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0:53 fish. shrinking.

Christian: this is really, really cool

@standupmaths splain

This is a reason why the slavery is a normal state of any state slavery system. Slaves just a region of stability.

Did anyone see the cube first?

love it

Fractal basin boundary. Cool 👍

This is a complete surprise to me. Never expected something like this to happen.

「安定の島」という表現が上手い

Cool. Now make bad apple out of this

I would sey the ant was always out side. it never was inside. toput this in perspactive a sphear is isolating the outside from the inside, but in this case for simplicity this shape is more of like a cup or a flusk: as small portion of it seems tobe enclosed an the othernis exposed, but over all its all exterior

thats not cutting the strip. you are elongating it

If you stop simulating pendulums that have definetly gone chaotic (maybe theres some algorithmic way of recognizing them) you can focus computational resources on the central/stable ones

"Puddle of stability" might be a more apt name, there seem to be waves travelling inside this Puddle

Another way to mentally form a Klein bottle is to start with a Mobius strip. A Mobius strip is only unbounded in one dimension - the path along the strip. If you turn 90 degrees and keep travelling across the strip, you will reach the boundary of the strip. So now, continue extending THAT boundary with a second half-twist until IT loops back on itself, so that now you will encounter no boundary either travelling along the strip or across it. The resulting manifold will be a Klein bottle.

Within these islands of stability, there should be some ponds of chaos. Regions that quickly deviate from their surroundings. You'd have to zoom in (reduce the angle ranges) and increase the resolution to find them.

Trial doing this with a hilbert curve next time

In its full glory!

Noticed you changed the thumbnail a few times. For what it's worth, i personally prefer the original one with all but the green ones in chaos Unless you're getting more impressions with this one 😁

Same sensation as seeing the afterimage shapes under my eyelids after staring at a bright source.

This is a real phenomenon and not caused by any computer rounding. Each double pendulum becomes chaotic after the lower pendulum makes its first full flip. For those in the bottom left and top right this always happens first on a leftward swing, while for those in the top left and bottom right this always happens first on a rightward swing. This means there has to be a saddle point where all four regions meet and this is the most stable point within this island of stability.

These are fun concepts to play with, although still impractical. e.g. The time travel Mobius Strip example: Still creates an infinite time loop. Also a paradox. Still impossible. But, sometimes fun to play with ideas.

Looks a bit like the USA 😮

i was waiting for the cube at the start

So what your saying is, I am seeing the 4th dimension in a 3rd dimensional visualization projected on my 2D retinas which is sent to my 1D brain. Truly amazing.

*Looks at map of Croatia.* "The answer's been staring us in the face the whole time!"

1:32 i know why its named annulus.

Looks like waves and erosion.

Oh boy this smells like fractal

It's really cool how after half the video the wave that crosses the island of stability can be clearly seen.

I saw it as a cube first

This particular Chaos God approves- Chaos IS Order. I really like this video, naturally. Seriously though, epic choices for the music! Not so Chaotic, as it should be but still great!

Is it in real time that they become this disorderly (like i n 5 mins) or is it sped up?

briefly, the island resembled the girl floating on a broomstick from bad apple, which gave me an idea: bad apple but it's double pendulum chaos graphs

excellent work! lol, i may have been a bit too high for it, but it was intellectually pleasing...thank you...

THIS IS WHAT A MIGRAINE AURA LOOKS LIKE. So many people have tried to visualize migraine auras but honestly this animation does it so much better. The blurb in the middle that shrinks is what the migraine Aura looks like

Awesome visualization

This is a pretty excellent visualization!

Cool video

Use radians and display as a sphere instead of a Cartesian plane

Obviously is a systematic error in the coding of it.

We stan loona

Artifact of digital simulation of the physical model but it is not physical !

I guess the shape of this island is fractal.

**my remaining stable neurons during an exam**

The stable pendulums all have a period of 3 swings (6 if you count back and forth as different). If you look at the behavior at the top of the arc, the connection between them has a pattern repeating over 1.5/3 swings. Its Above the end point Twice and then Below the end point Once.

0:01 chat i didn't see a hexagon 😭 i saw a square

"Ah, sweet child of Kos.... Returned to the ocean. A bottomless curse, a bottomless sea. Accepting of all there is an can be."

Entropy

everything is a donut