Full version of the song: kzfaq.info/get/bejne/g7yjnLJ8ucenlKs.html Visuals inspired by @Numberphile, kzfaq.info/get/bejne/bOBkpLWZ1aitqXU.html Stripped Python code below. Create a .py file and paste the code therein. Don't forget to create your "DestDir" folder in same directory. (There are much neater scripts elsewhere on the web on this topic. Analytical solutions in Python are not my strong suit...) *** import matplotlib.pyplot as plt import matplotlib as mpl import numpy as N from scipy import interpolate from sympy import N as symN from sympy.solvers import solve from sympy import sqrt,atan,sin,cos,Symbol,re,im,diff import scipy.linalg as SLA def mm(* args): tmp=N.dot(args[0],args[1]) for ii in range(len(args)-2): tmp=N.dot(tmp,args[ii+2]) return tmp def myangle(xp1,yp1): if xp1xp0: ivec[0] = abs(ivec[0]) ivec[1] = abs(ivec[1]) rvec = (ivec-mm(2*mm(ivec,nvec),nvec)) rvec = N.array([float(rvec[0]),float(rvec[1])]) rvec = rvec/SLA.norm(rvec) v0 = v0*rvec vx = v0[0] vy0 = v0[1] x = Symbol('x') sol = solve(x**2 + (vy0/vx*(x-xp1)-g/2/vx**2*(x-xp1)**2+yp1)**2 - 1,x) for ii in range(len(sol)): if abs(re(sol[ii])-xp1)>1e-8 and abs(im(sol[ii]))

Now like 3blue1brown i imagine if we can color all initial position according to final position after X seconds and see if it's a fractal.

A wallpaper based on this idea that has a random number of balls drop at a random area would be so fun.

Idk why but the one with the two balls + this choice of music, just feels so serene, like two siblings reminiscing about playing in a field together

I love how it's synchronous with the music especially in the 100 balls

Wow- those 10 seconds after 2:06 is just phenomenal. The whole thing is acting like a wave or something, its gorgeous!!!!❤

The last example is a great way to show the domain and range of a function. There's lots of small paths that they can take, but it is all bounded to the semicircular area.

I almost laughed uncontrollably when it said “2 balls” on the screen. I might be broken beyond repair

1:26 Also shows that, even when so much else has changed, they can still end up in the same place, if only for a moment.

2:13 looks like fireworks

2:06 Wow, that‘s so beautiful!

0:53 really hits hard

2:07 *ultimate satisfaction*

This is wonderful! Do know that your content is very much appreciated!

0:58 Give me them back please.

For those wondering, the trajectories of the balls after hitting the circle are calculated by using the fact that the angle of incidence equals the angle of reflection. The angles are measured by taking the tangent lines of the ball's path and the surface at the point of contact. Between bounces the trajectories are parabolic arcs because we are assuming uniform gravity.

100 Balls is what I imagine when I think of any other person also born on November 17th, 1999. All having the same experience as a newborn but, as our environment shapes who we become, we have all taken different paths. Some with similar experiences but no two ever the same. This is the butterfly effect. Every small decision we've taken, has driven us further apart from some yet closer to others, in a quite mesmerizing way.

Very nice one ! I should not have missed that numberphile video

with the two balls it makes me think its a couple dancing together alone but they are having so much fun. plus with the music it makes it much better

Beautiful! Not just a great visualization but the music is sensational.

This is very cool but it’s not what I expected based on my perceived knowledge of the Butterfly Effect. To me, I was expecting the balls to be able to interact with each other causing them to collide and move off in extremely different directions. That was my understanding of the butterfly effect. This is simply creating cool patterns by having the objects start from slightly different points in the beginning

Probably the most visually soothing and beautiful example of temporal chaos I've ever seen.

there's zomething fascinating about thatr moment at 2:05 where the 100 balls are mostly in sync, traveling in the same direction in the same order, and then just happen to hit a particular angle/segment of the sphere to make all their paths cross and spread out a ton more. they very quickly start to seem random and disorganized. It's like a turning point where order suddenly turns into chaos.

You're video really inspired me to try this too! I love simulations like that!

So pretty! Pls do more shapes!

I'm a little confused. What causes them to separate? Are they not truly in the exact same position to start?

I love how while the 100 balls all take a different path, they still share a bit of synchronization.

2:09 とても綺麗！

It feels like a soft dance . With dancers performing in coordination and seperately

For a moment there that was incredibly beautiful and I would love to have it as a screensaver

I see entropy increasing

2:12

I love when the 100 balls start dropping in the rainbow effect happems. It is so beautiful and colorful.

0:12 1 ball 1:06 2 balls 2:13 100 balls

I was watching as was just thinking what if you were to graph the distance between the red and white balls. Would it slowly move apart, would it form an interesting pattern? Also what would happen if you averaged the coordinates of all the points and drew that? how would it move around as the system evolved? Would it slowly jump around more and more violently? Would it fallow a pattern?

