fractal faq

[Anonymous No.8223311]

I'm trying to read Mandelbrot's book on fractal's but I really am not understanding a lot of it. The pictures are cool, but I'm missing the basics and not really understanding how he's doing all this stuff. Anyone capable of some basic explaining or pointing me to a more introductory text?

[Anonymous No.8223317]

>>8223311
take some math classes

[Anonymous No.8223333]

>>8223311
Fractals get real small but they always look the same.

[Anonymous No.8223350]

>>8223333
checked

>>8223317
I have a math minor but I'm out of school. I guess what I don't get is how you represent the "set."

So for the Koch curve for instance we start with an equilateral triangle, perhaps we'd represent this as a triplet of ordered pairs (the vertices) but then I don't see how you'd represent the relation to go to the next step where you put a triangular "bump" in each side. The mandelbrot set is stated as
[math]z_n+1 = z_n^2 + z_0[/math]
this is pretty clear that the "generator" is [math]f(z_n)[/math] and the "initiator" is [math]z_0[/math] but I don't see how to explicitly describe the relation in a similar way for the Koch curve or many other curves he draws.

[Anonymous No.8223354]

>>8223350
Here is why CS students sometimes make a little fun of math students. You don't put enough emphasis in language.

[OHP No.8223372]

The quality that sets fractals apart from "simple" shapes is that there is some torsion-free part in the endomorphism monoid on the object, or perhaps a subobject.

This basically says that the object contains a copy of itself, which contains a copy of itself, which... ad infinitum.

I don't know what else you want to know. Ask more specific questions.

[Anonymous No.8223420]

>>8223372
how about this: what would be the formula for the vertices of the above koch curve at the ith iteration?

[Anonymous No.8223433]

>>8223420
or maybe this: if we are to call the koch curve a set, what is it a set of? exponentially growing groups of vertices?

[OHP No.8223616]

>>8223433
I would call the Koch curve the bounadary of a colimit of metric spaces. I don't know what the formula is for vertices, but it can't be hard to figure out: if you give a description of the three points in the first stage in terms of the two endpoints, then you just have to replace the endpoints with the first and second point, or the second and third point, to get the formula for the next stage's points. The scaling factor can be put in terms of the distance between the two points, because the whole thing scales linearly.

You sound less interested in fractals and more interested in formulas for fractals.

[Anonymous No.8223876]

here you go faggots

http://math.uchicago.edu/~may/REU2012/REUPapers/Natoli.pdf

[Anonymous No.8224191]

https://youtu.be/NGMRB4O922I
>8223311
Benoit's a big guy for you to try to jump in and learn from directly. Try this on for size.

[Anonymous No.8224199]

>>8224191
>Benoit's a big guy
___ ___

[Anonymous No.8224320]

>>8224199
>for you

[Anonymous No.8224800]

>>8224191
>Centerpoint of a plane
I'm not even...