i'm going to grow a third shoulder bc of this video

@E-dart

Жыл бұрын

What

@bishop6308

Жыл бұрын

?

@defeatSpace

Жыл бұрын

they have a sodapeecanis

@virtualsocialretreat8234

Жыл бұрын

let us know how it goes pls

@cobalt2775

Жыл бұрын

​@@bishop6308 its the clear

It’d be pretty neat to see the billiard as a continuum, rather than a finite number of points

@Jasmixd

Жыл бұрын

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.

@EmeraldEmsiron

Жыл бұрын

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

@maxvangulik1988

Жыл бұрын

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

@maxvangulik1988

Жыл бұрын

@J4zzling dude where

@WalnutOW

Жыл бұрын

Idk how that would be possible to compute

That one green ball pissing us all off lol

This music sounds like the music at the end of an 80s movie where they write out what happened to the characters after the events portrayed in the movie.

@MattHudsonAtx

11 ай бұрын

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

So magical that it even created the symbol Ω

@DiamondSane

Жыл бұрын

truly

@neolithicz

11 ай бұрын

omega

@the_finkledinkle

Ай бұрын

Mart

I love this one green ball which doesnt care about what hes supposed to do and does his own thing

Interesting. At any moment, all of the balls can be grouped into arcs, of circles of different radii, but all centered at one of the two foci. When a ball bounces, it changes which focus it's centering on.

1:36 this also shows the butterfly effect as the two green dots become asymmetrical due to tiny imperfections

@luzellemoller6621

Жыл бұрын

Ok

@pressaltf4forfreevbucks179

Жыл бұрын

Some things cant be solved analytically. Only approximated

@user-pr6ed3ri2k

Жыл бұрын

​@@pressaltf4forfreevbucks179Is this really not solvable analytically?

@realburtle

Жыл бұрын

@@pressaltf4forfreevbucks179 tim ahh pfp

@dan-us6nk

Жыл бұрын

@@realburtle Burtle aah pfp

5:38 lol relatable

Pls make an hour long of this. I would watch it. Besides, i am curious if the balls will ever gather in a line again.

@trystanlamm6943

Жыл бұрын

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

@daanroelofs119

Жыл бұрын

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

@johnleclerc4507

11 ай бұрын

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

@firstnamelastname4582

11 ай бұрын

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

@vibecat7101

10 ай бұрын

​@@firstnamelastname4582 put the video on 4x speed

This needs to be longer! So good

the music is similar to the scene in Ferris Bueller’s Day Off when cameron stares at the details of one of the artworks in the gallery, which i find to be extremely appropriate.

@mikec6347

Жыл бұрын

I was thinking the Truman show.

@user-ro9md9wp3j

Жыл бұрын

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

Thanks! I'll make sure to look out for them.

This video was so much better than I expected Im so grateful that you make this content.

Thanks ellipse for reminding me of your focal points

Absolutely STUNNING to _see_ the properties of an ellipse. More of these and longer. Different start settings. Beautiful music too; matches the theme.

This makes my ADHD brain happy, the cool visuals combined with the uplifting soundtrack Thank you for producing this

lol what happened to the one green dot

@BarderBetterFasterStronger

Жыл бұрын

Something asymptotal, if I had to guess.

@artursruseckis4242

Жыл бұрын

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

@BarderBetterFasterStronger

Жыл бұрын

​​​@@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.

@mingyue_chen

Жыл бұрын

​@@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.

@PacoReer

Жыл бұрын

@@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

I'm cheerin for the lil green guys

sheesh. I have seen ur ellipse vid. That was amazing!

Beautiful.

I just knew the elipse would be the most fascinating conic section to do this sort of simulation with ... VERY captivating!

Fascinating.

This is awesome geometry!

I could watch this for like an hour

As someone explained a while ago under Nils Berglund's video, the reason is because points will always go through the horizontal axis on the same side of the foci they started in : • If the point first goes between the foci, then every bounce after that will make it pass between the foci again. • If it first goes between a focus point and the "wall" of the ellipse, then every bounce after that will make it pass between a focus point and the wall. In this case, every point starts out in the middle, moving towards the rightmost point of the ellipse. That means every point goes between a focus point and the wall. Try to imagine the line between the two foci, and watch that line. You'll notice that, except for a single point that's sitting almost exactly on that line at the beginning, there's never a single point going through it ! And so, they will spread out, but never actually go between the two foci, eventually "circling" around the foci. To show this, I'd love to see another simulation, but this time clearly showing the foci and the line segment between the two, and with the points starting in the top right corner, moving down to the right of the focus point. We should see them "circle" that line, but never actually cross it.

