Ellipse reminds you of its focal points 

What

?

they have a sodapeecanis

let us know how it goes pls

​@@bishop6308 its the clear

I'd say that would lose some information about the "density" of the formation. Or at least the ease of noticing the changes, since you could still use the colours for that, albeit with less ease.

​@Jasmixd maybe a colour spectrum representiny the 'density' of the function at any given point

@@EmeraldEmsiron ah, density rather than initial angle. Good idea!

@J4zzling dude where

Idk how that would be possible to compute

In theory I believe they would but it might take a very long time.

In theory, yes they will. In reality it might take longer than the time left till the heat death of the universe

@@daanroelofs119 not if i put the video on 2x speed

@@johnleclerc4507 I feel like even then humanity would destroy itself first

​@@firstnamelastname4582 put the video on 4x speed

Something asymptotal, if I had to guess.

Butterfly effect. Minor deviation at one point that lead to completely different trajectory pattern than the other dots in its initial proximity

​​​@@artursruseckis4242 I'm not sure this is a very good example of that. All the balls started at different coordinates with different initial angles of movement. The previous commentors question was more, why is the single green ball so out of sync when all other balls continue to follow fairly clear patterns. I think the variance of the paths of the balls seems to increase exponentially the closer it passes to the focal points of the ellipses. After a few viewings, you can see that the "new" circles in the pattern always appear first from the sample of green dots. Indeed, I suspect if we had a denser or continuous serious of dots (hey, that's a line) the single green dot's strange trajectory would just be part of the newest formed circle, one that the other dots in the video were not close enough in starting position to also be a part of. In a way, the first dot to appear out of sync with the others just implies that dot's closeness to being in line with the two focal points. You can also see that by the 5th/6th bounce, none of the dots' are even on the equator of the ellipse. And if you follow the paths of the closest green dots, by the 7th bounce, there would have been new circles forming that we can't even see because none of the dots were in line with the focal points enough to show them.

​@@artursruseckis4242 Clearly not. If you watched the other vidoes of this channel you would get a better idea of what butterfly effect really looks like. It's fundamentally different from what's happening here. Here, the green dots diverge in a very regulated circular pattern. The new, very large green circle cannot be correctly represented simply due to the limited number of the dots, but it's still a very large circle as apposed to being chaotic.

@@mingyue_chen it is still a good representation of butterfly effect. All the green dots start at nearly the same point, but their small deviation ends up separating them further. This is a great video to see how the horizontal axis has more deviation to the rest of the ellipse

The bluest ball eventually graduated and is now teaching the 2nd grade

Ok

Some things cant be solved analytically. Only approximated

​@@pressaltf4forfreevbucks179Is this really not solvable analytically?

@@pressaltf4forfreevbucks179 tim ahh pfp

@@realburtle Burtle aah pfp

truly

omega

Mart

I was thinking the Truman show.

The music made my ears bleed. Where do people even find this garbage lol

there are two

nvm it became one again

the erratic green balls formed their own "circle", and it was also the leading one. but there were only 5 balls to fill it, so it looks like they were singular divergent ones, but if you pay close attention you notice that they also constantly meet at the focal points

@@unitrader403 I've been wondering if the appearance of single green point seemingly floating around by themselves with no matching mirror symmetric counterpart on the other other side of the ellipse might be an illusion caused by there only being a finite amount of discrete points? Maybe the chain has just spread out so much by that point in time that the simulation is down to only a single point it can display, even though there's actually still a a constant continuum of a single wave, and it's forced to put that one dot somewhere that is either moving into the upper or the lower half of the ellipse. Or it could be a tiny rounding error at the start of the simulation that keeps getting bigger with each bounce.

Good question - I wonder that too :). I've tried hard to find initial conditions which resembles its original configuration within after a number of bounces (without success).

That's the Poincaré time right?

This is exactly how light focuses to a point on curved mirrors! Parabolas and ellipsoids have foci which by nature of ellipsoids and parabolas are always in the resultant set of reflections of points passing through a focus. The beginning of the video has the points converge to the focus of the ellipse (or so it would seem)

@@JW-oe6nw The entire video has the points converging to the foci of the ellipse. You can think of the spreading as being similar to chromatic aberration, which all optics experience to some degree.

@@totally_not_a_bot hey that’s awesome! Thank you for that explanation!

What is enigmatic about this?

@@momom6197 The fact that they show up geometrically, even tho they’re invisible

@@fanamatakecick97 It's not enigmatic, it's because they're the foci of a conic curve. Conics have been extensively studied for centuries.

@@momom6197 True enough. Most people would find it puzzling, tho

@@momom6197 Actually, upon rereading my own comments, i said they were enigmatic in their beauty