought it
| is impossible for any human brain. It would be fascinating
| if I am wrong.
| cantor_S_drug wrote:
| The blind French mathematician Bernard Morin is well-known
| for creating the first visualization of a sphere eversion,
| a method for turning a sphere inside out without creasing
| it. His work was based on Stephen Smale's 1958 proof of
| sphere eversion's existence and on ideas shared by Arnold
| Shapiro. Morin's method involved constructing a sequence of
| models, including his "Morin surface," to demonstrate the
| process.
|
| https://en.wikipedia.org/wiki/Bernard_Morin
| soulofmischief wrote:
| Your hippocampus has several special clusters of neurons
| whose members activate and deactivate based on your body's
| understanding of your position and momentum in a 3D world.
|
| The arrangement of these neurons physically corresponds to
| reality, and so things are pretty hardwired.
|
| Repurposing these neurons might be possible with advanced
| training and nootropics, but I'm not sure. You might have
| better luck engaging other parts of your brain, for example
| using metaphor or abstraction such as mathematics.
| slicktux wrote:
| 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 ;)
| pkspks wrote:
| This is absolutely stunning. Wonderful some function of the state
| of a point can give it colour.
| shashanktomar wrote:
| Author here, there is a setting to pick colour mode. I
| implemented it after similar suggestion by someone on twitter.
| Give it a try.
| pkspks wrote:
| It already supports colour!
| jerf wrote:
| "not sure if it's mathematically correct,"
|
| 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.
| Xophmeister wrote:
| Neat :) When I was a teenager, some 25+ years ago, I wrote a
| chaotic attractor visualiser like this -- but only in 2D -- and
| it occurred to me, "What if instead of visualising it, I rendered
| it to audio?" I don't remember the details: I think frequency was
| correlated with polar angle and amplitude to magnitude. It forced
| me to learn how to write WAV format -- which was my first
| introduction to endianness -- but the result wasn't completely
| inaudible! A bit like the sound effects for computers in old sci-
| fi movies; random(ish) but not discordant beeps and boops!
| gausswho wrote:
| Along these lines there are at least two modules that I know of
| in Eurorack focused on strange attractors, and they're both a
| LOT of fun adding this kind of unpredictable-but-cyclical
| movement to your sounds:
|
| - Hypster by Nonlinear Circuits
| (https://modulargrid.net/e/nonlinearcircuits-ian-fritz-s-
| hyps...)
|
| - Orbit 3 by Joranalogue
| (https://modulargrid.net/e/joranalogue-audio-design-orbit-3)
| metacortexx wrote:
| Love seeing projects like this, just pure curiosity, creativity,
| and fun
| Figs wrote:
| The demo makes some nice spirals on the ends. They look like
| galaxies with the rendering.
|
| 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.
| aniijbod wrote:
| I don't care about the math, the computation, the physics. This
| is just by far the most beautiful thing(s) I have ever seen.
| neilpmas wrote:
| Well that's my productivity blown for the day. Love it.
| srvmshr wrote:
| Coincidentally enough, I dug out my 11th grade CS project on
| generating fractals from 2002 & modernized it using SFML graphics
| lib just this week.
|
| 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)
| shashanktomar wrote:
| Thanks a lot, it was clearly worth the effort.
| navigate8310 wrote:
| The way you explained the mathematical theory was very intuitive
| and refreshing. It would be every interesting to read if you
| could also write more on other topics of your interest.
| tmshapland wrote:
| Beautiful. Reminds me of starling murmurations.
| https://www.youtube.com/watch?v=V4f_1_r80RY
| felipelalli wrote:
| I have no idea what is this, but it's beautiful.
| imoverclocked wrote:
| Reminds me of the xscreensaver, "strange" :)
| sunjester wrote:
| reminds me of phong. https://phong.com/
| Sreenington wrote:
| this is so cool! would be awesome if you can add params to mess
| with a and b value so we can "find" our own strange attractor
| patterns. maybe a free mode?
