Title: Fractals based on prime numbers Post by: elphinstone on June 12, 2013, 01:52:46 PM Random idea:
Prime numbers have a caothic distribution and are more dense near 0. For thoose who have more Mathematical backgrounds than me: is it possible to define prime numbers in an interesting way w.r.t some 2D or 3D space? Maybe over Gaussian integers? This could lead to sets (of prime numbers) with interesting shapes. Someone already tried? :) Title: Re: Fractals based on prime numbers Post by: Dinkydau on June 12, 2013, 04:02:13 PM I know there's Ulam's spiral that looks somewhat fractal, except it doesn't have infinite details when you zoom in.
http://en.wikipedia.org/wiki/Ulam_spiral In this image, the idea of this spiral is expanded by adding composite numbers to it. The size of the dots indicates the number of factors that the composite numbers have, or, you could say, how not-prime they are. The small red dots are prime numbers. (http://upload.wikimedia.org/wikipedia/commons/thumb/3/34/Spirale_Ulam_150.jpg/598px-Spirale_Ulam_150.jpg) Title: Re: Fractals based on prime numbers Post by: KRAFTWERK on June 12, 2013, 04:13:30 PM Interesting image Dinkydau... I see some patterns almost repeating...
...also looks like the roadmap of Barcelona, the roads "Diagonal" and "Parallell" is clearly visible! O0 Title: Re: Fractals based on prime numbers Post by: elphinstone on June 13, 2013, 09:44:12 AM Never saw the Ulam's spiral before... very interesting!
Anyway what I was looking for is an "interesting" (in fractal sense) way to define prime numbers in 2/3D real/complex space. Will try in the next days, but I don't know if I have enough math knowledges. :embarrass: Thank you guys! Title: Re: Fractals based on prime numbers Post by: hgjf2 on June 13, 2013, 11:56:40 AM I know there's Ulam's spiral that looks somewhat fractal, except it doesn't have infinite details when you zoom in. http://en.wikipedia.org/wiki/Ulam_spiral Wow! This "fractal" same as irregular kaleidoscope like in my topic "Polihedron many polihedrons" what contain a few examples of my unperiodic tilling :peacock: :wow: Title: Re: Fractals based on prime numbers Post by: hgjf2 on June 13, 2013, 11:59:23 AM Let's compare! Title: Re: Fractals based on prime numbers Post by: hgjf2 on June 13, 2013, 12:01:00 PM It's a really cubical kaleidoscope same as into rectangular irregular polihedron made from mirrors |