5 ms·

Strange Attractors (2018)

119 points by tzury 2y ago

snthpy 2y ago
I remember this from my dynamical systems class at uni. How useful are these for generating pseudo-random numbers? From what I recall they never retrace the same path so if you picked one of those narrow lines and take a cross section which you map to some space that you care about, say a unit interval, and then sample whenever it comes past that cross section you should have a pretty good source of randomness, no? Might not be the most efficient sampling scheme but should have the nice property of being aperiodic? I guess given simulation with finite precision it will have to repeat eventually but how long will those cycles be in practice? Also, if you're willing to trade off some space then you could track all points sampled and if detect a cycle then you rerun the previous cycle at higher precision and stay at the increased precision until you detect the next cycle, rinse and repeat.
- 01HNNWZ0MV43FF 2y ago
  Arbitrary precision and remembering every number you've ever generated aren't as nice properties as cryptographic security and random access, which you could get from a prng by throwing a counter into a hash function
pavel_lishin 2y ago
The Thomas attractor reminds me of the ship in the film Passengers.
krighxz 2y ago
A few years ago I implemented a lorenz attractor at audio rate to emulate non-linearities of vocal cords for the Adult Swim Choir: https://x.com/krighxz/status/1691365631793197056 https://x.com/krighxz/status/1691365631793197056
- pringk02 2y ago
  very creative!
JKCalhoun 2y ago
IMSAI Guy has a Lorenz Attractor PCB if you want to make a hardware version: https://youtu.be/0wD2WbG7loU https://youtu.be/0wD2WbG7loU
ddejohn 2y ago
Wonderful. Differential equations were my favorite subject in school. Unfortunately the chaos theory class was only offered every other spring and I missed out on it. As a heads up: the "Preset" button label seems to be a typo -- it appears to "Reset" the animation. A way to copy the parameters would be nice (even just allowing text highlight). Cheers. PS -- I stumbled across a very nice Thomas solution {b: 0.2, x_0 = 1.1, y_0 = 1.1, z_0 = -0.01}
magnat 2y ago
This reminds me of the Chaoscope [1], a defunct app from 2000s for creating a beautiful 3D renderings of Strange Attractors. [1] https://web.archive.org/web/20200710103948/http://www.chaoscope.org/gallery.htm https://web.archive.org/web/20200710103948/http://www.chaosc...
dspillett 2y ago
I've seen (though can't find immediately again right now) animations based on rotating through interesting parameter sets for some of these systems, rather than animating the progression through one parameter variation as seen on these analyses, which was rather mesmerising too (not dissimilar to the ifs module I remember from xscreensaver in the late 90s).
rmrfchik 2y ago
Me -- proudly drawing sin(x) plot. Guys -- doing astonishing graphics.
occamschainsaw 2y ago
Wonderful vizualization and library! Many years ago I made a Chua's circuit PCB for an electronics course[0]. We had to dust off an old Cold War era analog oscilloscope to actually see the attractors because the resolution of the newer digital ones induced too many artefacts. I want to use this library to vizualize this using the electronic component values now. [0] https://karan.sh/res/Chua_Circuit_report.pdf https://karan.sh/res/Chua_Circuit_report.pdf

119 points by tzury 2y ago

I remember this from my dynamical systems class at uni. How useful are these for generating pseudo-random numbers? From what I recall they never retrace the same path so if you picked one of those narrow lines and take a cross section which you map to some space that you care about, say a unit interval, and then sample whenever it comes past that cross section you should have a pretty good source of randomness, no? Might not be the most efficient sampling scheme but should have the nice property of being aperiodic? I guess given simulation with finite precision it will have to repeat eventually but how long will those cycles be in practice? Also, if you're willing to trade off some space then you could track all points sampled and if detect a cycle then you rerun the previous cycle at higher precision and stay at the increased precision until you detect the next cycle, rinse and repeat.

01HNNWZ0MV43FF 2y ago
Arbitrary precision and remembering every number you've ever generated aren't as nice properties as cryptographic security and random access, which you could get from a prng by throwing a counter into a hash function

pavel_lishin 2y ago

The Thomas attractor reminds me of the ship in the film Passengers.

krighxz 2y ago

A few years ago I implemented a lorenz attractor at audio rate to emulate non-linearities of vocal cords for the Adult Swim Choir: https://x.com/krighxz/status/1691365631793197056 https://x.com/krighxz/status/1691365631793197056

pringk02 2y ago
very creative!

JKCalhoun 2y ago

IMSAI Guy has a Lorenz Attractor PCB if you want to make a hardware version: https://youtu.be/0wD2WbG7loU https://youtu.be/0wD2WbG7loU

ddejohn 2y ago

Wonderful. Differential equations were my favorite subject in school. Unfortunately the chaos theory class was only offered every other spring and I missed out on it. As a heads up: the "Preset" button label seems to be a typo -- it appears to "Reset" the animation. A way to copy the parameters would be nice (even just allowing text highlight). Cheers. PS -- I stumbled across a very nice Thomas solution {b: 0.2, x_0 = 1.1, y_0 = 1.1, z_0 = -0.01}

magnat 2y ago

This reminds me of the Chaoscope [1], a defunct app from 2000s for creating a beautiful 3D renderings of Strange Attractors. [1] https://web.archive.org/web/20200710103948/http://www.chaoscope.org/gallery.htm https://web.archive.org/web/20200710103948/http://www.chaosc...

dspillett 2y ago

I've seen (though can't find immediately again right now) animations based on rotating through interesting parameter sets for some of these systems, rather than animating the progression through one parameter variation as seen on these analyses, which was rather mesmerising too (not dissimilar to the ifs module I remember from xscreensaver in the late 90s).

rmrfchik 2y ago

Me -- proudly drawing sin(x) plot. Guys -- doing astonishing graphics.

occamschainsaw 2y ago

Wonderful vizualization and library! Many years ago I made a Chua's circuit PCB for an electronics course[0]. We had to dust off an old Cold War era analog oscilloscope to actually see the attractors because the resolution of the newer digital ones induced too many artefacts. I want to use this library to vizualize this using the electronic component values now. [0] https://karan.sh/res/Chua_Circuit_report.pdf https://karan.sh/res/Chua_Circuit_report.pdf