Doing it over time is a great way to see what’s going on. It makes the chaos not come from nowhere. It kinda shows that the chaos isn’t particularly meaningful, it’s just a result of mixing
Actually, a lot of phenomenon exhibiting chaos generate fractal when you plot whatever measure of the ending state with a color as a function of initial conditions. The most famous examples are probably the magnetic pendulum with 3 or more magets, the fractals of Newton-Raphson's root finding method, and Hofstadter's butterfly
Man, this makes me wish I knew how to program parallel threads correctly, so running a simulation wouldn't be painfully slow. Using GLSL is a nice solution though
Nothing is chaos. We use this word every time, because of our shameless ego, we do not accept defeat in understanding creation. Nothing is chaos, there are simply rules of creation too complex to be analyzed with our poor and small logical systems. Life is commanded, in the invisible, by such and so many complex laws that, in order to begin compressing them, we will have to start being less selfish, less stupid.. Starting to think about what creation really is.. . We will be shocked.. but the truth is shocking and this is the wonder of life! much more than what the media, that our bosses, want us to believe..
Chaos actually refers to what our knowledge can predict but with a very short range of coherency. I don't know any physicist that believe chaos is stuff that we don't grasp because we physically can't. Chaos in science is used for systems that are very sensitive to initial conditions and that exhibit similar patterns across all the initial conditions space (explaining the relation with fractals). The "very sensitive" is obviously relative to how precision of control and measurement. When you hear a scientist talking about chaos, they likely do not speak with assurance that they are discussing an intrinsically unpredictable phenomenon. They are using the definition above (that is partially relative to us)
This has very "God doesn't play dice with the universe" energy. Unfortunately for you, that saying was disproven a while back with the introduction of fields like Quantum Physics...
this ball is from deep space 9, you know the episode. the goal is to get it all one color. if it looks like this, your mind is too cloudy and unfocused.
In these screen simulations involving bouncing balls, I always wonder how the amount of "bounce" is calculated. I would think that that particular variable is the key to the whole thing, and it could be set at any desired value in these simulations.
I think it might be interesting to try multiplying the brightness by distance to center, so a ball at exactly the center of the circle at the end of the time would appear dark
every point on a vertical line hit on the same spot the first time but not necessarily on subsequent ones due to different heights imply difference in velocities
I have an idea. Perhaps it isn't as easily implementable, but if the coefficient of restitution is lower than one, where on the circle does the ball start to just "roll"?
