Double pendulum | Chaos | Butterfly effect | Computer simulation

A system is considered chaotic if it is highly sensitive on the initial conditions.
If a system is chaotic it doesn't mean that it is random. A chaotic system is completely deterministic. Given enough time and precise initial conditions of the system it would be possible to calculate precisely, how it will evolve.
Given enough time, two identical setups, set to initial conditions that are as identical as possible, will look entirely different.
_________________________________________________________________
Support my animations on:
/ think_twice
_________________________________________________________________
Any further questions or ideas:
Email - [e-mail]
Twitter - / thinktwice2580
_________________________________________________________________
Overall render time: ~ 45 hours
Programs used:
- Cinema 4D (3D animation)
- Adobe Premiere Pro (Editing)
- Adobe Animate (Thumbnail)
_________________________________________________________________
Music:
Hvetter:
• Beautiful Guitar Loop ...
Sound Cloud:
/ hvetter-1

[@ThinkTwiceLtu]

Hey guys! If you enjoyed this video, you'll probably like this short Lorenz Attractor animation I made: instagram.com/p/BslCLk0FT-7/ If you'd like to see more animations like this - follow @thinktwice_ltu on Instagram. Thank you and have a great day:)

[@elianemartinez1509]

Thanks :3

[@rubenssilveira5765]

Jevilman: chaos time!

[@heeheehaahaahoohoo2585]

where can I get this background music can you please share us the link

[@visualmath4508]

You are putting a lot of effort into creating animations. Feel free to share your videos on www.reddit.com/r/VisualSchool. I've already shared this material. The community will appreciate it.

[@yashkatare3303]

Can we actually predict the motion of the pendulum? If no then we can maybe use them to generate random numbers, right?( I have no background in computer or anything related, just a curious hobbit )

[@josephaxp4292]

Turtorial: "Draw a circle" Brain : "Draw a circle" Hand:

[@AceTechn0]

Brain: green circle Hand: brown circle 0:05

[@echothefreak9396]

Best comment

[@-vines-7018]

Why is it so true?? 😩

[@doasisonim]

Sense is wrecking Also clipe by Miley Cyrius

[@laulaugag12]

True

[@Ultracity6060]

How To Dance At A Rave [Instructional Video]

[@ThePositivolp]

Ultracity6060 start it like everyone and get crazy

[@robertodelier9999]

Hoi

[@laula813]

@@robertodelier9999 I'm bob.

[@bidorz1316]

Crab rave

[@Whatismusic123]

OBAMA ------ IS GONE

[@Rowlett54]

The music was spot on, especially when the screen went black

[@S_O_U_P]

You ran stealing demon YOU WONT EVER GET IT. YOULL NEVER STEAL MY RAM

[@zircondeez]

@@S_O_U_P yummy ram

[@S_O_U_P]

@@zircondeez REEEEEEEEEEEEEEEEEEEEEEE

[@okl9182]

@@S_O_U_P Google: *proceeds to kill your pc with only 3 tabs open*

[@S_O_U_P]

@@okl9182 *Deletes Google via Task manager*

[@caradog1081]

I’ve seen two different opinions on this, either “we should make a ride based off this” or “double pendulum rides are a bad idea”

[@fairycars]

they are definitely a bad idea considering people could very often crash into each other, looks rly fun tho

[@theaxeforgets8774]

You could make a religion out of this..

[@muhammadaryasaputra6754]

@@theaxeforgets8774 NO DON'T

[@woooooooooooooooooooooooo]

12 hospitalisations and 3 deaths later...

[@pinkpuff8562]

1:33 XP from when you kill a monster in minecraft

[@kingofawesomeness5375]

Lmaooo

[@lindakristiani151]

True

[@lsudo]

Lul

[@dlrss1v274]

LOL

[@ithan0404]

No...

[@truji2582]

me trying to follow the steps on the pack of instant soup

[@pedropesserl]

David Trujillo me trying to follow the dance steps of my friends

[@rigoisvibing]

me trying to follow steps on how to tie a noose

[@Shadow77999]

Pedro Folloni Pesserl lol what is that

[@justminecraft2452]

me trying to keep the kids

[@blveberry8002]

me trying to tie my hair

[@horehoundbasedcandy8736]

I enjoy the anti chaos theory, that everything has order and true chaos doesn’t exist. It’s a fascinating read.

