Chaos | Chapter 7 : Strange Attractors - The butterfly effect

Chaos - A mathematical adventure
It is a film about dynamical systems, the butterfly effect and chaos theory, intended for a wide audience.
From Jos Leys, Étienne Ghys and Aurélien Alvarez, the makers of Dimensions, comes CHAOS, a math movie with nine 13-minute chapters.
More information is available on the website: www.chaos-math....

[@griseld]

Curious how even The butterfly effect itself shows exactly how small changes in the initial conditions make huge changes over long time iterations. If they had not chose that name but rather "The chaos of identical moving systems in time" we would not have all the movies today, this theory would not be so well-known to even simple people working as truck drivers(just an example). Just a small change as the name changed at the last second, in 40 years has generated a largely different reality compared to what it would've been if the name was not that. That insignificant change has indeed changed the lives of people all around the world(think of the actors of the Movie The butterfly effect who would've maybe never become actors if it was not the for fame they got with that movie). Astonishing

[@wubanizer]

Fantastic observation! It seems the butterfly effect is nearly everywhere.

[@henkteirlinck9283]

Oh yes, the simple people. Of course truck driver is just an example. More examples include cleaners, factory workers, cashiers. Boy, those simple people really are a kind of their own, aren't they?

[@wubanizer]

@@henkteirlinck9283 what is the point your trying to make in this comment? Did he say something framing those jobs ina negative light?

[@diegososa5280]

@Griseld brilliant comment. I salute you Sir.

[@henkteirlinck9283]

@@wubanizer Of course I went out of my way to think of more 'simple people', but yes: I feel the term 'simple people' is quite demeaning. I'm really curious as to what your profession is if you think a distinction between 'simple people', and in effect, intelligent people, is justified.

[@vman049]

The best introduction to chaos I've seen.

[@TopShockers]

Beautiful, just absolutely beautiful. I shall watch this again and again.

[@OPNURISYDER]

I never dreamed it possible for Chaos to produce such beautiful symmetry. Such a wonderful presentation.

[@davidrosset4457]

Chaos is far different from random as most people assume. A true chaotic system stays within boundaries.

[@megan7258]

this was beyond words. the soundtrack brought to life this beautiful branch of mathematics.

[@hc3733]

Give just a tiny bit more love to those around you. In 100 years it would be a better world.

[@Supertimegamingify]

Or maybe an awful one, it's unpredictable.

[@chrisjohnston2043]

Chaos is NOT JUST SENSITIVE DEPENDENCE ON INITIAL CONDITIONS! Another equally important requirement is topological mixing. For example; the map x of n + 1 = x of n ^2 (a discrete time model where the next value is equal to the previous value squared), is highly sensitive to initial conditions, but it has no topological mixing and is not chaotic.

[@ataraxia7439]

What is topological mixing?

[@kezadrone]

I'd like to also see an animation showing a series of dots moving in all directions showing what happens when a path is disrupted by those that hit each other sending the dots off in other directions, because that would illustrate how we affect each others destiny and the course of history. For example, you get up at 9am every morning and have breakfast, leave the house at 10:15, catch a bus to work at 11:00, every day, but one morning you leave the house at 11:00, miss the bus, get a taxi, miss a chance meeting with the woman you were to marry say and so on, the effects getting bigger and bigger, and the actions of one person change the outcome of the history that would have been had you left the house at 10:15 .

[@Einstein42069]

+Sten43 Since 1977 Yes, collisions would be nice. As for your scenario, that is not really what chaos theory is. Chaos theory is more about all the events of your life, and everyone else around you and before you, up to that point in your life. That is chaos: incalculable number of influential events, even before you were born. Your scenario is just someone being irresponsible, maybe bad parenting.

[@rynard33]

This captured the idea for me. Thank you for your efforts.

[@romawang9212]

i like how the background music is a perfect match for the content

[@alexanderheller2039]

You are insanely good at presenting physics

[@ranaalnasser13]

splendid.. I like the back ground music.. what is the resourse?

[@vulisritvars]

Thank You! Nicely presented complex idea, on a level accessible to most people. love the pacing, there is enough space to think about the concepts explained. And music is great.

