@@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)
@@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.
@@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.
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.
If you rewrote the equation to be more similar to the mandelbrot equation (z = z^2+c).
You could have z = -cz^2 + cz.
This has a lot more symmetry than the mandelbrot doesn't it? Please make more zooms of this!
Still contains some Mandelbrots, hehe...
WHY IT HAS MANDELBROT?!?!?
Wow! Logistic Mandelbrot!
z^2 - c^2 - 0.25
How to set equation in Kalle's Fraktaler?
2:01
What formula?
How beautiful
What is this? It looks different to Mandelbrot fractal
It's the logistic map equation, not the Mandelbrot. See the video linked in description for a full explanation.
@@MathsTown ok, what does collor mean? how do u calculate collor?
@@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)
@@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.
@@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.
This is actually a power 1 lambada fractal
I fear the brot has been beaten
That fractal is called the "Lambda" fractal.
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Me: Firsters!
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The fractal: A
what i think of he:
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Why Double
Hi maths Town, I get to be your first comment! Yay!
Does'nt its just a power 3 mandelbrot set?
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)
it does look similar to a rotated power 3 Mandelbrot set, but yes I understand that it's only 2 way.
its just a lambda or also known as logistic map from mandelbrowser and mirrored
its not z = -cz2 + cz its wrong
Nice
What's the equation for this?
z = c*z*(1-z)
I'm starting to think that manderbrots and fractal zooms are optical illusions
I don't get it but I like it.
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.
@@MathsTown That's is why I drop by: your experimentation and breakthroughs.
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thats a lambda
Cute
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