The Logistic Map - Fractal Zoom

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  • เผยแพร่เมื่อ 2 ม.ค. 2025

ความคิดเห็น • 41

  • @live22morrow
    @live22morrow 4 ปีที่แล้ว +7

    If you rewrote the equation to be more similar to the mandelbrot equation (z = z^2+c).
    You could have z = -cz^2 + cz.

  • @Randomness65535
    @Randomness65535 4 ปีที่แล้ว +12

    This has a lot more symmetry than the mandelbrot doesn't it? Please make more zooms of this!

  • @ponluxime
    @ponluxime 4 ปีที่แล้ว +2

    Wow! Logistic Mandelbrot!

  • @claudiamendoza3301
    @claudiamendoza3301 3 ปีที่แล้ว +2

    z^2 - c^2 - 0.25

  • @ScaryOldMan73
    @ScaryOldMan73 3 ปีที่แล้ว

    How to set equation in Kalle's Fraktaler?

  • @Magillt-1
    @Magillt-1 3 ปีที่แล้ว +1

    2:01

  • @가시
    @가시 3 ปีที่แล้ว +1

    What formula?

  • @amokaanimationz240
    @amokaanimationz240 4 ปีที่แล้ว +2

    How beautiful

  • @kapt0xa_by
    @kapt0xa_by 4 ปีที่แล้ว +5

    What is this? It looks different to Mandelbrot fractal

    • @MathsTown
      @MathsTown  4 ปีที่แล้ว +4

      It's the logistic map equation, not the Mandelbrot. See the video linked in description for a full explanation.

    • @kapt0xa_by
      @kapt0xa_by 4 ปีที่แล้ว

      @@MathsTown ok, what does collor mean? how do u calculate collor?

    • @freshtauwaka7958
      @freshtauwaka7958 4 ปีที่แล้ว

      @@MathsTown
      It seems that you have to use the starting value 0.5+0i instead of the 0+0i used in the mandelbrot set though.
      Do you know why this is required?
      Obviously zero won't work because znext=c*z*(1-z) would map 0 to 0 so nothing would happen.
      But I believe for the logistic map in real numbers the starting value doesn't really matter. (as long as it's not 0 or 1)

    • @MathsTown
      @MathsTown  4 ปีที่แล้ว +1

      @@kapt0xa_by Colour is the iteration count. The algorithm used to produce the image is the same as the Mandelbrot Set, just a different formula is used.

    • @MathsTown
      @MathsTown  4 ปีที่แล้ว

      @@freshtauwaka7958 The value is chosen because it maps back to zero, when you map the formula back into the Mandelbrot Set. If the logistic is x=rx(x-1), and the Mandelbrot z=z+c, then I think, from memory, the change of variable is z=r(1/2-x). So you start with x=1/2, to get z=0. (Additionally, there is also a change of variable for c/r, if you want to convert the full form). Your right, r is a parameter you can adjust in more normal uses of the function.

  • @OliverrandontheRails
    @OliverrandontheRails 3 ปีที่แล้ว +1

    This is actually a power 1 lambada fractal

  • @dxtrum
    @dxtrum 4 ปีที่แล้ว +2

    I fear the brot has been beaten

  • @horseshoehimself
    @horseshoehimself 2 ปีที่แล้ว +1

    That fractal is called the "Lambda" fractal.

  •  4 ปีที่แล้ว

    Lindo! Gostei Muito!

  • @FlyingSavannahs
    @FlyingSavannahs 4 ปีที่แล้ว +2

    Me: Firsters!
    Marvin the Robot: Can't bear them.

  • @igorjosue8957
    @igorjosue8957 4 ปีที่แล้ว +1

    The fractal: A
    what i think of he:
    🙂
    🙃

  • @liamtran4731
    @liamtran4731 5 หลายเดือนก่อน

    Why Double

  • @billtomson5791
    @billtomson5791 4 ปีที่แล้ว +2

    Hi maths Town, I get to be your first comment! Yay!

  • @DMdarkmatter
    @DMdarkmatter 4 ปีที่แล้ว

    Does'nt its just a power 3 mandelbrot set?

    • @MathsTown
      @MathsTown  4 ปีที่แล้ว +1

      No. The symmetry is only 2-way not 3-way. And its full of mini Mandelbrots. (See link in description for an explaination of the Logistic Map)

    • @soouG.
      @soouG. 4 ปีที่แล้ว

      it does look similar to a rotated power 3 Mandelbrot set, but yes I understand that it's only 2 way.

  • @AilahsCreation
    @AilahsCreation ปีที่แล้ว

    its just a lambda or also known as logistic map from mandelbrowser and mirrored
    its not z = -cz2 + cz its wrong

  • @jhomzkie123
    @jhomzkie123 4 ปีที่แล้ว

    Nice

  • @jimi02468
    @jimi02468 4 ปีที่แล้ว

    What's the equation for this?

    • @MathsTown
      @MathsTown  4 ปีที่แล้ว +2

      z = c*z*(1-z)

  • @transformerfoxyfloof8341
    @transformerfoxyfloof8341 4 ปีที่แล้ว +1

    I'm starting to think that manderbrots and fractal zooms are optical illusions

  • @jimmerhardy
    @jimmerhardy 4 ปีที่แล้ว +2

    I don't get it but I like it.

    • @MathsTown
      @MathsTown  4 ปีที่แล้ว +2

      It's just a slightly changed formula, instead of the normal Mandelbrot formula. More of a curiosity for us nerds, because the Logistic Equation is quite well known in science. I hadn't seen a fractal zoom before, so I thought I'd make one.

    • @jimmerhardy
      @jimmerhardy 4 ปีที่แล้ว

      @@MathsTown That's is why I drop by: your experimentation and breakthroughs.

  • @arriettyclock
    @arriettyclock 4 ปีที่แล้ว

    ❤❤❤

  • @chrisrodriguezm13
    @chrisrodriguezm13 3 ปีที่แล้ว

    thats a lambda

  • @Scscsc23453
    @Scscsc23453 3 หลายเดือนก่อน

    Cute

  • @Ленад-е1ш
    @Ленад-е1ш 4 ปีที่แล้ว

    ❤️🌈

  • @euclidea1507
    @euclidea1507 3 ปีที่แล้ว

    한국인 ㄷㄷㄷㅈ