[@lukehardin9]

Really one of the best videos I’ve been able to find on this fascinating topic, well done!

[@larryjones6291]

Extraordinary way to explain the forces of Nature!

[@Towalak]

Jesus, dude, this made me want to cry. A math video, made me want to cry. Hats off.

[@jpick319]

Excellent series!

[@jovanan9745]

The car animations and strips of paper example were very helpful to imagine and make sense of the information. Thank you so much!

[@liceous]

Just sublime. Thank you

[@TrAcKandFEeL]

Lorenz was a genius! very informative and profound stuff!!

[@Einstein42069]

+TrAcKandFEeL Yes, he discovered by accident like all great findings.

[@mayazhussain]

try Lorenz chrunchips Paprika then

[@TheCStrike2]

Brilliant video. I'll definitely check out more of your stuff. You deserve way more views. Beautifully done.

[@soumyadipgoswami1721]

You are doing a noble work

[@thevivos]

Now I've seen the video! At last a good real documentary! I've seen very few documentaries as good as this on such a complex subject (not saying it's the most complex subject in the world, but it's not "insect deathmatch")

[@dankmemesstudios3987]

The music from 6:00 goes by the name 'Masques I pour violon et violoncelle'.

[@ShirleyJPreston]

Love this further depth into butterfly effect and the amazing possibilities of Lorenz and chaos.

[@TheSentientCloud]

Oh I actually understood this... I've heard of the term "Lorenz attractors" for a very long time; but only now do I understand them.

[@khaledadams4329]

Holy cow that was well-described! Thank you!

[@kevinhewitson1998]

The Lorenz Attractor What occurred to me watching this was how it models the learning relationship between the class and the students. Just considering the two attractors at 6minutes into the clip there is a chaos about the relationship but in time they settle down into the butterfly shaped object. The same is true of the multiple trajectories, after a while they all accumulate on the same butterfly shape. From a learning environment the key would be that there is an initial time of “chaos” once the trajectories are initiated and that after time things settle down but that this happens only if there is no disturbance. Lorenz’s attractor theory demonstrates why it is important that at classroom level, and at a political level, leadership gives time for the chaos that is the initial stage of developing the learning relationship between teacher and students, is given time to accumulate on the same harmonious trajectory illustrated by the butterfly shape. The shape itself demonstrates the controlled dynamics of responsibility in the learning partnership too as it passes from teacher to students and back again during the learning cycle. Anything that prevents the attractors from forming this butterfly shaped object is perpetuating chaos in terms of the learning relationship. For more on the learning relationship see my Responsibility Diagram at: wp.me/p2LphS-kk

[@rogerperry5428]

Class

[@Tadesan]

Kevin Hewitson shut the fuck up Kevin.

[@jishnun4537]

great presentation and details..highly appreciate the effort..thanks!!

[@minerscale]

That was absolutely awe-inspiring. Thank you so much :)

[@Total1Now]

When we look at the weather we realize that it is infinitely more complex than that of the (mumble) . . . to avoid mumbling during your verbal delivery I recommend you 1) take some drama lessons and 2) listen to some Ray Charles. He is a showcase of clear diction. Thanks for the great vid . . .

[@bobf9749]

Another movie example: Ron Lola Run. We see essentially the same events several times, each with minor changes that lead to vastly different outcomes.

[@blim0n]

For the people wanting to know what music was used: www.chaos-math.org/en/thanks

[@rv.9658]

Chaos is perfectly compatible with "Newton's cold determinism". It IS deterministic. Even if it weren't, the whole point of chaos is that the most significant changes can arise from causes too minuscule for us to know about.

[@changliu7123]

This is a great talk!

[@sinaicoons]

I love the timing, yay Fibonacci sequence. 🦋

[@livesimple-ub9qd]

Lorenz simplified and simplified His equation=X, Y, Z 3 numbers Butterfly fx 7:30 and it's long term pattern

[@rotarolla1]

Can this find my other sock?

[@mayazhussain]

just wear any other sock

[@notsoclearsky]

2years now, did you find it yet?

[@RenyxGhoul]

when you don't look for it, it appears around you as long as it was lost in the vicinity that you are always in.