The twisting illusion makes it look 3D

I imagine this must be how timelines and how one change can completely change the future would be. The ball can bounce slightly different then the other balls even though they all started the same way. Each bounce has is like a choice being made and the chances it bounces one way versus another can highlight how a person has multiple choices in each scenario and this shows how slight changes in “choices” can have a vastly different outcome in the future. Or am I doing to many drugs lmao

Not only is he the former UFC LHW champion, but he’s a heck of a scientist.

This is such a nice depiction and representation of the butterfly effect

2:12 The fireworks in my backyard during New Year

Now imagine if one of these balls were a meteor holding elements capable of kickstarting life on a planet, and a small change alters whether or not it lands on a planet capable of housing life.

The Butterfly Effect seams really useful if you eg. want to exhaustively search an entire space, but don't really care about efficiency, or somehow can't optimize the search.

its so bizarre how a 0.0000001 radii difference is so major

My man went from fighting Jon Jones to making animations... respect

This is just wonderful. One of the most interesting things I've seen in a while.

100 balls looks like a 3d rainbow at first but later it creates a mess

0:40 this feels like the DVD logo when it perfectly hits the corner

Small imperfections are just enhanced.

This makes me very happy.

given infinite time maybe it will all return to its original position? This video was very pretty thank you for making it! :)

The sequence with two balls made me rethink about my lifechoices

綺麗！！

This is what the molecules look like on top of a freshly poured glass of soda or beer.

It must be in a vacuum and with 100% elasticity because each ball does not seem to be wasting any energy at all.

Ahh that makes sense they’re together at the beginning then manually released later

When you started doing the 100 ball drop, it kind of looked like fireworks. This is so relaxing. I love this.

I think this is a great way to get an explanation why mathematical simulation for weather or germ spread do not work for long term prediction. After a while even some minor influence will take over on some variables, so the prediction rate decreases drastically at a certain point, after this point no model will deliver a result you can relay on! It´s getting worse when you raise the amount of variables ( balls in this case ), so the tilting point takes over after few iterations.

Mathematics : shows beautiful patterns Physics: scratches the head why does not the ball loses the energy?😂

The two balls are like two lovers that have a difficult relationship but still try to stick together

The end of the video was visual stimulation for me! ❤

Very beautiful and unexpected. What about in a cylinder? Great job. Thank you.

Me:mom isnt it satisfying Mom:RAE U TAKING DRUGS!?

ive been spiritually touched

Like. A perfect demonstration of what dynamical chaos is

2:07 It is the most beautiful thing in the world 🌎

The 100 balls one,so satisfying and beautiful

Please run it with an additionaly function. When two balls separete from a certain distance, seed in an intermediate ball what it's variables interploatly inherit it's parents velocityes an positions. This way you will dinamically simulate battlefly effect more accuratly with saving so much calculation, and you will not be limmited by the resoulution what you set at the starting point of the simulation.

what i see in tv screens on a tv shop

Proof of how Random Number Generators work

I thought the 1 ball simulation was taking a while to spread out, I did not know it was just one ball! Sorry for bad english

Reminds me of old Algodoo marble races.

I don't know what we can learn from this show, but one thing is for sure: it's beautiful!! ❤️

I feel its symbolic that there will always be ups and downs for everybody, so dont judge your position compared to someone they started from the same place as you

I need 10 hours of this

Reminds me of Phun/Algodoo marble tracers used in marble races etc

I love the artwork I love it

Someone: *asks something about me* Me: 1:43

The 100 ball reminds me of a national holiday (4th of July, Canada day, Bastille Day, etc) and going outside in the cool summer breeze to see a fireworks show

This is beautiful. It's like watching a unicorn projectile vomit rainbows.

100 balls version would make a great fireworks show

To quote Anchorman: "Boy, that escalated quickly!"

Nothing could’ve prepared me, holy

That's really beautiful!

The 2 balls one was an cinematic masterpiece

Someone the simulation combined with the music reminds me of that lines simulation in Workbench 1.3 for Amiga.

All of these would make the world's greatest screensaver

I watched this like how a cat watches lasers. So cool!

2:10 Its so soothing to look at... Twisting and Turning

100 balls look like a rain bow

This is amazing! Can you share the source code that you used to make this simulation?

The definition of all hell breaks loose

The conclusion is that no matter what you do, you always end up at the bottom

0:54 got me off guard

U know what confuses me, when there’s two balls why wouldn’t they just fall in sync when they fall at the same time but when it got to 100 balls it was so mesmerizing for a second

So calming

And this is why meteorologists can't predict the weather very far in advance. It's mathematically impossible.

I'm seeing 3D when they spread

IT's so beautiful!

This is a piece of art!

100 balls looks like a screensaver