What if it's a circle with a circumference that's 4 times its diameter?
FRACTALS GENERAL
Jordan Baker
Gabriel Hall
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.
Oliver Thomas
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.
Mason Bell
But is it a fractal?
Alexander Hill
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.
Hunter Collins
The line y = x/0
Carson Martin
Yes, I was specifically talking about the "circle" shape generated by that process.
Colton Phillips
No it looks like a curve. It might be "straighter", but it still holds the same structure.
Alexander Rodriguez
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.
Hudson Sullivan
> clearly not the purpose of the classification
> will just irritate everybody.
> deferring to the purpose or social status of ideas, and not the law or the literal meaning