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Adding dx, dy, dz to x,y,z repeatedly is called vertex integration. It is an easy way to break down and simulate a lot of complex interactions. Often used in games. (I was a game developer) in the early days every game was it's own engine. These days the 'game engine' takes care of all this 'complex' mathmatics. But if you have the brainpower for it, it is amazing to play around with. You'll never look at the world the same. I made (and sold) about 200 of these early games-that-are-game-engines in my life. Very thankful for that experience. Attractors are important, but they are just the tip of the iceberg.. most things are not really expressable in language.. possibly in maths.. currently trying that..

oow man, this is beautiful

lorenz attractor is similar to how i picture the universe except the "2 wings" are the surface of 2 blackhole like objects and we are in the x shape between them somewhere but they are also traveling so the trail is dna shape

Konrad was here.

i understand absolutely none of this but i like the funny moving dots

why do we possess the ability to find beauty in a concept so abstracted from the nature we evolved in and from? why did we evolve the ability to receive pleasure upon observing certain mathematical functions?

Chaos and Love. You have found an amazing discovery my friend. I am a very creative person, and this video strikes at the cores of my abilities. So thank you, just for sharing this. Beautiful find.

5:32 If I wanted to see a "Finance Attractor" I could just head over to Silicon Valley and look at the newest dumb VC startups

the chen-lee attractor reminds me of the Sistine Chapel

Good choice of music - _Engulfed Cathedral_ - Debussy

5:34 I need one of those

But how does this affect side-fumbling on the grammeters?

Which tool is used to create these mathematical graphs and stored as a video

The riemann Zeta function plotted on the critical strip looks also like an attractor.

Magnificient!

"Mommy, what constellation is that?" "Shut up, have a cookie."

I could watch these for hours

Fuaa sarpado en hermoso

What visualization software is used here?

*windows screensaver joke*

I don't understand math behind these but chaos is truly amazing and beautiful

Great job! Have you tried Ikeda map? I like it a lot

Absolutely Beautiful, thank you for taking the time to create this. 🙏👏👏

Perfect choice of music!

I wish you would add some info on what this attractors modulate. Maybe in the pinned comment with the links or something. They are pretty, but I believe understanding of what they stand for would add to the experience

Halvorsen attractor, very sick!

Debussy was transphobic

essentially a torus sliced into thin planes

Many examples are far too brief. Beautiful visualisations; please consider uploading more video, for the sake of humanity! How about a visual comparison of successive iterations of different inputs to the Mandelbrot equation?

All in All. the 1. when the lights move in harmony the All is visible. its like the darkness is appearing on itself as light its flip side, awesome

Very fascinating. Looks like energy being simulated.

watch on acid... 10/10!!

it looks like stars dancing on the canvas of a blank cosmos.

🧲🌡️📡🔆☢️🔌🔊🔋♻️🌐☯️⚛️ It's facinating how all this complexity with-in the Universe. It basically comes from: ~{"Differences"}~ That "factor" seems to be the key factor in keeping dynamic systems functioning. Just look at the detail with-in Jupiter as an example: *{High pressure/low pressure, hot/cold temperatures, different densities, viscosities, turbulent flow, static electric charges/discharges, electromagnetism north/south poles, different velocity/angular momentum, different amounts of energy/mass/frequency/vibrations. Different boundary layers between different regions such as: (Land/water/air/layers of the atmosphere/space/ the different regions in space with different particle density/background radiation, solar wind/membrane layers/bubble's/cloud regions, nebula's/Galaxy's/Galaxy clusters/ Cosmic filaments/less dense regions of space compared to dense regions of space.) All of these things are basic differences but create a way for the dynamic engine with-in Nature to continue flowing and operating to create and convert energy.} Just Like How a battery 🔋 transfers + charges through a membrane layer to a - charged side. Like how regions of high/low temperature 🌡️ create winds. In water- add some factors and It creates ocean currents and flow. Then internally inside our planet it creates plate tectonics, planetary convection, geothermal activity, a magnetic field around our planet, to hold a atmosphere. The list goes on 🧲🌡️📡🔆☢️🔌🔊🔋♻️🌐☯️⚛️ The natural world around us is just utterly facinating to me.

If you can get the drones with the LED's With formation control to Play this😊

Are there other Chaotic Attractors? Why yes there are, my ex is one of them.

What if you weren't British

Bro makes a single video and it is incredible

They call my stepdad a chaotic attractor

Never in my life have I felt the need to have a screensaver. Until now.

The only other chaotic attractor I see is myself.

very attractive video

The piano is a very nice touch

So stupid, it's just a screen saver lmao

Wouldn’t the attractors make the equation and point less chaotic? Is it only called chaotic because it’s unpredictable to when the point will come near the attractor?

there’s something so philosophical to this kind of math, it’s so mystical in its abstractions whenever you derive some sort of physical idea from it, it feels so much better than just saying it.

So many of these remind me of illustrations of a toroidal field created by a magnet, sets my brain on fire thinking about possible reasons for the similarities

Someone please turn this into a 3D display that can sit on my desk.

The chaos theory rabbit hole is complex

1:50 what in the