[@Arkay24]

I agree, though I thought Chaos theory didn't throw order out the window and simply stated that the variables involved in the calculation were too many and too complex to accurately calculate?

[@ibotomele1640]

Is it a book. How do i read it

[@Echo-hg7gu]

@@ibotomele1640 with your eyes

[@frankflight9951]

Nerd

[@Arkay24]

@@frankflight9951 So?

[@shiny4984]

1:28 now's when things start to get *_funky_*

[@josephgennaro1270]

now when do you get funky?

[@CZORCH]

@@josephgennaro1270 when designated funk time begins

[@josephgennaro1270]

@@CZORCH yes

[@Liletter]

I have the best/worst idea ever; instead of having pendulum rides at amusement parks, make double pendulum rides.

[@sarangtamirisa5090]

The more unpredictable the motion, the more unsafe the ride

[@Liletter]

Sarang tamirisa, that’s why it’s the best/worst idea ever.

[@pmteclas]

If you like chaos, go for it

[@copycat500]

Jevil be like:

[@L1M.L4M]

That would kill people... carry on

[@TRRailfan]

1:37 this could be really useful to animate a swarm of flies

[@gasun1274]

blender has a feature that takes in python script. implementing chaos in python is pretty easy but im not sure how blender will handle it.

[@amyisaway7800]

I THOUGHT THE SAME THING

[@flora4884]

Or bees

[@Shifsabre]

You absolute genius, I might have to use this when I'm done with my studies

[@siar073]

U have exactly 666 likes. How do you feel?

[@oneesama9058]

That just looks like a mother accidentally letting all her 12 children loose in the park...

[@Zboy707]

Or a dog walker releasing dogs from their van 😜🐶

[@leversandpulleys9274]

Imagine living your whole life getting stuck in a dark room with pendulums and you can only see the balls, you wouldn't guess the pendulums move the balls, you would guess god, then you make a religion out of it

[@doplop]

we can make a religion out of this

[@skeleletonboi4533]

this is very cave analogy

[@earlymodern]

why is the obvious guess god?

[@seistoYT]

@@doplop No, please don’t

[@Name-co5qi]

@@earlymodern i think they mean god as in a higher deity

[@slowlydecomposingcorpse829]

I have no idea what's going on or how I got here but there is coloured dots swinging back and forth so I'm happy edit: every time I see a comment about my vriska pfp it takes a year off my lifespan. You’re killing me. You’re all killing me. Murderers

[@kingofawesomeness5375]

Are you high

[@hanareta]

are you a cat? )

[@slushyface307]

Here before 1000 likes

[@djangorainbow]

me too

[@misterturkturkle]

Science

[@deepslates]

At a group project... 1:44 Yellow: working Everyone else: deletes what he does.

[@rannnndm]

Which yellow ?n

[@deepslates]

The one who just does a semicircle like normal.

[@ford7372]

I don't get it

[@fagioli7063]

Poor yellow going into overtime to carry them though the project 🥺

[@deepslates]

@@ford7372 the joke is that yellow is going in a perfect semicircle, actually doing something and the rest are chaotic.

[@th8r065]

I know they’re each doing different things but it looks so coordinated.

[@Zboy707]

Says the aliens watching us

[@cara-seyun]

Pattern-seeking brain

[@officialwyattthesans12345]

For some reason this feels oddly satisfying for me.

[@joshinils]

Mad juggling skills, in the dark even

[@thehiddenninja3428]

I want that as a screensaver

[@orb7326]

hellorandomperson cant you tell a joke??

[@VESPERTlNE]

oxylorvoxIsWOOHOO wowowowowowowowowowoowowowowowoôooooosh

[@orb7326]

hellorandomperson dammit i git wooshed

[@VESPERTlNE]

oxylorvoxIsWOOHOO ikr

[@davidcotand6051]

Not sure if you've been notified or not, Ted-Ed have used this video in their Turbulence video without giving you the credit.

