A zoom into the Butterfly Effect

Рет қаралды 23,686

Ай бұрын

Welcome back!
In this video I show the great impact that a small variation-just 5 pixels at the outset-on the future. I also increase the sampling of balls to bring order to the apparent chaos that unfolds.
Did you know that with every ball collision in a single frame, the algorythm solves at least one 4th degree equation with a precision of 34 decimal figures?
Technical part:
Since last video, I've been hard at work refining the precision of the bouncing mechanics, upgrading from 64-bit double floating-point to 128-bit decimal calculations, which has resulted in more natural ball bounces. I also fixed bouncing in some challenging edge cases and addressed several pesky bugs along the way.

Пікірлер: 64

@thecomet8759 11 күн бұрын

Butterfly effect? Entropy? Nah, this is art

@LetsBounce1 11 күн бұрын

Thanks! It's great to hear you see the art in it too! 🌟

@EmreEgeGurbuz 2 күн бұрын

Me too

@abdijabarkhalif 18 сағат бұрын

@@LetsBounce1 it is mesmerizing

@Peluceus Ай бұрын

With the last animation, Tom Scott's video on snow and confetti in video comes to mind. It's an interesting connection between when the order starts and the video is crisp and clear - and you can see the compression begin to struggle to keep up once the balls start to act as noise; all in real time.

@LetsBounce1 Ай бұрын

Well spotted! I watched Tom Scott's video when he first published it; he did a fantastic job explaining the effect :) It's great to see more people enjoying the same kind of videos as me. I noticed that it struggles even in 1080p... I didn't catch this because I only watched the exported video, which is almost lossless.

@mayorzulungo Ай бұрын

This shows perfectly how small variations compound into completely different results. I really enjoyed watching this!

@LetsBounce1 Ай бұрын

Glad to hear you enjoyed the video! Indeed, small initial variations can lead to vastly different outcomes. What I found particularly intriguing was demonstrating that no matter how far into the future you project, there's usually a relationship between parallel futures; it's not just chaos. It's just that we only perceive this relationship when observing many closely spaced variations.

@mayorzulungo Ай бұрын

@@LetsBounce1 Yeah, I agree. There is an order in what we perceive as chaos and it's perfectly symmetrical at all times.

@frankyanish4833 6 сағат бұрын

I feel it necessary to point out that this is not an example of chaos. It is a closed system of perfectly elastic impacts. The same starting conditions for the balls will give the same result every time.

@theepicninja1936 3 күн бұрын

I am your 200th subscriber!! I'm so excited!❤

@LetsBounce1 2 күн бұрын

Thank you for being my 200th subscriber! If you're excited, imagine how I feel! ❤

@jazzabighits4473 16 сағат бұрын

Reminds me of some of Mikan's stuff. Very soothing to watch.

@Operator256 2 сағат бұрын

I felt like I was sitting close to the one screen on old tvs

@lunchannelhiv709 3 күн бұрын

I call this butterfly insanity

@adelinasoniapetcu2711 Ай бұрын

Is there any chance that, after every ball gets separated from each other (chaos), they start reordering themselves?

@LetsBounce1 Ай бұрын

Unfortunately, achieving periodicity is unlikely due to the unpredictable nature of the initial impacts and the irrationality of trigonometric functions. Additionally, the presence of gravity further complicates the situation. In the absence of gravity, more trajectories would form loops, but the influence of gravity prevents such regularity.

@RoonieBarberien Ай бұрын

beautiful pattern

@LetsBounce1 Ай бұрын

Glad you like it :)

@MenacingPerson Ай бұрын

Would've been faster to generate the animation on a gpu, surely?

@LetsBounce1 Ай бұрын

In principle no, since the calculations are sequential, but it just occurred to me that the calculations of the trajectories of the balls could be parallelized using the different cores of the processor, since their trajectories are independent. Thanks for your comment!

@LetsBounce1 Ай бұрын

I just tested this improvement (parallelizing balls trajectories in CPU), and the execution time has dropped from 3 hours to just under 39 minutes!

@MenacingPerson Ай бұрын

@@LetsBounce1 Nice!

@andremarquesdossantos5423 Күн бұрын

Your mind if your an artist 3:16

@user-vm5tt1ql7l 6 сағат бұрын

Wow That was good

@hust_man Ай бұрын

wow! very underated!