[@greg77389]

Does your lost sock exist between 2 and 3 dimensions?

[@conradgarcia4850]

I love the fact that the comments below resemble the Lorentz system, only containing more attractors, and much much more jerk systems. ;)

[@josephsimpson4295]

Is it possible for a path to be irrational, that is one that never repeats.

[@corey333p]

Very nice video.

[@realzey]

This was a kind of spiritual experience.

[@Kawaljeet-qu7or]

Can we say galaxies merging also follow this butterfly effect ? when we look for merging of galaxies it appear to follow the same butterfly effect (atleast to me ) .

[@euclidofalexandria3786]

This music is depressing and ominous, I would choose somethign more upbeat... in truth however, Thank you for posting and thank you for your efforts in making the video, it is good. Have a good day, and stay warm.

[@MaTTheWish]

At 1:00 it is stated that he simplified his equation so much that it may not be based in reality. correct me if I'm wrong but it seems that there are many real-world experiments and natural occurrences that coincide with his findings.

[@I77AGIC]

very awesome video!

[@davidwilkie9551]

The simple Singularity-point Mathematical ideal of projecting onto a futue precision is inevitably restricted to the inflated probabilistic ground state of Actuality, between one and zero-infinity, that is wave-particle Reality in cause-effect Perspective.. So.. Observation in terms of learning by doing Engineering Intuition, and Math-Physics measures of Quantum-fields potential logarithmic connectivity oscillation, combines the collective resonances, "state of being" as oscillation integration/superposition "governance" Hunting, ie temporal/temperature Annealing, ..toward flat space ground state of metastability and empirical "laws" of "governed" continuity, as seen in WYSIWYG Physics that is everything from the CMB to Black Hole Singularity positioning, Timing-spacing here-now-forever Hologram. Great illustration.

[@VikashPandey5]

Very well presented! may i ask the list of software used in making this presentation? Any help will be appreciated.

[@morganspencer1789]

why is the strip a mobius strip and why does the symbol look like infinity?

[@AveryMcChessney]

+morgan spencer Shhh... You can't let them find out that you know too much...

[@RenyxGhoul]

They all link together somehow

[@charliai6398]

I am not a numbers person at all, but a character in 'Heroes' mentioned that Strange Attractors are elements that are not supposed to be with each other but somehow end up together to create something phenomenal and amazing.... Wanted some clarification on that

[@RenyxGhoul]

One idea is when you watch a video of someone drawing a portrait upside down. At the start, you had no clue how it is remotely an artwork but when it was completed? It became an artwork. You could say that drawing upside down is impossible but it created masterpieces as well. Another example could be graffiti art where a non traditional canvas is used to create pieces of work. Two opposites coming together and creating something great.

[@thePrinceOfPurpose]

You did a very nice job, thank you very much.

[@JeremyDangerPictures]

Thank you for the visual.

[@descheleschilder401]

Great , very clarifying video!

[@iamtiggerthetiger]

the music........ i want to cry

[@sc-ek6qz]

Talia H heres a tissue... ..

[@sc-ek6qz]

Ha, darn now i might need a tissue... ..

[@MrZero12132]

The simplified equation shown at the start 1:12 is time dependent not position dependent (finite element) so it doesn't calculate the state of the atmosphere at each point unless the atmosphere is seperated into zones?

[@maestrosk]

Amazing video. thank you for posting!

[@vyaasshankar7605]

I should watch this video when I'm high lol 7:50

[@elberethlorian470]

Nature doesn't play dice, it writes straight on crooked lines...

[@astropgn]

The conclusion at the end is misplaced. Because albeit chaotic, these systems are deterministic.

