Chaos Theory - Analog Circuit Lorenz Attractor PCB

[@yucao1101]

Best video I have seen on analog Lorenz solver. The double Pendulum chaos demonstration is also great. Keep going!

[@markmilliren1453]

clear all close all clc the beginning of every .m file I've ever authored. You're too smart for me, I feel like I would need to rewatch this video 30 times to absorb all of the information!

[@reedosbrink2428]

I primarily am in the "only watch" category of the KZbin audience. I have only left comments on two other videos in my life, so just know I mean it when I say your channel and content is amazing! It is refreshing to see such quality content on here keep it up. P.S. I hope your 7 seg display got a tic because I just subscribed!

[@ZacksLab]

Thank you Reed! That really means a lot to me. :) I’ve been busy with a newborn but plan on getting back to making videos as soon as things calm down! Cheers!

[@xsirfr1958]

Awesome work and Beautiful presentation! Butterfly effect, not to be confused with the Lorenz butterfly.

[@campbellmorrison8540]

Love it, Ive wanted to build one of these ever since I saw the Paul Horowitz lecture but got a bit of a fright at the price of the multipliers. Thank you for sharing the PCB, Im very tempted, I have an idea for this slow motion tracking

[@ZacksLab]

thanks for the beer Campbell! glad you enjoyed. please share your slow motion tracking project if you end up building it :)

[@cactodagod9236]

Damn you are really underrated

[@okal7706]

Artistic and elegant. Great work.

[@billfang3664]

Well polished video! That's super cool! I like the old school scope the most, the best type scope for this analog circuit!

[@JianGongWeb]

Thank you for this beautiful video. Love the oscilloscope dance and music in the end :)

[@robertv4076]

I tried this in LTSPICE but could not get it to start. What initial values will make it work in LTSPICE? Thanks.

[@ZacksLab]

you need to plot the outputs in XY mode, try looking here: electronics.stackexchange.com/questions/365545/how-do-i-achieve-xy-mode-on-ltspice#:~:text=Assuming%20you%20are%20using%20.,all%20there%20is%20to%20it. initial conditions are σ = 10, ρ = 28, β = 8/3, with XY mode set up, set z(t) as y-axis, and x(t) as x-axis. hope this helps!

[@BLau-oi4zc]

i will try to build this, it will be a good project for learning basic electronics

[@ZacksLab]

it's a great analog project! only down side is that the analog multipliers are quite expensive.

This is incredibly inspiring! Thank you!

[@Dhruv.Wadhwa]

That was just breathtakingly gorgeous 😍😍😍😍😍 this is what math is!

[@ZacksLab]

❤️

[@edgeeffect]

Gotta love a Lorenz Attractor!

[@serginx]

How can I set above 20Khz?

[@bthl1215]

Why does your butterfly keep flickering in the anallog display? Is it noise creeping in and causing the butterfly to change, due to sensitive dependence on initial condition?

[@ZacksLab]

Which flicker are you referring to? At the end of the video I actually imposed two videos on top of each other and synced to the music just for visual effect.

[@bthl1215]

I'm reffering to the part at 3:30

[@ZacksLab]

@@bthl1215 i think this has to do with the speed setting of the integrators (the cap in the feedback of the opamp adjusts the display speed). the "flicker" is due to the nature of the attractor, the point will periodically collapse into one of the basins of attraction and then spool back up to bouncing between the two attractors.

[@JoelBondurant]

5:10 wow!

[@BasteG0d69]

awesome video

[@valwold3567]

This is beyond fascinating. Red pill me on analog computing. I thought that was entirely a fad from the 70s.

[@ZacksLab]

Hah definitely not a fad. Analog computing shines when attempting to simulate highly complex systems, like those found in biology, chemistry, or physics. Digital computing is only practical when you over simplify the system and make a lot of assumptions. Often times this is good “enough”, but there are many cases where making these simplification lead to results that aren’t meaningful. It will also be interesting to see quantum computing evolve and expand our ability to simulate and solve complex problems with many states.

[@valwold3567]

@@ZacksLab Hmmm, so that's one end of the spectrum. Simulating complex nonlinear systems for the purposes of research into their general behavior. Large, complex, imprecise, somewhat general in application. How well does analog processing work at the other end of the spectrum? Doing simulations for a smaller nonlinear system you're trying to control in real time? The speed of calculations is still a headache even for things like motor control, which isn't that fast.

[@ZacksLab]

​@@valwold3567 I don't know of any real world applications (today) using analog computation for real time control... the advantages of digital computing far outweigh the speedup potentially gained from analog computations, namely that it's easy to modify a digital algorithm, bit error correction can be done on digital signals, and digital signaling is not as susceptible to noise. I believe the second coming of analog computing (in the form of analog co-processors) is still in the research and development phase... for example, DARPA launched a program a few years ago: www.darpa.mil/news-events/2016-05-06

[@Troynjk]

Amazing ! Are you able to show the Lorenz attractor on a Smith chart or on a 3D smith chart ?

[@ZacksLab]

hey! you could definitely plot the 3 variables of the lorenz equation in 3d cartesian space, the smith chart would be tricky given that it is more of a "calculator" (kind of like a slide rule) where the input is a vector (a complex number with real + im) and it is transformed onto the chart for the purposes of interpreting impedance and s-params. you could plot one variable as the real part and one as the imaginary part and watch it evolve over time, it might be interesting!

[@Troynjk]

@@ZacksLab Hi, thanks. Someone made the smith chart in 3D, based on Riemann sphere with complex plane and what not. Is it the same as Cartesian 3D space ? Im not math proficient. I found online a comparison between a signal (simple wave) on oscilloscope and the same signal on a smith chart and how different they looked. I thought since Lorenz attractor is in 3D it would be cool to see it in 3D smith chart.

