The Chaotic Beauty of the Double Pendulum Fractal

The Double Pendulum Fractal & It's Chaotic Beauty

Dive into the mesmerizing world of chaotic systems with "The Double Pendulum Fractal." This video explores the double pendulum, a fascinating example of chaos theory where small differences in initial conditions lead to dramatically different outcomes.

Motions in chaotic behavor is based on nonlinearity of the mechnical systems. However, chaos is not a random motion. As you have seen, the motion can be described with a specific nested structure, which is called fractal.

While the chaotic behavior of the double pendulum is well-known, its fractal nature based on initial conditions remains a relatively uncharted territory.

Using advanced numerical simulations, we reveal the intricate fractal patterns that emerge over long timescales in the double pendulum's time evolution. You'll discover how energetics shape the gross structure of these fractals, exhibiting quasi-self-similar properties reminiscent of classic fractals like the Mandelbrot and Julia sets.

Let's unravel the dynamic pendulum's secrets and the beautiful, chaotic fractals hidden within. Whether you're intrigued by the butterfly effect, dynamic pendulums, or the satisfying gradients of periodic motion, this video is a simple explenation through the double pendulum chaos and the stunning fractal landscapes it creates.

#chaostheory #pendulum #fractal #SoMEπ #SoMEpi

[RecordedSpace]

Visualizing the varying angles progression as a fractal evolving over time is such a creative way to view chaos theory that I haven't seen anywhere else before. And it looks so beautiful.

[ellingeidbo]

Breaking computers by asking questions too hard for them is one of my favorite things to do.

[Savahax]

Woah amazing. That's the typical misunderstanding, or rather misuse of fractals shown right here. A fractal typically isn't self familiar. The reason we focus on those is because they're beautiful and easily produced but a fractal usually is way more chaotic, like the one shown here. It's awesome man, great vid

[thelightmare]

Superb video, very nicely explained ! I would have loved to see a zoom into the fractal !

[samevans]

Some clips from this video could be dropped right into an Apple keynote and no one would bat an eye.

[AlanZucconi]

The production on this video is SO! high! 💪

[Byron_Vega]

I love the narration style, it brings back so many memories.

[dante]

To find videos like these, that are high quality and full of information is a rarity these days. So thanks Nicogs Playground, Great Video!

[JRMI]

The video quality and production level 🫡 worth the sub

[Froany]

Thank you for sharing such beautiful, inspiring animations!!

[DanteValenzuela-fgco]

Finally my home of content in the internet

[Makememesandmore]

Who agrees this guy is criminally underrated:

[sdf_]

love this video, cool asf. surprised you don't have way more views

[FoxDog]

2:07
I love how the corners can become a seizure trigger

I don't know how else to describe it, this is not a negative comment

[pnintetr]

Beautiful representation :)

I have always wondered whether the double pendulum would retain any sort of continuity after having heard of chaos theory.

But hey, it did (somehow)! and that is a nice looking turbulence.

[TobiasSchoenke]

Wow really great video - didn´t know these kinds of fractals - loving it! 👍

[holygod]

this is so good, it deserves a place in the yt trends ngl

[朕是神]

2:05 there's obviously something wrong with this simulation. Look at the pendulums at the bottom right corner. It's spinning around faster and faster, which means the mechanical energy involved is increasing over time.
Now, if I were to guess it's rounding errors which is unavoidable, but there are some simple error smoothing you can add: for every frame, after you calculate the angular velocity/angles of the next frame, first calculate the total energy invovled with that, and then normalize it back to the value you started with, then have the normalized result be fed into the next frame. You'll still get slightly off results, but it won't be quite this drastic.

[WhyIsJupiterInTheFridge]

For anyone wondering:
Blue = Pendulum at lowest
Red = Pendulum at highest
Darker = Low Velocity
Brighter = High Velocity

[EdwardNavu]

It's like splitting hairs when the differences accumulate to the point the conditions part ways and become no longer similar