>>9070737 No actually it isn't. Fractal doesn't even have that well defined of a definition and still there is no way of understanding fractals correctly that would lead to calling a circle a fractal. A circle has integer dimension, its smooth, and nothing about it bears any self similarity.

>>9071113 me here. that wasn't funny and added nothing to the thread. i feel ashamed with myself. please disregard me i am a huge faggot and need to go to bed

You could argue that it would have to have infinite circumference, because that means that it would have to have some kind of Weierstrass function-like shape

>>9072024 Problem with that is that as you keep inverting corners, you create a polygon with an infinite number of sides, but at no point does it actually become a circle. Remember that a circle is the locus of points equidistant from a defined center.

>>9072024 The limit of you process is not a circle. In fact, only a countable number ([math] {\aleph}_0 [/math]) of the points of the resulting zig-zag noose will be on the circle, while all the rest, of which there are uncountably many ([math] 2^{{\aleph}_0} [/math]) won't be on the circle.

>>9072098 Yes it is. Can't tell, but are you trying to argue that circles are fractals still? Because this shape we are talking about is not a circle even though it looks like one. The fact that it's circumference/diameter ratio isn't pi should make that obvious.

>>9072285 Ok look, it's true that the concept of a fractal doesn't have a very well established definition, but it actually has nothing to do with self similarity. The fact that something "preserves structure" (whatever that actually means) has nothing to do with it being a fractal. A circle technically is a fractal because it has a defined Hausdorff dimension, but that's not going to stop anyone from rolling their eyes out of their sockets when you insist on this shit. If the concept were to be given a more strict definition that actually made sense, clearly circles would not be included. Describing things like circles and straight lines is clearly not the purpose of the classification, it's to describe things that have "infinite roughness". The name itself comes from the idea that shapes could have fractional dimension, so circles are only included in that they have dimension equal to 2/1 which is technically a fraction but saying it's your favorite fractal will just irritate everybody.

>>9072448 Ok if this anon is OP then you are fucking retarded. You didn't even understand the literal meaning of fractal before people here explained it to you, every time someone told you that a circle isn't a fractal you defended it with "hurr scaling preserves structure". The reason why a circle """"""technically""""""" counts as a fractal isn't even for the reason you thought it was because non of that structure bullshit has anything to do with anything. You are dumb and non of this "literal meaning" bullshit changes how fucking lame of a fractal a circle is and how much of a fucking beta you must be for it to be your favorite fractal.