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/sci/ - Science & Math

File: 24 KB, 502x511, fractal.png [View same] [iqdb] [saucenao] [google]

Whats your favorite fractal? Mine is the circle

 >> Anonymous Sat Jul 29 01:25:52 2017 No.9070693 >>9070686the empty set
 >> Anonymous Sat Jul 29 01:31:25 2017 No.9070699 >>9070686A circle isn't a fractal sage
 >> Anonymous Sat Jul 29 01:54:37 2017 No.9070737 >>9070699>A circle isn't a fractalActually it is
 >> Anonymous Sat Jul 29 01:56:50 2017 No.9070741 >>9070737>A circle isn't a fractalNot OP but it's radius is a finite number so it can't be?
 >> Anonymous Sat Jul 29 02:03:16 2017 No.9070752 >>9070737No 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.
 >> Anonymous Sat Jul 29 02:14:01 2017 No.9070764 >>9070752Perhaps if you take a scissor and cut the circle and then straighten it. A line is a fractal.
 >> Anonymous Sat Jul 29 02:39:49 2017 No.9070784 >>9070741>>9070752It'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.
 >> Anonymous Sat Jul 29 02:46:22 2017 No.9070788 File: 7 KB, 248x165, 1500509369156.png [View same] [iqdb] [saucenao] [google] >>9070764correct, 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
 >> Anonymous Sat Jul 29 03:03:20 2017 No.9070817 >>9070788>line is fractalNo, the line is smooth and has dimension 1; fractals have non-integer dimension and are nowhere differentiable.
 >> Anonymous Sat Jul 29 03:20:30 2017 No.9070839 >>9070817> fractals have non-integer dimensionwtf are you talking about
 >> Anonymous Sat Jul 29 03:40:53 2017 No.9070868 File: 67 KB, 720x570, trees.jpg [View same] [iqdb] [saucenao] [google]
 >> Anonymous Sat Jul 29 03:54:48 2017 No.9070882
 >> Anonymous Sat Jul 29 05:58:30 2017 No.9071043 File: 60 KB, 640x480, 1375863058_1-640x480.jpg [View same] [iqdb] [saucenao] [google] probably this one.theres one of a lion too but its not as fractal as this one so
 >> Anonymous Sat Jul 29 06:11:48 2017 No.9071057 >>9071043Cute!!
 >> Anonymous Sat Jul 29 06:18:47 2017 No.9071061 ITT : Not fractals.
 >> Anonymous Sat Jul 29 06:22:48 2017 No.9071066 >>9070686The circle is not a fractal.
 >> Anonymous Sat Jul 29 06:23:56 2017 No.9071068 >>9071043that just looks like a neon colored dogoo
 >> Anonymous Sat Jul 29 06:24:40 2017 No.9071071 File: 159 KB, 736x744, 49f172036b5d44f8c26249400f862d7a--sacred-geometry-art-higher-consciousness.jpg [View same] [iqdb] [saucenao] [google] i have ascended to the fractal dimensionfear me
 >> Anonymous Sat Jul 29 06:33:43 2017 No.9071082 >>9070741>it is radius>>9070784>It is structureLrn2engrish you faggots
 >> Anonymous Sat Jul 29 07:02:24 2017 No.9071113 >>90706861+2+3+... = DMT
 >> Anonymous Sat Jul 29 07:15:10 2017 No.9071129 >>9071113me 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
 >> Anonymous Sat Jul 29 09:35:37 2017 No.9071362 >>9070882>One non-trivial example is the fractal dimension of a Koch snowflake. It has a topological dimension of 1
 >> Anonymous Sat Jul 29 09:37:58 2017 No.9071365 1 dimensional fractal
 >> Anonymous Sat Jul 29 09:47:27 2017 No.9071383 File: 2.08 MB, 2304x1728, mandelb.jpg [View same] [iqdb] [saucenao] [google] It's just so pretty.
 >> Anonymous Sat Jul 29 13:20:32 2017 No.9071748 >>9070868I did my BSc thesis on using L-systems to generate vegetation. It was a total mess but it was fun.
 >> Anonymous Sat Jul 29 15:14:14 2017 No.9071974 >>9070784No it's not If you "zoom in" on any point on the circumference of a circle it looks like a line
 >> Anonymous Sat Jul 29 15:16:09 2017 No.9071979 File: 47 KB, 1024x1093, Screenshot from 2017-06-09 14:25:16.png [View same] [iqdb] [saucenao] [google]
 >> Anonymous Sat Jul 29 15:18:16 2017 No.9071982 >>9070741The 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
 >> Anonymous Sat Jul 29 15:20:37 2017 No.9071989 File: 16 KB, 682x682, 14695_10_06_17_3_10_21.png [View same] [iqdb] [saucenao] [google]
 >> Anonymous Sat Jul 29 15:38:58 2017 No.9072024 File: 46 KB, 574x574, pi-4.png [View same] [iqdb] [saucenao] [google] >>9070699>>9071066What if it's a circle with a circumference that's 4 times its diameter?
 >> Anonymous Sat Jul 29 15:54:50 2017 No.9072055 >>9072024Problem 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.
 >> Anonymous Sat Jul 29 16:08:27 2017 No.9072069 >>9072024The 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.
 >> Anonymous Sat Jul 29 16:24:52 2017 No.9072098 >>9072055>>9072069But is it a fractal?
 >> Anonymous Sat Jul 29 16:57:23 2017 No.9072171 >>9072098Yes 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.
 >> Anonymous Sat Jul 29 17:06:09 2017 No.9072192 >>9070686The line y = x/0
 >> Anonymous Sat Jul 29 17:11:55 2017 No.9072206 >>9072171Yes, I was specifically talking about the "circle" shape generated by that process.
 >> Anonymous Sat Jul 29 17:58:35 2017 No.9072285 >>9071974No it looks like a curve. It might be "straighter", but it still holds the same structure.
 >> Anonymous Sat Jul 29 18:47:33 2017 No.9072364 >>9072285Ok 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.
 >> Anonymous Sat Jul 29 19:43:07 2017 No.9072448 >>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
 >> Anonymous Sat Jul 29 20:06:52 2017 No.9072487 File: 340 KB, 500x405, 697bc7ae6aa0937981c3dd124223276a4fe843a2_hq.gif [View same] [iqdb] [saucenao] [google] >>9071071D:*Is 'fraid*
 >> Anonymous Sat Jul 29 20:16:23 2017 No.9072499 >>9072448Ok 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.
 >> Anonymous Sat Jul 29 23:18:03 2017 No.9072866 >>9072285It becomes arbitrarily straight:You could show that for any given "tolerance" for straightness, you could produce a zoom factor that hits that tolerance
 >> Anonymous Sat Jul 29 23:21:28 2017 No.9072871 >>9071071are we /fractals/ now?https://www.youtube.com/watch?v=6HCz1tFqIcs
 >> Anonymous Sun Jul 30 00:19:44 2017 No.9072942 File: 55 KB, 791x798, image.jpg [View same] [iqdb] [saucenao] [google]
 >> Anonymous Sun Jul 30 02:59:01 2017 No.9073136 File: 11 KB, 512x512, fractal-1.png [View same] [iqdb] [saucenao] [google] >>9072499Here is my second favorite fractal
 >> Anonymous Sun Jul 30 16:15:54 2017 No.9074129 bump