/sci/ - Science & Math

File: 201 KB, 900x600, toggaftagnikooluoyeratahw.jpg [View same] [iqdb] [saucenao] [google]

Fractals Sat Oct 19 22:18:40 2013 No.6101641 [Reply] [Original]

prove this thread isn't full of retards and tell my friend here all about fractals

>>	Anonymous Sat Oct 19 22:22:40 2013 No.6101648 >>6101641 so far the only one to post in this thread is you, so technically it is full of retards.

>>	Fractals Sat Oct 19 22:41:10 2013 No.6101681 >>6101648 yet another retard

>>	Anonymous Sat Oct 19 22:45:09 2013 No.6101693 4 for 4, all retards

>>	Anonymous Sat Oct 19 22:47:40 2013 No.6101696 >>6101693 NOW it's 4. Retard posting.

>>	Anonymous Sat Oct 19 22:48:39 2013 No.6101699 I suspect this one is a variation of a julia set.

>>	Anonymous Sat Oct 19 22:55:39 2013 No.6101706 File: 7 KB, 627x84, hausdorff_dimension.png [View same] [iqdb] [saucenao] [google] The number of non-retards in this thread, N, is given by the formula in this picture. Here S, the space of all posters on /sci/, is equipped with the discrete metric.

>>	d'oh Sat Oct 19 22:57:39 2013 No.6101708 >>6101706 As can be seen by my use of <span class="math">\subseteq[/spoiler] instead of <span class="math">\supseteq[/spoiler], the result is indeed correct.

>>	Fractals Sat Oct 19 22:59:10 2013 No.6101709 >>6101699 how can you tell? other than google

>>	Anonymous Sat Oct 19 23:00:11 2013 No.6101712 File: 338 KB, 900x808, yo-mandelbrot.jpg [View same] [iqdb] [saucenao] [google] It's a thing made of itself.

>>	Anonymous Sat Oct 19 23:05:40 2013 No.6101723 >>6101709 I don't, however those swirly behaviors are what make up the infinite number of the julia sets.

>>	Fractals Sat Oct 19 23:15:09 2013 No.6101741 >>6101706 nice, you can give me the general formula for non-retards but not the general formula for fractals

>>	Anonymous Sun Oct 20 00:02:46 2013 No.6101810 File: 1.03 MB, 1920x1080, fractopolis_fractal_wallpapers_2701.jpg [View same] [iqdb] [saucenao] [google] A pattern or shape with no definable edge and/or infinite surface area. Pic is my wallpaper btw

>>	Anonymous Sun Oct 20 00:32:34 2013 No.6101865 File: 55 KB, 806x241, how_to_make_a_fractal.png [View same] [iqdb] [saucenao] [google] >>6101741 >the general formula for fractals ...is a trivial extension of the first formula.

Anonymous Sun Oct 20 00:33:34 2013 No.6101868
File: 28 KB, 799x233, gabhorn.png [View same] [iqdb] [saucenao] [google]

>>6101810
>A pattern or shape with no definable edge and/or infinite surface area.

That's not a good definition of a fractal. For example see pic related, not a fractal but fits your definition.

A fractal is a set whose fractal dimension exceeds its topological dimension. Essentially that the set fills the space it lives in in a complex manner.

>>	Anonymous Sun Oct 20 00:37:04 2013 No.6101875 >>6101865 This is good, but it only provide a sufficient condition, not a sufficient and necessary one.

Anonymous Sun Oct 20 00:52:03 2013 No.6101894
File: 57 KB, 821x251, how_to_make_a_fractal_v2.png [View same] [iqdb] [saucenao] [google]

>>6101875
Actually the condition given at the end is both necessary and sufficient.

Also, new version fixing some of the errors, in particular the overloaded notation with the fractal and the feasible open set B.

Anonymous Sun Oct 20 01:09:04 2013 No.6101915
File: 653 KB, 1920x1080, fractopolis_fractal_wallpapers_401.jpg [View same] [iqdb] [saucenao] [google]

>>6101868

>That's not a good definition of a fractal.

True.

This type of math is not my specialty but as the thread still lacked any good description, I felt obligated to chime in.

My description was based off a description given in "I Am a Strange Loop".

Your image (though potentially a single unit of a fractal pattern) is not what I was attempting to describe.