[@Monochrome_math]

Holy shit! Ur right. The animation is way too similar to this video to be called a coincidence.

[@ntptjello5896]

Yep they took a part of his video, ted ed still didn't credit him

[@factjuniorroll]

Linky pls?

[@willmad3734]

@@Monochrome_math it literally could be it just some pendulums and they don’t own pendulum

[@EJTunaFish]

@@willmad3734 That’s not the point though. They used footage from this video without permission and didn’t give credit.

[@allisonthefox9900]

I'm not smart enough to understand this but damn if it ain't hypnotic.

[@px776]

I just couldn’t get my eyes out of the screen

[@kujojacobo]

nobody: minecraft exp orbs: 1:50

[@MaybeNotARobot]

my legs when i walk downstairs to eat shredded mozzarella cheese at 3 am

[@tawnysue5268]

Dope

[@partycreature9937]

Underappreciated comment

[@Basic666]

Just curious, how has your life changed in the 2 years since you wrote this comment?

[@MaybeNotARobot]

@@Basic666 i haven't had the opportunity to eat shredded mozzarella recently, which sucks...

[@Basic666]

@@MaybeNotARobot oh no! That's like the worst possible outcome!

[@snoergee]

Ok this is legit sick. I didn't even know it's THIS easy to demonstrate the butterfly effect without time travel!

[@Zboy707]

What do you mean by this? I’m actually trying to write a time travel story that may involve the butterfly effect and I’m thinking of using this double pendulum idea. Any inspiring (what-if) ideas would be appreciated!

[@rudrodeepchatterjee]

@@Zboy707 I think they just alluded to a possible theory that if you time travel to the past, the slightest change in your actions after time travelling to the same point in time a second time will give a totally different outcome. If I remember correctly the name "Butterfly" effect came from some book where a person time travels and comes back saying he did not change anything, so it's fine, but then he looks at the sole of his shoe and there's a crushed butterfly which was not there before.

[@Zboy707]

@@rudrodeepchatterjee ahh I see I see. Thank you!

[@epicdude61388]

@@Zboy707 also, in a very technical yet still relevant point, this video involves time travel. One second forward per second, ha.

[@rowanmcalpin]

@@rudrodeepchatterjee I've always heard it referencing a theoretical situation where a butterfly flaps it's wings in one place, which compounds with some existing wind and makes it just strong enough to compound with additional wind and it keeps going until eventually there's a hurricane on the other side of the world. If the butterfly never flapped its wings, the hurricane never would have happened

[@somethingaboutsomeone7641]

Yo, first thing i thought was "you believe life is like this?" and then it all turned to 12 different circles and it was so chaotic that i got a lil horrifyed cuz it was like a representation of life

[@a_dolph808]

Interesting video! I find it pretty cool how you can just demonstrate the butterfly effect so easily with just a nice and simple simulation. You've earned a sub from me!

[@taro.s]

1:32 this could be a screen saver

[@nightmareinaction629]

one the took 45 hours to render

[@gabriel.pessoa]

Or an Android boot animation

[@kingofawesomeness5375]

I think you should add more dots though

[@juulesmann9519]

@@nightmareinaction629 well it could be a loop nobody would notice...

[@jaguarr314]

Exactly what I thought

[@billyjoeparker8054]

[does a gay little dance that is highly sensitive to the initial conditions of the system]

[@ViridianAubergine]

[and also pisses you off]

[@thecrimeskeleton4848]

i like your shoelaces

[@billyjoeparker8054]

@@thecrimeskeleton4848 death is only the smallest challenge ye now face

[@imagoat273]

@@thecrimeskeleton4848 thanks I stole them from the president ♡

[@bonelessmice6828]

🕺🕺 this emoji has gay energy and i dont know why

[@RyanCalhan]

When I looked up “DP” on the internet, I wasn’t expecting this.

[@RyanCalhan]

@Velvet Warrior [GD] ;)

[@RyanCalhan]

@Velvet Warrior [GD] How do I put this as pg as possible? What is a word that starts with “P” that is also a synonym for the word “puncture” or “pierce”? When you figure it out, DP = Double…that.