If you were to place in the ellipse points of a random angle, but visualized them as near transparent circles, it would highlight areas where the points become concentrated

Ive never felt this calm before in my entire life

This was mathematically truly beautiful.

let this thing go on for an hour pleaaase!

I have no idea what I'm watching... but for some reason, I can't stop

Love it to watch this

The fact the the green balls that were sort of outliers ended up coming back to the main constant area thing is just incredible!!!! Math, wowww?!,!

I wonder if we would see the same divergent behavior with the green balls, if those were idealized points, instead of finite sized balls. Would they stay in line with the rest of the balls if they were? And if the balls were larger, would we see more spreading like the green balls?

@unitrader403

Жыл бұрын

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

@Yora21

10 ай бұрын

@@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.

this is kind of like how light focuses to a point on curved mirrors

@JW-oe6nw

Жыл бұрын

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)

@totally_not_a_bot

Жыл бұрын

@@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.

@JW-oe6nw

Жыл бұрын

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

I could watch that for a very very long time

It's like failing to tie a knot over and over again

Thanks Ellipse! I almost forgot where your focal points were!

Focal points? More like “Fantastic? Sure is!” 👍

That was ellipse points😍!

what a nice ellipse. saved students from minutes of work 😊

Focal points playing peek-a-boo

I love this because I forget everything around me when I Watch that

Interesting to see circles continue to emerge

Thank you, ellipse :)

Nice title! Nice video!

Feels like a couple of the green balls glitched out of the regular path considering how out of place they looked.

This is what's happening in my cat's brain at 4 AM.

My satisfaction is immeasurable

I have been reminded

I love the green dots.

The song is like a mashup of Ravel's "Bolero", Lorde's "Royals", and Glass's "Naqoyqatsi"

❤😮

Joined for the video, stayed for it and the gta v loading theme

Please, make 10 hours version of this! 🥺🥺🥺

I have some weed called Amnesia, and it has 34% THC. I watched this video while high, and I'm pretty sure I just went back in time. I certainly feel younger now.

how long would it take for all of those dots to assemble back into its formation at the beginning of the video?

@animations_ag

Жыл бұрын

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).

@jamiewalker329

Жыл бұрын

That's the Poincaré time right?

Server: Omega has joined the game...

Imagine if you had to calculate and plot this by hand, every single frame for every individual piece would need to be perfect or it all falls apart.

Get you someone who looks at you like that red dot and that purple dot looked at each other

Hey. Maybe you could make this with the full rotation?

Does it recover its initial config after a long time? Is it cyclic?

DVD screensaver vibes

that's a lot of balls

Literally everyone waiting for it to make circle

Pretty neat. Whats with the green odd bois off doing their own thing?

it keeps making little omegas

The foci of ellipses are enigmatic in their beauty

@momom6197

Жыл бұрын

What is enigmatic about this?

@fanamatakecick97

Жыл бұрын

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

@momom6197

Жыл бұрын

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

@fanamatakecick97

Жыл бұрын

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

@fanamatakecick97

Жыл бұрын

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

0:57 omega!!!

2:04 Omega lol

That one dot....

It is interesting to see what happens if pieces 🚫👻& can collide with each other pices

idk what tf a focal point is but this vid hits different

2:47 Dolby Atmos? XD

My brain is having an aneurism

1:28 ablittle smiley face :)

Watching this on 1.5x speed with the sound muted so I don’t go insane

0:56 OMEGA Ω

Im going to grov a third eye

i should watch this video when i'm high

Circles and ohm signs.

1.75 playback speed is where it's at for this one...

Those are circles. But their center shifts inwards over time. So these are not the focal points. The centers probably drift to the focal points, but that is just a hypothesis right now.

Can you do 1 MS WIndows logo in a rectangle?

Mathematical hypnosis

I think its a metaphor

Why the green dots do not influenced to the courses of others?

4:29 kind of looks like a sideways division sign

This is just clever marketing for DC comic!

One green ball kind of got out of sync toward the end. I felt sorry for it. Maybe it represents me. Lol 😆

The earth is also an ellipsoid as are the orbits of the planets O_o

those green ones get pretty goofy

but HOW though??

Try to guess the eclipses foci: Level EASY

2:28 "Don't care" WHAT DID U SAY TO ME?

Why am I watching this?

0:44

0:48

2:31 dc?

0:58 O