Varying the break-off condition when iterating the Mandelbrot set

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  • Опубликовано: 12 окт 2024
  • The Mandelbrot Set is the set of complex numbers c that remain bounded when plugged into the sequence
    z_0=0
    z_n=z_{n-1} ^2 +c.
    Practically that means you keep iterating the sequence until it has a bigger absolute value than a certain boundary, where you are sure it will diverge to infinity. Then you color that number according to how any iteration steps it took you to get there.
    After enough iteration steps you give up, assuming the number will never excel the boundary and thus is part of the Mandelbrot Set, so you color it black.
    For this to work you must choose a boundary as your break-off condition that is at least 2.
    In this viedeo I tune up the break-off condition from 0 to 4. So in the first half of the video we do not see the real Mandelbrot set, because we exlude numbers that are actually part of it.
    Music: Beginning of "Algorithms" by Chad Crouch
    licensed under a Attribution-NonCommercial License. (Link: www.freemusica...)
    This Video is licensed under a Attribution-NonCommercial-ShareAlike License. (creativecommon...)

Комментарии • 54

  • @mheermance
    @mheermance 3 года назад +8

    Interesting twist on rendering the Mandelbrot.

  • @СергейБолдин-в9м
    @СергейБолдин-в9м 2 года назад +3

    Yeah, I've finally understood how the Mandelbrot set gets his complicated recursion!

  • @XX-35withtophat
    @XX-35withtophat 10 месяцев назад +8

    The Mandelbrot zoom after eating too much brocolli:

  • @chrisrodriguezm13
    @chrisrodriguezm13 3 года назад +22

    this happens when you plant a mandelbrot seed

    • @shnmang25
      @shnmang25 10 месяцев назад +3

      And you eat the Mandelbrot fruit

    • @jahabarintos1518
      @jahabarintos1518 4 месяца назад

      and you die with it

    • @EvonaAstropod456
      @EvonaAstropod456 2 месяца назад

      ⁠@@jahabarintos1518and you turn into a Mandelbrot and then u be the most famous

    • @bhimgurung880
      @bhimgurung880 2 месяца назад

      Bro...

  • @zfloyd1627
    @zfloyd1627 3 года назад +19

    This is how the mandelbrot set grows from a seed.

  • @momiswatchingyou2488
    @momiswatchingyou2488 2 года назад +2

    0:20 perfect

  • @hyperbolictesseract6609
    @hyperbolictesseract6609 5 лет назад +18

    i bet you could stack the slices and make a 3D mandelbrot set!

    • @NonEuclideanDreamer
      @NonEuclideanDreamer  5 лет назад +7

      Yes, that should work.

    • @hyperbolictesseract6609
      @hyperbolictesseract6609 5 лет назад +2

      @@NonEuclideanDreamer you should do that and put it on your instagram!

    • @NonEuclideanDreamer
      @NonEuclideanDreamer  5 лет назад +5

      @@hyperbolictesseract6609 We'll see. I suspect it won't look good without shading and I haven't got around to that yet.

    • @chrisrodriguezm13
      @chrisrodriguezm13 2 года назад +2

      @@NonEuclideanDreamer Well this is the video what happens when you plant a Mandelbrot Seed.

    • @ryanmapping7944
      @ryanmapping7944 Год назад +1

      @@chrisrodriguezm13 MANDELFLOWER

  • @not_estains
    @not_estains Год назад

    One second lemme inflate my Mandelbrot

  • @chrisrodriguezm13
    @chrisrodriguezm13 2 года назад +2

    00:20 this bailout in ultra fractal is 4
    in Kalle’s Fraktaler is 2

  • @waterdragonlucas8263
    @waterdragonlucas8263 2 года назад

    I was expecting a jumpscare for some reason

  • @mistymysticsailboat
    @mistymysticsailboat 4 года назад +5

    interesting!

  • @N0vbzgv
    @N0vbzgv 11 месяцев назад

    I like this in 0:08

  • @chongkim-fh4zp
    @chongkim-fh4zp 22 часа назад

    I studied mandelbrot set in msc maths. Mandelbrot set is nothing but endless reiteration. Nothing spiritual, supernatural or remarkable.

  • @Nohandleok
    @Nohandleok 3 года назад +4

    made by ???

  • @AnComplexFraktal
    @AnComplexFraktal 11 месяцев назад

    This is also called "bailout growing"

  • @honeyobando883
    @honeyobando883 8 месяцев назад

    What z replace with )
    )^2 + C

  • @pasirhaurlogam5283
    @pasirhaurlogam5283 2 года назад +1

    1

  • @Md.Mars69
    @Md.Mars69 6 дней назад

    Formula:
    Initialization Code:
    bailout = Any Value
    Iteration Code:
    z = z2 + c

  • @para3668
    @para3668 3 года назад +2

    love mandelbrot crap also whats the song

    • @NonEuclideanDreamer
      @NonEuclideanDreamer  3 года назад

      Thanks! That's Chad Crouch, they have really cool Creative Commons Music. Check out the link in the description!

    • @para3668
      @para3668 3 года назад

      @@NonEuclideanDreamer crazy that you're still responding to comments after october 2019

    • @NonEuclideanDreamer
      @NonEuclideanDreamer  3 года назад

      @@para3668 what was in october 19?

    • @para3668
      @para3668 3 года назад

      @@NonEuclideanDreamer upload date lol

  • @vizart2045
    @vizart2045 2 года назад

    Theres a speed issue, but it doesnt matter all that much as long as its reasonably large.

    • @NonEuclideanDreamer
      @NonEuclideanDreamer  2 года назад

      Not sure what you mean.

    • @vizart2045
      @vizart2045 2 года назад

      @@NonEuclideanDreamer If you increase the break off condition you get more colours for your visualization but also a more heavy computation.

    • @NonEuclideanDreamer
      @NonEuclideanDreamer  2 года назад

      @@vizart2045 ah yes. In this code I use the computation from the previous frame for the next, so I don't need a lot more computation for the entire video then for the last frame.

    • @vizart2045
      @vizart2045 2 года назад

      @@NonEuclideanDreamer I was thinking in a more general framework.

    • @NonEuclideanDreamer
      @NonEuclideanDreamer  2 года назад

      |z|>2 is the most efficient condition. But for some Mandelbrot Variations it is difficult to determine.

  • @pomni_tadc_real
    @pomni_tadc_real Год назад

    If C Is Replaced By ꧅, It Is z2 + ꧅.