[@RyanCalhan]

@Velvet Warrior [GD] Oh I’ve done more than tried friend.

[@MilannesaNapolitana]

Green circle: do you remember how to gravitate right? Brown circle: yeah... hold on... i think i... i got i got give me a minute

[@RahulRoy-id5yf]

45 hours to render it...wow...what system did you use and how did you manage to keep it cool?

[@ThinkTwiceLtu]

Rahul Roy i just used my wooden laptop and it was overheating like crazy haha

[@RahulRoy-id5yf]

Think Twice haha...😂

[@llkk3557]

Think Twice Why does it take 45 hours to render that, isn’t it a simple animation?

[@tylerburney8576]

ll kk Nope, it’s rendering the actual physics of what’s happening. Well, I assume so, that or they have a shitty computer haha

[@ThinkTwiceLtu]

Tyler Burney both haha

[@SittunSwayamPrakash]

Came straight from 3blue1brown. Marvellous, my friend!! Please keep making content!!

[@TeaLurker]

Well you turned out the lights so off they can't see and go in different paths.

[@Briarbark]

The double pendulum connected to the centre makes me laugh because it looks like an arm going wild and it's 4 am

[@jamiewaaler2957]

Thank you for making a diagram of how I dance. One arm just swings and the other’s just... flopping.

[@EvanCaritopTV]

Am I actually earlier than Justin .Y?

[@valentinov901]

I don't deserve subs yep

[@dothmotherknowyouwearth]

Y u p

[@ripstats9753]

We made it

[@venb]

I don't deserve subs uve seen him before

[@fuzzzbrain2318]

You do realise there are probably hundreds maybe thousands of accounts like Justin’s, who comment on a whole lot of videos just like he does. The only reason you see him so often is that other crawl the comments section see Justin’s comment and they like it, which in turn upvotes it.

[@camilacantero5746]

Es increíble que todos tengan su propio camino y aún así, en conjunto se vean como un único ritmo. Que como unidades parezcan incompletos pero en conjunto todos pertenecen a un mismo mecanismo para crear un sistema desordenado e independiente de sí. ♡

[@eldave178]

This was beautiful. Thank you.

[@kristoffervatshelle1418]

The music is so perfect! It makes the whole thing satisfying and calming instead of making it stressful. Well done!

[@dylanhdog]

When a mom gives their kid some crayons and a blank wall

[@coffee-lc]

This looks gorgeous and i love it so much. It also seems like the way people make screensavers.

[@313shanali]

It looks silly but I just can't stopped clapping like I witnessed a really good performance, Math is really beautiful.

[@joeroman3404]

Please never do a face reveal, I love the mysteriousness of this art

[@ThinkTwiceLtu]

:)

[@joeroman3404]

Think Twice do you agree?

[@joeroman3404]

Think Twice do one at 100000 subscribers

[@ThinkTwiceLtu]

Joe Roman yes, i'm not going to do a face reveal. (at least not soon)

[@ThinkTwiceLtu]

Joe Roman haha sure! I don't think i can get to that number any time soon (if ever). But If I'll still be making videos by then, I'll do a face reveal.

[@WatrDragn]

Single pendulum: the story I’m trying to tell. Double pendulum: the way I’m telling it.

[@The_Kosmus]

For some reason this video appeared in my recommendations and I don't regret it

[@vpambs1pt]

Loved this as always! What about triple pendulum? hahaha But If i dropped two double pendulums at the same height with the same conditions their path'd be the same right?

[@devanshutanna]

If perfectly same, Yes.

[@ThinkTwiceLtu]

thank you:) triple pendulum is a chaotic system as well, I've actually made an animation of it as well but decided not to put it in the video. In a controlled environment 2 pendulums with same initial conditions would have same path. But in real world at some point the two systems will slightly differ in some parameter (for example air resistance) therefore as those systems evolve, at some point they will be completely different. Great question

[@vpambs1pt]

hmm, if we disregard air resistance and those "forces" from earth that disturbs the system (Except gravity of course) and all the data/information, height.... could we "calculate" the trajectory/path? Even if it were a quadruple pendulum or pendulum with "n continuations" ? Sorry for my english, I'm not used write such terms in english. If you didn't understand what i wrote tell me and I can be clearer. Edit: Like make a formula, and know for example if the 3rd pendulum with ever pass cross a certain point or calculate that probability, or even when will it cross.

