This would be interesting to see but "scaled through time" (or bounces). So, you use the same system with the bounce & colors, choose some good resolution. Than you fill it out by using 1 bounce, take a snapshot, then reset & do the same with 2 bounces, then snapshot & reset, then 3 bounces, and so on... Or alternatively, you can use time, like after 0.1 second, then after 0.2 second, then 0.3 second, and so on. It would also be useful with unique colors, currently the green & blue is duplicated, so you can't really know if the "tile-color" belong to the left or right green, or so.

Do you have the actual image files? On KZfaq, even with max resolution, the details still look pixelated

PLS make an online simulator

Same.

This comment sounds like it was written by an AI, and not even a good one

@@enricofaa9302 Your comment sounds like it was written by a human, but not a good one

Oddly specific

@@olbluelips That is a very good comeback. I consider myself defeated

That's a nice way of putting it for someone that hasn't made the connection

Well said

For midair balls, would color be assigned by nearest point, or point directly below, or some other rule?

​@@kevinmathewson4272 i don't know

@@kevinmathewson4272 I'd say color below

I think it would be more fair to assign the color according to the nearest point Or we can make two versions of the animation, one with the nearest points and another with the point below

Last contact

My son has taken a keen interest in becoming a landlord but has also started insulting me for not owning and not owning my own house. Billy Ilish is not the return of an astronomer. How are you, Tommy, Tommy, I visited TCT this weekend, not just because I'm a Cystro fan.

HAHAHA I DIDNT NOTICE THAT

Bounce twice, then place a point halfway along the arc. Maybe?

​​@@mygills3050 you can take the halfway point of the arch and use the point below, or you can take the nearest point in the circumference

half a bounce

Every bounce is predictable. It's a chaotic system because a very small change in the initial condition (drop point) cause large change in ball location as time advances. In short, two balls dropped a pixel apart might be in very different locations on bounce 20. However for any single drop point bounce 20 will always occur at the same point, very predictable. Chaos has nothing to do with predictability.

Thank you :). I have yet to see 3B1B's fractal beauty though. Another viewer suggested doing something similar like this. That user referred to 3B1B, so indirectly I'm obviously inspired therefrom. I'm saying this since I think it's important, or at least good practice to cite inspiration and ideas properly.

@@animations_ag I think it's well known enough that chaotic iterative and dynamical systems lead to fractals in the numerical methods community that it's hard to associate the inspiration to any one person. I had generated similar patterns 10 years ago in my undergrad course (which led to grad studies), and I love how KZfaq creators are now popularizing the beautiful resulting patterns.

haha

haha

Are you talking about ray-casting ? It looks like you are but with multiple rays by pixel, which doesn't make a lot of sense (you would just get a blurry image, it's like when someone that have glasses isn't wearing them, the focal is not in perfect and thus create something similar)

A ball is being dropped onto half of a circle according to simulated physics. The circle is colored certain colors on every part. The ball is let bounce a number of times, and wherever it stops is recorded as the original positions color. so drop a ball from a certain position, let it bounce some number of times (I'm not sure what it is, I'm sure you could count the number of bounces they let it do), then see where it lands on the circle, and map the color that it landed on to its original position. The positions get more and more specific as the video goes on: i.e. they are dropping much more balls from much more positions. Interestingly, this forms a "fractal": a shape that repeats. If you look at the top, you can vaguely see a pattern that is getting smaller and smaller towards the top. It would probably be more accurately visible if he dropped more balls and let them bounce for longer, since: ultimately, this video is made to be in relation to a different video about the Butterfly effect simulated by dropping balls at VERY slightly different positions, and watching the balls slowly come apart as the slight change in position continues to multiply everytime it is bounced.

I always strive for high resolution but that wasn't possible here. I blame my bad coding skills. The "high res" fractal images had ~600x600 px and they took ~30 hours each to compute. I know this sounds silly, but I couldn't make it faster.

Oh wow it is😮

It's titles This equation will change how you see the world

Yes look at the top.

I think you are right. This images shown here are no "true" fractals. On the other hand, I guess the video suggests how to generate a fractal for this system. For that to happen, we'd probably need an infinite number of bounces (or infinite time).

@@animations_ag I think infinite bounces/time wouldn’t make sense because almost everywhere there would be no limit (if we don’t lose energy on bounces) or the same limit (if we do). Anyway, computable finite approximations to that would be prone to the nonfractalness described above.

​@@enhydramatic Your are probably right, again :). It's puzzles me a bit, though - when do we actually have a fractal here, if at all possible? I should perhaps mention that I'm a physicist and not even close to an expert here.

@@animations_ag I’m no expert either - and am puzzled by the very same question! From what I’ve found without digging too far - known fractals are either explicitly defined as repetitions of actions (e. g. Sierpinski triangle) or they arise from properties of infinite iterative processes (Mandelbrot and Julia sets and the like). An intuition of one such case and a reason for its fractalness is explained really nicely in a recent 3Blue1Brown’s video (kzfaq.info/get/bejne/Y7iUgtqZ0te0Zac.htmlm56s). Bouncing a ball is an iterative process indeed. What’s lacking is the opportunity for discretely different behavior - akin to Mandelbrot set’s members not escaping to infinity and non-members’ doing this. This behavior has to be affectable by arbitrarily small changes (which is necessary but not sufficient, you’d need additional reasoning and/or zooming into resulting images to verify). You could make the bowl escapable (like part of sine wave between two maximums) and maybe plot how many bounces / how much travel distance is needed to escape for a given starting point. Introducing tiny loss of energy will probably make this more interesting. I’m still not sure whether that would yield a true fractal, but seeing the result of this will inspire further thinking and tinkering (and I’ll come back if I can think of anything as well). I wonder if your code would generate the fractal picture from this video (or something with a similar idea) quickly enough, and what is going to happen with its speed when it suddenly needs to handle numbers with hundreds of decimal places (so that zooming is possible). This way, you could explore and find interesting locations, and then generate a smoothly zoomed visualization.

In principle yes; however my script is too inefficient to do something visual out of it in that respect. I compare 6 and 10 bounces in the end though.

Or a ring, roughly analogous to a torus?

That's a good question, which we discussed in a comment here some year ago. I think someone more mathematically talented than me has to answer that question.