A zoom into the Butterfly Effect - Part 1
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- Опубликовано: 29 авг 2024
- 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.
Part 2: • 100,000 BALLS!! A zoom...
As some of you have mentioned that my videos could be screensavers, please let me know if you would be interested in purchasing, for a symbolic price, screensavers of some of my videos 🤗
Butterfly effect? Entropy? Nah, this is art
Thanks! It's great to hear you see the art in it too! 🌟
Me too
@@LetsBounce1 it is mesmerizing
Yeah
Agreed
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.
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.
This shows perfectly how small variations compound into completely different results. I really enjoyed watching this!
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.
@@LetsBounce1 Yeah, I agree. There is an order in what we perceive as chaos and it's perfectly symmetrical at all times.
I love adding the butterfly effect to time because even the slightest change in the past can completely change the future
I am your 200th subscriber!! I'm so excited!❤
Thank you for being my 200th subscriber! If you're excited, imagine how I feel! ❤
I like looking for the shapes they make. Usually flowers, sometimes a face. Always beautiful.
The last 25 seconds are what we’d see if we could see through time, I bet.
I find it interesting that a circular boundery causes chaos and a hyperbolic boundery doesn't, or at least i havent seen a video of a hyperbolic boundery go on for long enough to tell if its chaotic or not.
That sounds interesting! I'll check out some videos to see the difference
10K was beautiful!!
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.
I agree, it's true that the system is deterministic for the reason you mentioned. But sometimes we call it chaos when a system's state is so complex that we no longer understand how it got to that point. Another example is Brownian motion. Fundamentally, it's not random because we could determine the cause of each movement if we analyzed every impact in detail, but we call it chaotic because it escapes our ability to analyze it.
@@LetsBounce1 my point is that each of the balls only interact with the wall. The interactions involve no entropy(chaos); they are perfectly elastic. That makes each ball a separate instance of a closed, 1-body system.
The animation(which looks rather cool) is overlaying these different systems upon each other to give an illusion of complexity.
@@frankyanish4833would a 2 pieces pendulum count as chaotic?
@@stefperb9531 if it’s not in a perfect vacuum with frictionless bearings? Yes.
@frankyanish4833 You have a good point, it's just an illusion of complexity
i find it interesting and cool that at one point you can kinda see the balls form a butterfly shape. a very trippy, hard to make out butterfly shape, but a butterfly shape none the less. kinda makes me question why butterflies look the way they do, even if the evolution of the butterfly probably (most definitely) has nothing to do with a bunch of small circles bouncing around in a bigger circle
4:11 that’s my jar of jellybeans😂
😂
Interesting, that no ball goes beyond the initial height, because of energy conservation, so you have a sea of static and that tiny part on the top with nothing
I felt like I was sitting close to the one screen on old tvs
Is there any chance that, after every ball gets separated from each other (chaos), they start reordering themselves?
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.
Thanks! I hope that my small token of appreciation sets the butterfly wings in motion for your piggy-bank to fill so that you can be further inspired to present us with more future relaxing and awesome,thought-provoking animations.
Reminds me of some of Mikan's stuff. Very soothing to watch.
beautiful pattern
Glad you like it :)
I call this butterfly insanity
I can confirm taht 65536 balls would be chaos.
@@truongquangduylop33yyuh34 why 2^16? 😄
2^32=broken @@LetsBounce1
I can call “The art of random”
okay THIS is what i was looking for!!✅ the science behind the bounce path, if that makes sense? idk but i imagine someone understands or knows the math behind this
The science behind bounces is well studied and understood in the right scientific comunity
I would call it the mirroring effect
Gumball machine at the end. Interesting how gravity stops everything.
Idk why but I think the patterns it forms are symmetrical
Although seems like it. Not a chaos at all. The most orderly thing there is.
😂
Would've been faster to generate the animation on a gpu, surely?
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!
I just tested this improvement (parallelizing balls trajectories in CPU), and the execution time has dropped from 3 hours to just under 39 minutes!
@@LetsBounce1 Nice!
wow! very underated!
I appreciate that!
this is technology
if you have a very powerful computer that is
What's the music name?
It's called 'Wandering', but I don't remember the exact title. I downloaded it from Pixabay
love ya vids
Glad you enjoy them!
Looks like a dmt trip at some points
nice processor btw
Thanks! It gets the job done well :)
@@LetsBounce1 I only have 13700F :(
that's still very good!
Is it possible to extrapolate the starting state from later states? Does it stop being possible at some point?
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
so satafing
Which game engine do you use to create this videos?
Just plain old java with javafx
So cool animations and 88 subscribers? Lemme fix that🔨🔨🔨
Thank you so much for subscribing! I really appreciate your support and I'm glad you're enjoying the animations. Welcome aboard! 🚀
4:09 how it feels when my foot falls asleep
I personally call it "a bunch of circles in a much bigger circle", but y'all seem to like to overcomplicate things
Your mind if your an artist 3:16
what software do you use to make these animations?
I dont use a third-party software, I coded it in java :)
Wow
That was good
This isn't really the best display of chaos. You've created perfectly predicable motion instead.
A double pendulum is a much better example.
You are right, from a scientific point of view it's not a chaotic system, as @frankyanish4833 also pointed out, it's just an illusion of complexity :)
Make it an interactive website
@truongquangduylop33 It could be possible with simpler animations and a rectangular frame, which would require less computing power compared to the circular one in this video. However, creating an interactive website would be a huge time commitment. Unless RUclips starts paying me to make this a full-time job (Subscribe 😂🤭), I can't dedicate the time needed because I already have a full-time job.
Touhou eat your heart out
M I R R O R
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?
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 😄
@@LetsBounce1 ah nice yes the 128 bit will be a killer
Can you do this but with Collision
"I'm currently working on the physics of collisions between balls. I'm facing some challenges when three balls collide in the same frame, but I hope to create videos featuring collisions like that in the future
How can i do this as i really liked what you did and would to do some tests on my own
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.
@LetsBounce1 I guess I've got work to do
But like can't you make it an website or something or can't you
@@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.
@LetsBounce1 thanks for the effort you put in your videos
Go go gadget pixel reducer 3:45
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)
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.
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.
100,000 balls?
It would be crazy, a mess! :D
uhhh I want to see I’m exciting
You asked, I delivered! Check the new video "100,000 BALLS!! A zoom into the Butterfly Effect - Part 2" now available on my channel!
4:10
It's a masterpiece ✨
Who agrees with me?
👇
524th sub
@@truongquangduylop33yyuh34 thank you!
1:13 op
👏🏼👏🏼👏🏼
*SILLY STRING*
This is not entropy
Wdym
One word can have multiple definitions. It's entropy as a measure of disorder or randomness in a system.
Is Pt.2 out yet?
It's in my channel, check it out in Videos tab
4:20 old
lets increase the number of balls
3:21 this was all just to flex his i9 cpu
Name game 😮
I believe it was coded in Python, it's not a game.
You're right, it's not a game, it's coded in java :)
Realizing the ball will never hit the top