>A pattern or shape with no definable edge and/or infinite surface area.

adding the line

>Which has exponential similar complexity

>>	Anonymous Sun Oct 20 01:24:04 2013 No.6101929 >>6101696 it's retards all the way down

>>	Anonymous Sun Oct 20 01:24:33 2013 No.6101928 >>6101894 >Actually the condition given at the end is both necessary and sufficient. Oh really? Awesome. You should point that out in the paper, or have you done so elsewhere?

>>	Anonymous Sun Oct 20 01:25:33 2013 No.6101931 >>6101641 I can't prove this thread isn't full of retards but I can prove it is full of retards because OP is in it.

>>	Anonymous Sun Oct 20 01:34:34 2013 No.6101943 >>6101929 turtles are not retarded. TAKE THAT BACK MOTHERFUCKER!

>>	Anonymous Sun Oct 20 01:44:03 2013 No.6101948 >>6101943 It's simulations all the way down http://www.youtube.com/watch?v=0qiLLrmyqTM

>>	Anonymous Sun Oct 20 03:15:03 2013 No.6102022 >>6101894 I'm actually interested by this shit How do you get to F sub q? Do you keep applying the union of images thing to the previous set

>>	Anonymous Sun Oct 20 10:41:43 2013 No.6102558 >>6101943 what if retardation was self-similar and therefore a fractal?

>>	Anonymous Sun Oct 20 10:48:00 2013 No.6102569 >>6101865 Not orthonormal qS? I mean wouldn't to big Qs make shit grow to infitinty?

>>	Anonymous Sun Oct 20 10:57:30 2013 No.6102586 >>6101894 Are you sure the <span class="math"> f_i(F)\cap f_j(F) = \emptyset [/spoiler] is correct? cuz i feel like that would make sure all fractals are non-connected.

>>	Anonymous Sun Oct 20 10:58:29 2013 No.6102590 >>6102586 ( for instance this would force a "bloated" szipersky triangle to not be a fractal).

Anonymous Sun Oct 20 11:03:29 2013 No.6102600

Also the "will terminate in finite number of steps" seems weird. (i mean this would make it so that after a finite zoom the object would no longer be self similar).

Or i could just be spouting shit cuz i don't understand your not neatly written definition.

Anonymous Sun Oct 20 11:23:00 2013 No.6102652

>>6102600
>"will terminate in finite number of steps"
Yeah, that was a mistake, I was doing an unrelated recursion question concurrently and in my sleepiness got the two mixed up.

But the iteration does converge to a set F, as all fixed-point theorems assert.

>>6102569
Fuck, you're right too -- in infinite dimensions an 'orthogonal' basis is implicitly understood to be normalized, and I forgot to turn that part off when going back to finite dimensions.

>>6102586
I've corrected that in the second version -- you need that for the feasible open set, but not for the similitude operation itself. But you do need <span class="math">f_i(F)\cap f_j(F)[/spoiler] to have Hausdorff measure 0.

Honestly, I typed up that thing as a (very very) indirect joke here >>6101706, which involved basically copying off Wikipedia and making it unnecessarily pretentious. If you're genuinely looking for a readable explanation you should just go straight to that page:

http://en.wikipedia.org/wiki/Hausdorff_dimension#Self-similar_sets

Disclaimer: I know enough to translate between English and mathspeak, but have zero familiarity with fractals, so you should definitely trust Wikipedia over myself.

>>	Anonymous Sun Oct 20 11:36:29 2013 No.6102678 >>6102652 All fractals don't have hausdorff measure 0? Or did i misinterpret.

>>	Fractals Sun Oct 20 21:35:12 2013 No.6103792 are you retards even trying? you can't even explain the simplest of fractals

Advanced search
Text to find
Subject [?]Search by post subject. Leave empty for any.
Username [?]Search for user name. Leave empty for any user name.
Tripcode [?]Search for tripcode. Leave empty for any.
Email [?]Search by email. Leave empty for any.
Filename [?]Search by image filename. Leave empty for any.
From Date [?]Enter what date to start searching from. Format is YYYY-MM-DD
To Date [?]Enter what date to start searching until. Format is YYYY-MM-DD
Image hash
Search in	All Posts OPs Only
Deleted posts	Show all posts Show only deleted posts Only show non-deleted posts
Internal posts	Show all posts Show only internal posts Show only archived posts
Order	New posts first Old posts first
Capcode	All Posts Only by Users Only by Mods Only by Admins Only by Developers
Results	Posts Threads
Action	[ Simple ]