FRACTALS GENERAL

>>9070686
the empty set

>>9070686
A circle isn't a fractal
sage

>>9070699
>A circle isn't a fractal

Actually it is

>>9070737
>A circle isn't a fractal
Not OP but it's radius is a finite number so it can't be?

>>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.

>>9070752
Perhaps if you take a scissor and cut the circle and then straighten it. A line is a fractal.

>>9070741
>>9070752

It's structure is the same at every level.

Can we just talk about fractals? The circle is just my favorite, but it's not the only one.

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>>9070764
correct, line is fractal.
circle is not.

just zoom to different levels on a point in either set and ask yourself does it look the same

>>9070788
>line is fractal
No, the line is smooth and has dimension 1; fractals have non-integer dimension and are nowhere differentiable.

>>9070817

> fractals have non-integer dimension

wtf are you talking about

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>>9070686
>https://en.wikipedia.org/wiki/L-system

>>9070839
https://en.wikipedia.org/wiki/Fractal_dimension

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probably this one.
theres one of a lion too but its not as fractal as this one so

>>9071043
Cute!!

ITT : Not fractals.

>>9070686
The circle is not a fractal.

>>9071043
that just looks like a neon colored dogoo

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i have ascended to the fractal dimension

fear me

>>9070741
>it is radius
>>9070784
>It is structure
Lrn2engrish you faggots

>>9070686
1+2+3+... = DMT

>>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

>>9070882
>One non-trivial example is the fractal dimension of a Koch snowflake. It has a topological dimension of 1

1 dimensional fractal

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It's just so pretty.

>>9070868
I did my BSc thesis on using L-systems to generate vegetation. It was a total mess but it was fun.

>>9070784

No it's not

If you "zoom in" on any point on the circumference of a circle it looks like a line

>>9070741

The area of the mandelbrot is finite as well.

What is your point?

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

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>>9070699
>>9071066

What if it's a circle with a circumference that's 4 times its diameter?

>>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.

>>9072055
>>9072069
But is it a fractal?

>>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.

>>9070686
The line y = x/0

>>9072171
Yes, I was specifically talking about the "circle" shape generated by that process.

>>9071974

No it looks like a curve. It might be "straighter", but it still holds the same structure.

>>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.

>>9072364

> 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

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>>9071071
D:

*Is 'fraid*

>>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.

>>9072285

It becomes arbitrarily straight:

You could show that for any given "tolerance" for straightness, you could produce a zoom factor that hits that tolerance

>>9071071

are we /fractals/ now?

https://www.youtube.com/watch?v=6HCz1tFqIcs

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>>9072499

Here is my second favorite fractal