[@Stickyxgo]

Yes you can simulate those.

[@ThinkTwiceLtu]

Yes, in fact if you know all of the initial conditions you can calculate precisely the position of a double pendulum or a pendulum with n parts at any time. However the complexity of calculations increases rapidly the more "pendulum parts" you have.

[@MagicGonads]

Essence of psuedorandomness.

[@thomaspappas8946]

That's deep

[@mike4ty4]

Yes. And actually the best pseudo-random number generators, such as those used in cryptography, will satisfy much stronger forms of the chaotic conditions like "total mixing"/"avalanche" (a single bit flip in the seed should cause the immediate next successor to be entirely different, which isn't the case with a differentiable, real-time chaotic system like this or even the classical discrete systems, where the divergence is only exponentially growing), uniform distribution, etc. This is necessary because there are very sophisticated methods that people can use to attack the system, and thus to ensure it is not vulnerable to them its output must be as unpredictable and close to genuine randomness as it possibly can be.

[@thatoneguy9582]

Magic Gonads Pendurandomness

[@JorgetePanete]

Magic Gonads pseudo*

[@georgewashington9161]

U first

[@ray7538]

1:00 gymnasts on the high bar

[@ArmorWolf]

That was beautiful and mesmerizing. More. I DEMAND MORE.

[@eiiesig2651]

0:30 *"Hi, my name's Renata Bliss and I'll be your new freestyle dance teacher-"*

[@hahalord7294]

I don't know what's happening but this is satisfying so, ok.

[@janwith-context]

THIS HAS BEEN IN MY RECOMMENDED PAGE FOR SO LONG!

[@_Iceygt]

Me: ok guys watch me draw a pirfect circle. Also me: 0:05

[@PABITRABADHUK]

3b1b brought me here! I am glad they did.

[@JorgetePanete]

PABITRA BADHUK they? you mean he

[@SylwesterYT]

This is some good work you did. Respect

[@JustDEV1]

The brown dot is just a master of dodging the blue dot.

[@Pollytulip41]

I haven’t watched something this mesmerising and eye catching in a long time, such a great animation!👏🤩

[@lailaalbuquerque5036]

Thank you for helping me rediscover my love for learning about the little things around us :)))

[@maziarjamshidi4505]

Amazing... I am so happy that 3Blue1Brown introduced me to this channel.

[@haydnwilliams6227]

this is always in my suggested and i finally caved and watched it. it thoroughly excited me.

[@jj_judah365]

When the background went black and all the colors were dancing around it looked strangely beautiful

[@KiluaRotmg]

Simply beautiful ❤

[@nuthapot]

1:32 it looks like a light show wow!

[@JSON047]

I have no clue why I've been chosen to see this by the KZbin algorithm but I am not disappointed. Oddly satisfying 😂

[@Roni_mcconi]

This could entertain any man for atleast 2 hours.

[@dsblocks]

I've had an idea: what if you take 10 double pendulums, and you mark their positions over and over again. Wouldn't you get a kind of "probability cloud"? And does it look different to doing the same thing with immovable pendulums, but the two angles being chosen randomly?

[@only2ndplace]

Yes, that is in fact the way to go with chaotic systems. While you can't predict exact trajectories, you can calculate probabilities of the pendulum being in a certain postion (for example nearly hanging down). If you look at the system for a long enough time or at a lot of pendulums at once, these probabilities will always be correct even though the system is chaotic.

[@forsaturn4629]

0:55 When I dislocate my arm.

[@adrianghandtchi1562]

This was very relaxing to watch. Thank you

[@Tartarsauce.]

I never thought I needed to know this, but I did. Thank you.