@LetsBounce1 Ай бұрын

I appreciate that!

@TexasCountryBaller Күн бұрын

*SILLY STRING*

@tenhayz1889 2 сағат бұрын

Is it possible to extrapolate the starting state from later states? Does it stop being possible at some point?

@LetsBounce1 Сағат бұрын

Yes, it is possible (within the limits of the precision allowed by finite decimal places), since the bounces against the walls are always symmetrical with respect to the perpendicular, regardless of the direction from which the ball comes

@TosGD 22 сағат бұрын

nice processor btw

@LetsBounce1 21 сағат бұрын

Thanks! It gets the job done well :)

@TosGD 21 сағат бұрын

@@LetsBounce1 I only have 13700F :(

@LetsBounce1 12 сағат бұрын

that's still very good!

@AstroMicroBro 2 күн бұрын

What's the music name?

@LetsBounce1 2 күн бұрын

It's called 'Wandering', but I don't remember the exact title. I downloaded it from Pixabay

@TheSyporg Ай бұрын

How can i do this as i really liked what you did and would to do some tests on my own

@LetsBounce1 Ай бұрын

You need proficiency in programming, understanding of trajectory dynamics (physics), and the ability to solve 4th-degree equations (mathematics). If you manage these, I can give you some hints to develop it.

@TheSyporg Ай бұрын

@LetsBounce1 I guess I've got work to do But like can't you make it an website or something or can't you

@LetsBounce1 Ай бұрын

@@TheSyporg It might be feasible with a rectangular frame, unlike the circular one in this video, which would require more computing power. However, I don't have enough time to develop a user-friendly/online playground as I have a full-time job during the day.

@TheSyporg Ай бұрын

@LetsBounce1 thanks for the effort you put in your videos

@boscoyuen8970 Ай бұрын

So cool animations and 88 subscribers? Lemme fix that🔨🔨🔨

@LetsBounce1 Ай бұрын

Thank you so much for subscribing! I really appreciate your support and I'm glad you're enjoying the animations. Welcome aboard! 🚀

@zebraforceone 12 сағат бұрын

Your render times are awfully high, 10k particles with no self collision should be possible in real time. Maybe slightly slower if you're encoding HD video on the fly. You're using the GPU right?

@LetsBounce1 12 сағат бұрын

First, let me say that I am by no means an expert in animations, collision detection, rendering, or reallife simulations. This is just a hobby project. To answer your question, for rendering, I use the GPU, but for collision detection (even if it's only with the circular wall), I currently have to do it on the CPU because it's more complex. The reason it takes so long to process is because I use 128-bit precision decimal numbers (which enable me to operate with up to 34 significat digits where needed) to solve quartic equations (4th grade). The double-precision floating-point type has two issues: first, the calculations were incorrect because some operations require more than 16 significant digits, and second, the imprecision of binary decimals. Operations with this type of numbers (decimal) are much slower than with typical double/float/integer primitives. However, I have made many optimizations and parallelized calculations (using all 32 CPU cores), so now what used to take me 3 hours when I made the video can now take 5-10 minutes. That said, the computer does heat up my room 😄

@zebraforceone 8 сағат бұрын

@@LetsBounce1 ah nice yes the 128 bit will be a killer

@adelinasoniapetcu2711 Ай бұрын

👏🏼👏🏼👏🏼

@adsadadadadadadadassa 7 минут бұрын

lets increase the number of balls

@JordanEr-vy8xy 9 күн бұрын

4:20 old

@JordanEr-vy8xy 9 күн бұрын

1:13 op

@AdvikTekkieTalk Ай бұрын

Dude I am pretty sure in the beginning you're changing the wrong variable in your experiment, you shouldn't change the number of balls as that has 0 effect (no collisions), you should've changed things such as gravity (which you did later on)

@LetsBounce1 Ай бұрын

You're correct, adding more balls won't affect the trajectories of the other balls. But what I found particularly intriguing was demonstrating that no matter how far into the future you project, there's usually a relationship between parallel futures; it's not just chaos. It's just that we only perceive this relationship when observing many closely spaced variations.

@LetsBounce1 Ай бұрын

In fact, as long as gravity is not 0 and the initial velocity of the balls is 0, as in this animation, the gravity doesn't affect the trajectories of the balls other than their speeds.