In this thread, I will try to explain you the chaotic systems and if chaos and random are the same.
This is a really fun to watch video. But what happens here? Let me explain.
What they do is chaotic motion rather than random motion. Chaos is between predictable and random. Chaotic systems can indeed be predicted but they are very sensitive to initial conditions. Even the slightest deviation can cause unexpected changes, which is kinda what Butterfly Effect is.
When it's just a single pendulum with only one point of freedom, it is pretty easy to guess what kind of motion the pendulum will do. But when the second pendulum is set free, things change. As you can see, there is no visible pattern. But as I explained before, not having a distinct pattern does not always mean that it is random. In fact, this motion also is a chaotic motion. Better visualization:
And the chaotic part of it, just a minor difference in initial conditions can cause serious deviations as can be seen below:
Butterfly Effect in A Circle
This is a really fun to watch video. But what happens here? Let me explain.
1 Ball
At the first animation, we see a single ball with radius R doing free fall motion inside of a circle. It is an easy to understand animation, just a single ball falling.2 Balls
At the second one, we can see there are 2 identical (except their colors) balls separated by a hundredth of R (0.01*R). They are so close to each other that most would think they would follow a similar path. Well, they do, for a while. But after a certain period of time, things change. They act way different than each other, almost... Randomly? Well, no.What they do is chaotic motion rather than random motion. Chaos is between predictable and random. Chaotic systems can indeed be predicted but they are very sensitive to initial conditions. Even the slightest deviation can cause unexpected changes, which is kinda what Butterfly Effect is.
100 Balls
And finally, for better visualization, 100 identical balls separated by 1-e6*R (0.000001*R) fall inside of the same circle. They start to create a beautiful view after a while. But then, it's total chaos.The Double Pendulum Experiment
When it's just a single pendulum with only one point of freedom, it is pretty easy to guess what kind of motion the pendulum will do. But when the second pendulum is set free, things change. As you can see, there is no visible pattern. But as I explained before, not having a distinct pattern does not always mean that it is random. In fact, this motion also is a chaotic motion. Better visualization:
And the chaotic part of it, just a minor difference in initial conditions can cause serious deviations as can be seen below:
