The Logistic Map - Fractal Zoom

This video is a little demonstration that the Logistic Map equation is in the same family as The Mandelbrot Set. The Logistic Equation & Map come up a lot of places, such as biology where it can model the growth of animal populations. It also has many other uses. The Logistic Map, is the discrete version of the Logistic Equation (it is the recurrence relation.) If you are interested in this equation, how it appears in real life, and how it relates to the Mandelbrot, please see this great video by Veritasium:

Equation: z = c*z*(1-z). [The initial value of z is 0.5].

Thank-you to my supporters on Patreon.

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[livemorrow]

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

[Randomness]

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

[FlyingSavannahs]

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

[OliverrandontheRails]

This is actually a power 1 lambada fractal

[horseshoehimself]

That fractal is called the "Lambda" fractal.

[billtomson]

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

[igorjosue]

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

[AilahsCreation]

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

[ScaryOldMan]

How to set equation in Kalle's Fraktaler?

[transformerfoxyfloof]

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

[kaptxa_by]

What is this? It looks different to Mandelbrot fractal

[DMdarkmatter]

Does'nt its just a power 3 mandelbrot set?