[@astropgn]

@Divergent Integral I never said these systems are predictable, but rather deterministic. Determinism is concerned with the fundamentals of the system itself, regardless if it is predictable or not. If chaotic system were non deterministic, the same input would result in a different outcome. Which it is not true. Chaos relies on non linear properties that makes slight changes in the initial condition (but not the same initial conditions, this is crucial) can give you different results. The fact that we cannot predict is just a limitation in our measurements, but as far as the physics goes these are not stochastic systems. Non determinism, that is, truly stochastic systems

[@RenyxGhoul]

There is order within chaos, similar to there is chaos within order. For if there is none of one in the other, it ceases to exist. The Butterfly Effect is an ordered start but at a infinitesimal change, very minuscule that could lead to an entirely different outcome. Chaos within order. The Strange attractor, or Lorenz attractor shows that no matter where you start, you will always end up in this infinite butterfly cyclical shaped object. Hence order within chaos. Therefore, it is not necessarily deterministic as the trajectories and outcomes are indeed stochastic. The two however, exists to a certain extent in Chaos theory.

[@aletheabodine4819]

A great metaphor for the internet ... with out the fourth coordinate (time).

[@DavidMatine]

You're not clear about what sets the atmospheres in their trajectory. Is it historical data? Why don't you include that? That's a critical piece of information.

[@TxRambo]

What software did you use to make these animations? -One of the most beautiful videos I have seen, simply exquisite. Not only for content but execution too.

[@skimaskj999]

The Chinese were way ahead of us, they already knew about Yin Yang, this butterfly effect also happens in birth, upon daughter cells dividing etc.

[@quambambalujimini81]

7:37 - 8:14

[@bratanvonehre3559]

what a gorgeous video.

[@AndyPayne42]

Since you can represent any function with a Fourier series, couldn't any shape be possible if you do a FFT assuming we have the computing power to do the transform?

[@mirkoaveta3983]

Learned your FFT haven't you? ;) That's what Ruelle did with the turbulence problem in Navier-Stokes equations with Boussinesq conditions... 14 coefficients, telling something with elegancy! Try reading Robert Gilmore's book about catastrophe theory for more detail

[@AndyPayne42]

Coming back, yes, I think the frequency domain is under appreciated because of how we assume time has meaning. I'm not sure it does because how can time mean something when according to a particle of light time does not exist---created and absorbed simultaneously (delta_time=0). If I see zero in a equation I remove it, yet we invent this time vector even though a modern perspective of the universe is that of no zeros just uncertainty as you approach zero because zero, in my opinion, is more of a concept like infinity. And the final straw is that it's not symmetric and I have a feeling that you can infer non-symmetrical eqns are imaginary.

[@haoli9220]

Is it ergodic?

[@ARCANEmateCLAN]

If you plotted the x and y component (height and distance) of a double pendulum along with time (z), would you get this butterfly shape?

[@SabrinaXe]

I wish more people get to see the beauty of math(or reality). Love the background music, name?

[@glory_duck5897]

Darude sandstorm

[@HelloWorld-xc4xd]

I honestly don’t get a bit of what he was saying

[@ptaylor3304]

This is an astounding video. I'm high, but even still.

[@IanAtkinson555]

Chaos | Chapter 7 : Strange Attractors - The butterfly effect

[@samirelzein1978]

great work!

[@abcxyz9852]

okay, so how does this play into the loonaverse other than small things having a big impact?

[@owleye-nuclei1401]

beautifully done

[@weltering]

But how is the field evaluated ? Based on what data?

[@johnbatchler8551]

this math does work even with knowing the theory and math of it

[@poppymoon777]

This damned butterfly is a menace

[@YCV624]

in 3:59 where the atom spheres split completely, what was the main reason that one of the spheres left behind so greately in a way that they are following the same path at different times, so now this has to do with time, please explain why the difference in time at the beginning, Thanks!

[@hadrianblaq]

In Lorentz's original experiment, the initial values were entered to six decimal places but when he re-ran the experiment a second time, the numbers were entered only to three decimal places and the deviation is the result of the accumulation of these very small variances over time.

[@IITECHxNiNEII]

So would this mean ,say in another time line I may have something or someone I don't have now but that life would be very different or that it would end up being the same as it is in this one?

[@kocaksaid]

amazing, thank you very much.

[@ChrisOrillia]

What happens if it's at exactly .5 ?

[@andrasfogarasi5014]

The paper strip crashes.