[@ZacksLab]

can you share a link to the comparison you're talking about?

[@Troynjk]

@@ZacksLab uspas.fnal.gov/materials/08UCSC/mml13_matching+smith_chart.pdf Last page

[@WildEngineering]

CAn i get the schematics for this? :D I wanted to build one myself but I like the idea of doing it on a PCB and where I work I have access to that stuff (;

[@ZacksLab]

Hey WildJarvi! Paul Horowitz's schematic: seti.harvard.edu/unusual_stuff/misc/lorenz.htm Gerber files for PCB: drive.google.com/open?id=1l46raWf1ubtuAP7miUUhpqJdYFwiuHHE Bill of Materials: www.digikey.com/short/phmt0q

[@paragmahajani5450]

You are awesome

[@michaelrtreat]

Fabulous

[@NicksAreOverrated]

maybe stupid q: what do the axes actually stand for? I mean you said theyre all functions of time, but what happens during that time? what does single point in that butterfly tell us about the system?

[@ZacksLab]

good question! from wikipedia: “The equations relate the properties of a two-dimensional fluid layer uniformly warmed from below and cooled from above. In particular, the equations describe the rate of change of three quantities with respect to time: x is proportional to the rate of convection, y to the horizontal temperature variation, and z to the vertical temperature variation. The constants σ, ρ, and β are system parameters proportional to the Prandtl number, Rayleigh number, and certain physical dimensions of the layer itself.” basically Lorentz wanted to create a model for atmospheric convection. when looking at the plot over time, you are looking at the “phase space” where each point in 3d describes the complete state of the system. interestingly, as the point moves, it never crosses itself. it is an infinite curve in finite space. this means that its future cannot be predicted even though the equations are completely deterministic. the essence of chaos is that a system can be both deterministic and unpredictable. our solar system is chaotic at large enough time scales, contrary to newtonian physics that allows us to pinpoint where planets and stars will be in the future. given enough time, the future is completely unpredictable... ...unless you are Laplace’s daemon. ;)

[@NicksAreOverrated]

@@ZacksLab but a convection chamber (if you can call it that) isnt the only system that creates a lorenz attractor, right? Rate of convection couldnt describe a pendulum for example or am i missing sth

[@ZacksLab]

remember that the lorentz equations are models, not actually reality. but with that being said, the lorentz equations can be used as simplified models of other systems that are seemingly unrelated to convection.

[@flyingtarantula9091]

nice

[@underarmbowlingincidentof1981]

Amazing video !! :D

[@geroldngoudjou7035]

A quel niveau S'il vous plait??

[@CUBETechie]

I'm looking for a video it was about device's which use a pen or a printer needle and used control knob one go for X - axis and one for Y- Axis

[@ZacksLab]

this? kzbin.info/www/bejne/Y6PLmYiQesmAY6c

[@STMARTIN009]

So there is a possibility I can win the lottery. Good video!

[@ZacksLab]

Hah, I honestly don’t know. Reading about chaos theory just left me more confused about the nature of reality. But I hope you do :)

[@STMARTIN009]

@@ZacksLab Thank You Have a Good Day. It's an interesting theory.

[@friedmule5403]

Thanks wary much for sharing this amazing video! :-) I have sometimes thought of, if chaos is complex order that is beyond what we right now can handle, is random not the same? I mean random is something doing something in an totally unpredictable way, but nothing in nature is random, everything do happen according to some conditions and events. So is random not "just" chaos 2.0?

[@ZacksLab]

You're welcome. :) I believe from a classical mechanics point of view (Newtonian), randomness doesn't exist. However, we now know that things that are much smaller than we are (quantum) and things that are much larger than we are (relativity) behave very differently than we would expect based on Newtonian physics. From the perspective of quantum theory, randomness should exist because a wave function is a probability distribution. I don’t think we actually know the true answer as to whether or not randomness exists… just because we can’t see a pattern doesn’t mean there isn’t one, I’m not sure how you strictly rule that out. I could be wrong on this though. Chaos is specifically in reference to systems that have a very high dependence on initial conditions. This makes them highly unpredictable.

[@friedmule5403]

@@ZacksLab Thanks for a really grate answer!!

[@duality4y]

how do you determine the speed ?

[@ZacksLab]

hey! you can vary the speed by changing the value of capacitance in the opamp's feedback. see schematic here: seti.harvard.edu/unusual_stuff/misc/lorenz.htm

[@duality4y]

@@ZacksLab thanks I had found this video too: kzbin.info/www/bejne/enPXlqKtoriBbsk At one point he mentions the capacitors. i find it so fascinating that this circuit can produce these kind of results.

[@geroldngoudjou7035]

s'il vous plait vous pouvez traçer ça avec arduino??

[@ZacksLab]

oui, cela pourrait être fait! vous devrez résoudre les équations de Lorenz sur l'arduino et piloter un convertisseur numérique-analogique en utilisant les sorties des équations de Lorenz

[@geroldngoudjou7035]

@@ZacksLab c'est ce que j'ai fait mais ça ne marche pas. Si j'avais votre e-mail je devais vous envoyer ça pour que vous m'aider. Pardon j'ai vraiment besoin d'aide s'il vous plait?? 🙏🙏

[@ZacksLab]

bien sûr, vous pouvez me contacter par ici: www.mule-labs.com/

[@geroldngoudjou7035]

@@ZacksLab mais avec l'adresse e-mail ça sera plus facile. Si tu en a tu envoies également s'il te plait

[@ZacksLab]

si vous cliquez sur le bouton d'idée de projet, il m'enverra un e-mail, je ne veux pas publier mon e-mail sur les commentaires youtube car les robots le spammeront

[@familystuff2873]

Cicada