Andrew's Campfire
Andrew's Campfire
  • Видео 5
  • Просмотров 2 793 418
Order Within Chaos in the Double Pendulum (Island of Stability Simulation)
LONG-FORM VIDEO COMING SOON
In this video, every double pendulum consists of two weightless, rigid rods, each one meter long, with identical one-kilogram bobs at their ends. All 1600 double pendulums are simulated from rest in a vacuum, devoid of friction or air resistance, allowing gravity alone to influence their motion. The simulations are programmatically generated using the Dormand-Prince 8th-order method, with relative and absolute tolerances set to 1e-9 and 1e-11, respectively.
MUSIC
00:01 Fata Morgana (Instrumental Version) - Yehezkel Raz
03:23 Out of Flux - cdHiddenDir
06:21 Digital Abyss - Stephen Keech
SUPPORT
Patreon : www.patreon.com/andrewscampfire
GCash: imgur.com/a/3UOUHG6
Просмотров: 143 784

Видео

Intro to Topology - Turning a Mug Into a Doughnut
Просмотров 91 тыс.2 года назад
How can a doughnut be equivalent to a mug? CHAPTERS: 00:00 - Turning a Mug into a Doughnut 01:30 - Geometry vs. Topology 02:05 - Review on Polyhedra 02:58 - Euler Characteristic of a Sphere 04:07 - Euler Characteristic of a Torus 04:51 - Euler Characteristic Formula given no. of Holes 05:10 - A Homeomorphism Puzzle 05:42 - Puzzle Solution 06:54 - Topology Complexity Iceberg 07:07 - Closing Prev...
Paradox of the Möbius Strip and Klein Bottle - A 4D Visualization
Просмотров 2,5 млн2 года назад
Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you on a whirlwind tour of time travel, geometric paradoxes, 4D visualization, and sentient primitive shapes. CHAPTERS: 00:00 - A Hexagon Illusion 00:50 - Defining Topology, Manifold, and Boundary 02:11 - An Open 2D Manifold 02:25 - Riddle #1 ...
Why the Moon Doesn't Fall to Earth
Просмотров 29 тыс.3 года назад
Ever wonder why the moon doesn't fall to earth? Watch this short video to intuitively learn the simple reason behind it. SUPPORT Patreon: patreon.com/andrewscampfire GCash: imgur.com/a/3UOUHG6
Quantum Superposition and the Double Slit Experiment
Просмотров 24 тыс.4 года назад
This is my entry for the annual Junior Breakthrough Challenge. Thanks for watching! SUPPORT Patreon: patreon.com/andrewscampfire GCash: imgur.com/a/3UOUHG6 REFERENCES: Young's double-slit experiment with Single Photons and Quantum Eraser research paper: www.researchgate.net/publication/261011417_Young's_double-slit_experiment_with_single_photons_and_quantum_eraser Piezoelectric Resonator paper:...

Комментарии

  • @cultspina
    @cultspina День назад

    0:53 fish. shrinking.

  • @kipper1668
    @kipper1668 День назад

    Christian: this is really, really cool

  • @19phin
    @19phin День назад

    @standupmaths splain

  • @ufi9540
    @ufi9540 2 дня назад

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

  • @ChessCapital
    @ChessCapital 2 дня назад

    Did anyone see the cube first?

  • @rdkilla6414
    @rdkilla6414 2 дня назад

    love it

  • @sevenstars004
    @sevenstars004 2 дня назад

    Fractal basin boundary. Cool 👍

  • @Number_Cruncher
    @Number_Cruncher 2 дня назад

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

  • @user-slashed-O
    @user-slashed-O 2 дня назад

    「安定の島」という表現が上手い

  • @lepage7120
    @lepage7120 2 дня назад

    Cool. Now make bad apple out of this

  • @mositithulo287
    @mositithulo287 2 дня назад

    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

  • @mositithulo287
    @mositithulo287 2 дня назад

    thats not cutting the strip. you are elongating it

  • @cosimobaldi03
    @cosimobaldi03 2 дня назад

    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

  • @mastershooter64
    @mastershooter64 2 дня назад

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

  • @Mystikan
    @Mystikan 2 дня назад

    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.

  • @StarkRG
    @StarkRG 3 дня назад

    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.

  • @LazyUggugg
    @LazyUggugg 3 дня назад

    Trial doing this with a hilbert curve next time

  • @wada-wada
    @wada-wada 3 дня назад

    In its full glory!

  • @basiliotornado
    @basiliotornado 3 дня назад

    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 😁

  • @databang
    @databang 3 дня назад

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

  • @sophigenitor
    @sophigenitor 4 дня назад

    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.

  • @PALADINOFPALADIN
    @PALADINOFPALADIN 4 дня назад

    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.

  • @nicodesmidt4034
    @nicodesmidt4034 4 дня назад

    Looks a bit like the USA 😮

    • @nicodesmidt4034
      @nicodesmidt4034 4 дня назад

      Not that’s an island of stability now😂

  • @yusufunbilgisayardunyasi7454
    @yusufunbilgisayardunyasi7454 4 дня назад

    i was waiting for the cube at the start

  • @D2014isbackyt
    @D2014isbackyt 4 дня назад

    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.

  • @NWRIBronco6
    @NWRIBronco6 4 дня назад

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

  • @driske_real
    @driske_real 5 дней назад

    1:32 i know why its named annulus.

  • @TwilightStormshi
    @TwilightStormshi 5 дней назад

    Looks like waves and erosion.

  • @danigarcia2294
    @danigarcia2294 5 дней назад

    Oh boy this smells like fractal

  • @SomeoneCommenting
    @SomeoneCommenting 5 дней назад

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

  • @fan_of_fox
    @fan_of_fox 5 дней назад

    I saw it as a cube first

  • @Chaos_God_of_Fate
    @Chaos_God_of_Fate 6 дней назад

    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!

  • @mahimasanthosh3153
    @mahimasanthosh3153 6 дней назад

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

  • @ezdispenser
    @ezdispenser 6 дней назад

    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

  • @jeffgreiner4007
    @jeffgreiner4007 6 дней назад

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

  • @Memington
    @Memington 6 дней назад

    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

  • @ccederlo
    @ccederlo 6 дней назад

    Awesome visualization

  • @AsymptoteInverse
    @AsymptoteInverse 6 дней назад

    This is a pretty excellent visualization!

  • @ET-oq9mg
    @ET-oq9mg 6 дней назад

    Cool video

  • @erikig
    @erikig 7 дней назад

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

  • @mmokhtabad
    @mmokhtabad 7 дней назад

    Obviously is a systematic error in the coding of it.

  • @caleb__841
    @caleb__841 7 дней назад

    We stan loona

  • @michelfrance75
    @michelfrance75 7 дней назад

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

  • @joparicutin
    @joparicutin 7 дней назад

    I guess the shape of this island is fractal.

  • @andrewmynhier7733
    @andrewmynhier7733 7 дней назад

    **my remaining stable neurons during an exam**

  • @ParadoxProblems
    @ParadoxProblems 7 дней назад

    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.

  • @Dootcm
    @Dootcm 8 дней назад

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

  • @melijahv
    @melijahv 8 дней назад

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

  • @KythiraBF
    @KythiraBF 8 дней назад

    Entropy

  • @JohnPaulBuce
    @JohnPaulBuce 8 дней назад

    everything is a donut