| shashanktomar wrote:
| Author here, it already supports that for the best attractors.
| On phone there is a menubar at bottom, on desktop you can't
| miss it.
| Atiscant wrote:
| Absolutely great. Thank you for sharing.
| bntr wrote:
| Great visualization! It would be good to add some fog for a
| better perception of 3D.
| gigatexal wrote:
| This is mesmerizing and very cool. Thank you!
| GistNoesis wrote:
| How do I write my custom attractor equation ?
| eps wrote:
| Mesmerizing stuff.
|
| Can you allow changing attractor control constants without
| resetting the sim? E.g. going from 0.19 to 0.21 in Thomas while
| it's already in a stable state.
|
| It's be interesting to see what'll happen.
| axi0m wrote:
| I'd like one of these as my screen saver. Great work!
| nxpnsv wrote:
| This is really pretty. A loong time ago when I wrote a Lorentz
| attractor on my 486 with turbo pascal and inline assembler, I
| could only dream of such smoothness back then...
| ilovefood wrote:
| Super cool and well done. They are much better in 3D! :)
|
| I made a similar experiment a while ago and randomized the
| parameters. Given it's difficult to stumble on a stable
| arrangement, I turned it into a small game to find pretty ones:
| (big disclaimer: this involves NFT tech, please skip if you're
| against that sort of stuff) https://karimjedda.com/symmetry-in-
| chaos-my-first-generative...
| Libidinalecon wrote:
| 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.
| sometimes_all wrote:
| This gives me Johnny Quest theme song vibes.
| dmarinus wrote:
| very nice, if you want to know more of the history of chaos I
| recommend the following book:
| https://en.wikipedia.org/wiki/Chaos%3A_Making_a_New_Science?...
| virgil_disgr4ce wrote:
| It's a nice coincidence to find this post on HN today as I JUST
| finished reading Gleick's book. But it was the audiobook
| version, which I immediately realized was not going to be very
| effective if I can't see any images or equations. And so it's
| perfect timing to see this outstanding interactive
| visualization!
| teunlao wrote:
| Learned more about attractors dragging this around than from
| wiki. This is how math should be taught.
| atombender wrote:
| 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/
| AlexeyBrin wrote:
| The book software
| https://sprott.physics.wisc.edu/fractals/bookdisk/
| alansaber wrote:
| I am shocked by how well this runs
| evanb wrote:
| > A small change in the parameter a can lead to vastly different
| particle trajectories and the overall shape of the attractor.
| Change this value in the control panel and observe the butterfly
| effect in action.
|
| I think this is slightly inaccurate. The butterfly effect is
| about the evolution of two nearby states in phase space into
| well-separated states. But the parameter a is not a state. To see
| the butterfly effect by changing a we would need to let the
| system settle down, give the parameter a small change, and _then
| change it back_. The evolution during the changed time acts as a
| perturbation on states.
|
| Instead, showing that the attractor changes qualitatively as a
| function of the parameter is more akin to a phase transition.
| aenis wrote:
| Fabulous.
|
| Now I just need to find a monochrome laser projector and my home
| office design is complete.
| tannerjames711 wrote:
| Thank you for sharing. This really inspired me to check out
| three.js. This website of yours might be one of the more
| beautiful things on the internet.
| __MatrixMan__ wrote:
| It would be so much fun to use these as a setting for some kind
| of gaming experience. Like, I wanna hide behind parts of these
| and pop around a corner and blast my friend with a laser. Or to
| race gocarts along the surface of one, or I dunno, something
| frogger-esque to get a feel for the directionality of the
| flows... I love how they look, but I need more interaction to get
| a feel for the thing.
| dehugger wrote:
| I can confirm that Simone (Maybe) is my favorite :) I especially
| like looking through them with the color set to Angular instead
| of Solid, so you can see where the peak acceleration is
| happening. Makes the big curves prettier :) great project!
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