[@TheOneLichemperor]

This topic came up in a discussion at a philosophy group that I attend, and one member came up with an analogy of this effect involving billiard balls. The premise is that with each additional ball lined up in a shot - the path that each would take further down the line becomes ever more chaotic. I just thought I'd share this here, in case it interested anyone else!

[@only2ndplace]

The interesting thing is, this only happens if the billiard balls are more than half a ball length (if I remember correctly) apart. If they are closer, the opposite effect occurs, i.e. even large pertubations make no difference. If you put a line of billiard balls really close together you can hit them very off-center but the last ball will still set off in the direction of the line rather than the direction you pushed the first ball. So in a sense the ball distance controls the amount of chaos and stability.

[@guillermocruz2440]

1:32 that would be a nice screensaver!!!

[@Fidnnfu]

The red one was just hoppin back and forth while all the other ones were having a panic attack

[@apexxvsounds1812]

Masterful work.

[@ipsharoy7398]

Me: * looks at my hand * My hand: "Don't you dare try it on me"

[@DuhNoU]

"Its unpredictable!" Said human "Its cursed!" Said scientist

[@trevojan]

Hours of this result with a music on the background would make my day

[@aaronlouis6706]

watching this while being sleepy and high was beautiful, thank you

[@kennethmanuel1094]

Make a bullet hell game instead of regular bullet pattern, make a 12 double pendulum bullet pattern

[@altairraphael3817]

one question: do these movements relate in any axis to the lissajous curves? nice animation btw

[@juanantonioromeroparra9178]

The black screen one looks like an octopus juggling glowing balls in the dark

[@micyoz5283]

This was beautiful to look at, thanks for the experience!

[@naialain9731]

one of the best midwest emo songs i have ever heard

[@onmyknees9108]

Yea !!just puts a smile on your face 😀

[@gptt1233]

Wats the name?

[@naialain9731]

@@gptt1233 if it were a real MW emo song it would probably be like "Friendship on the pavement" or something

[@900n1]

Jevil: *This is my FINAL chaos!* **Summons 12 double pendulums**

[@ThatOneShortieHo]

This is very calming to watch

[@_idkwtnm_]

This made me so happy for no reason

[@realcygnus]

Cool.......essentially its MORE about a systems intrinsic susceptibility to tiny variations in initial AND operating conditions RATHER than the fact that, in reality, none of the conditions can be either measured OR set with infinite precision. As the latter is true of ANY system(including the most "predicable" types). & that is even ignoring Quantum fluctuations & such.

[@devilvocano420]

Shh nerd

[@gustavonunes631]

DevilVocano lmao

[@carbon273]

Wat

[@diamondjub2318]

*Jevil would like to know your location*

[@Vinny_3041]

CHAOS,CHAOS!

[@DarkGamer-qh7ql]

I CAN DO ANYTHING

[@christophermoore6110]

Idk why, but something about this music reminded me of the best parts of my childhood. Thank You!

[@Creepsington]

thank you i love this

[@mlgproplayer2915]

Noice!

[@gaspaja27]

0:17 saturn

[@eternal6434]

Happy hundred K subs

[@gayningabe871]

This was perfectly well explained thank you!

[@Sabagegah]

1:09 WHEEEEEEEEEEE

[@thingsfromspace]

This was great! Are you fully healed now?

[@ThinkTwiceLtu]

things from space thank you!! unfortunately no, It might take few more months until I'm fully recovered. Thanks for asking:)

[@thingsfromspace]

Oh, that sucks, great video though

[@ThinkTwiceLtu]

ya I'm trying my best to recover:) Thanks again

[@shadowfury428]

This is oddly super satisfying and very relaxing, and I don’t even now how I got here, but I’m enjoying it.

[@j-red147]

This video has been getting recommended to me for the past couple months.

[@zurielbabida8162]

CHAOS CHAOS

[@rubenssilveira5765]

1:55 *CHAOS! CHAOS! CHAOS!*

[@skywe_]

This video pops up in my recanted every day and i watch it every time like 10 times, it hypnotizes me

[@tizzzzy2]

This video is an accurate representation of my thought train.