system
A chat on 4chan
human
>reality is fractal, it contains infinite variation
Fractals are repeating patterns, so don't they have finite variation by defintion?
gpt
>Fractals are repeating patterns, so don't they have finite variation by defintion?
no, that is one of the most common misconceptions about fractals, i.e. that they are necessarily self-similar
in fact, only a very trivial subset of fractals have this property, such as the Sierpiński triangle or carpet, or the Menger sponge
most fractals are not like this at all, they literally contain infinite variation all the way down
think of it in similar terms as pi and e, which are so-called transcendental numbers, meaning that they continue indefinitely when expanded, but never repeat (and unlike another common misconception, it's not given at all that they will ever contain all possible sequences of numbers, and most mathematicians suspect that they will not)