[@blackholecicle8959]

The car splits in half

[@andrewaronson3364]

@Peter Rabbit didn't really answer the question, did you, dumbass

[@andrewaronson3364]

@Peter Rabbit just because you wouldn't expect it to happen doesn't mean it doesn't exist in the set of all possible answers

[@andrewaronson3364]

well?? we're waiting!

[@randycalifornia]

which is the first song on the background??

[@estefaniarnico]

Están súper las animaciones!!!

[@161157gor]

The Cyclic Expression of Reality... 👽

[@kylemaccc]

Does anybody know the title of the music used in this video? thanks in advance

[@ericrocha2266]

What program do you use to do these incredible simulations?

[@gameo2001]

MIND = BLOWN

[@ComputerBoyVN]

Wow.... just GREAT! :)

[@firatsanliturk]

The philosophical interpretation of the butterfly effect is sorely misunderstood imo since it disregards the 'limits of causality': For causality to be meaningful, the number of interactions (x) between the cause and the effect must be limited. If x^n=0 then there is no causality since there is no event to speak of. If x^n=1 then it's safe to say that said cause caused said effect. If x^n=infinity (or if n is an unknown number), then it's meaningless to assume causality between the so called cause and the observed effect. It's just poetry which breaks physics in real life. There has to be a limiting factor. Entropy, transfer and dissipation of energy. Something that prevents causality between a butterfly in China and a tornado in the US. If the butterfly effect did not have "an effective radius" for a given event, then any number of world ending event that happened, is happening or will happen somewhere in the universe would have caused catastrophic "effects" here on earth which is not the case. Having the attention of the public is good but mathematicians/physicians should stick to logic and stay away from sentiment lest we the ignorant get confused/misinformed badly.

[@RenyxGhoul]

If x^n = 1, assuming that n=0 is also included, the cause and effect is indeed, 1:1 if and only if the numbers are discrete. Numbers in general however, is not discrete. It is continuous. Therefore, even if it was x^n

[@RenyxGhoul]

It has been mentioned in the video that people enjoy reading and tackling things that are simple but it is oversimplified in many occasions hence not an effective solution but a good breakdown.

[@dawid_dahl]

"Instead of describing the future, starting from a given initial position, which we know is impossible..." Does anyone know why it is impossible? It can not be because of metaphysical randomness, since chaos theory is deterministic.

[@edwardfanboy]

We can only measure things to a limited accuracy, and if the system is chaotic, the tiniest inaccuracy in our measurement of the present will cause our prediction of the future to be completely wrong.

[@rzalman96]

Ohh that video was CRAZY

[@arcturusk649]

"Good news for us" in the end lol

[@ikaeksen]

Its a kind of fase change that happens obviously.

[@frankmorris626]

Does the attractor have any correlation with the law of large numbers? "The LLN is important because it "guarantees" stable long-term results for the averages of some random events." ???

[@huntervallejos3645]

I think it depends. The law of large numbers assumes independence, and your random variables being identically distributed. I would say that for a chaotic system, this may or may not be true.

[@haoli9220]

Hunter Vallejos however if you think of pseudo random sequence generators actually uses deterministic algorithms which can be interpreted as dynamical systems... there might be more that are not understood yet

[@zimingkong8839]

Astonishing

[@bobert4him]

What do I one do with a Lorenz, now that I have captured it?

[@andrewaronson3364]

run

[@04blueboy]

Cool video

[@ZiplineShazam]

Do we have free will ?

[@op-cq7hw]

no its just endless entropy that gives the illusion of free will.

[@SabrinaXe]

In some cases yes we do, when it comes within us. All of our psychology is different hence we decide different things. Is our psychology determined? It sorta is, isn't it? But it's not cold determined, there's fluidity within. That's why we're able to break habits Yes it's true the universal laws are determined, they follow a pattern, hence if I was falling off a cliff, if I wanted to I wouldn't be able to fly My thoughts on this are kind of vague as I don't draw a clear dichotomy between free will and cold determinism because there's air gaps between them

[@chasalv]

Could someone explain how the model which starts at 1/3 is chaotic?

[@billwhoever2830]

everybody gangsta until he starts with an irational fraction of 1 (lets say π/4) and get a never repeating fractal

[@sinaicoons]

I almost waited for the weather AFSC.