The only thing I got about fractals is that if you keep zooming you will see the same pattern repeated, but I don’t get it. First of all, you have to zoom on the border, so you technically can’t zoom anywhere and you get the same pattern, second why is the Mandelbrot so weird? Why all those weird shapes? Couldn’t it just be something normal? Also, why you can dezoom from a Mandelbrot fractal and those weird things happen. It’s just too complicated for my little brain
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You are very correct that the Mandelbrot set, islands and many other things often sold as “fractals” are actually not so; their boundaries/coastlines are! Coincidentally, I already went into some details of this on this sub yesterday: https://www.reddit.com/r/explainlikeimfive/comments/v2a8vg/comment/iasu7p0
It is correct that most fractals are self-similar, meaning that they somewhat repeat their structure at arbitrary small levels. The definition, however, is usually quite different and based around dimensionality of the object. Fractals behave under scaling not the same as one would naively expect. Quoting my own reply in a thread here:
A line segment can be turned into 2 segments of 1/2 the size; as 2^**1** = 2, it is **1**-dimensional.
A square can be cut into 4 smaller squares of 1/2 the size; as 2^**2** = 4, we say it is **2**-dimensional.
And by 2^**3** = 8, a cube has dimension **3**.
But when applied to the [Sierpinski triangle](https://upload.wikimedia.org/wikipedia/commons/thumb/4/45/Sierpinski_triangle.svg/1200px-Sierpinski_triangle.svg.png), one notes that it can be cut into 3 copies of 1/2 the size; and as 2^**1.58[…]** = 3, it has dimension **1.58[…]**, or more formally, log_2(3).
There are even examples of line-like structures that end up having dimension 2 (or 3 or more). And, maybe completely unexpectedly, the boundary/coastline of the Mandelbrot set has itself dimension 2 in this sense!
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