Full version of the song: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-MVsiOKTaCdw.html Visuals inspired by @Numberphile, ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-6z4qRhpBIyA.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]))
Hello, Thanks for an interesting comment! I made a video closely related to your thoughts: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-7G4kfVAznGA.html
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.
it is! sadly we as a society butchered the idea of a rainbow and use something naturally beautiful that exemplifies physics in order to push a political agenda. #FeelsBadMan
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.
But why? They're not in collision with each other, so the entropy of the system should be the same whether you have 1 or 100 no? It's like they're in different phase, so it shouldn't matter.
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.
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
That's the point, 1 slight change in the past can alter the future in a drastic way. Let's say in the 2 ball example, white is our time period while red is another where cars weren't invented until a day later, a LOT of things would be different from our reality.
Every one of the 100 balls dropped from almost the exact same point in space. And yet the tiniest fluctuations to spread all the balls out by end. That's the effect.
They all started at almost the same point, but hit the first wall at a slightly different angle because of the curve, which became more and more significant of a difference over time
@@simplyatableI think they did start at the exact same point, so why do they have different paths if their historical trajectories are exactly the same?
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.
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.
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
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.
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.
@@soumickdas9674 think about the simplified case with no gravity - if the angle the ball makes with the circle is a rational fraction of a circle, then after tracing out a star polygon it will return to its original state, but if the fraction is irrational, it will never complete an integer number of rotations and thus never return to its original state. adding in gravity only makes it harder for the system to perfectly return to an earlier state because there’s more chaos (in the precise mathematical sense).
@@tedkostek100 I don't know how I missed these notes in the description: "2. Two balls separated by 0.01*R 3. 100 balls, each pair being separated by 1e-6*R." But thanks for satisfying my curiosity, haha
Sorry for the disappointing cliffhanger :). I needed to stretch out the video a bit to cover most of the song. Plus I'm myself embarrassingly entertained by just watching a ball bouncing back and forth.
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
So, this is what happened to my life, just constant changes in the little moments spread throughout the years, creating branching timelines in the tunnels of time. Just a small change in the decision making could significantly avert the whole course of my life, and so here I am now, living the life of a failure, while maybe some other versions of me in parallel universes have better courses of life.
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
