ITT we're strangely attracted... - by mol
OnionBob on 3/8/2006 at 16:02
ahhahah the AMBIENT one is fucking lol
DOOOOO DOOOOOOOOOOOOOOOOOOOOO DOOOOOOOO DOOOOO
Para?noid on 3/8/2006 at 18:26
<img src="http://img517.imageshack.us/img517/8128/hurpbk7.jpg">
Vigil on 3/8/2006 at 20:05
There are times I feel moved or deleted too :(
mopgoblin on 3/8/2006 at 21:34
I wasn't able to get the program to stop crashing, but I already had a primitive fractal-drawing program I'd started writing some time ago, which I was able to adapt into a program for drawing strange attractors.
So far I've only managed to get it to draw the Lorenz attractor (images <a href="http://homepages.paradise.net.nz/jhaskell/chaos.html" title="Lorenz attractor, fractals">here</a>, 523KB), but I also made a few images of fractals when getting the program to work, which I've put on the same page. There's an older page with a few fractal-ish things (<a href="http://homepages.paradise.net.nz/jhaskell/fractal.html" title="Things defined by recursion">here</a>, 283KB), too.
Para?noid on 4/8/2006 at 04:49
Speaking of which, I never understood how fractals are represented. I understand it's something to do with recursion and graphic representation on an Argand plane (real vs. imaginary). Anyone?
Mingan on 5/8/2006 at 02:26
It has not really to do anything with recursion, unless you mean that it is self-replicating (ranging from statistically self-rep to exactly) on different scales. I don't know what it has to do with the Argand plane. But really, check this out and make your head asplode with the maths:
(
http://mathworld.wolfram.com/Fractal.html)
mopgoblin on 6/8/2006 at 05:42
Quote Posted by Para?noid
Speaking of which, I never understood how fractals are represented. I understand it's something to do with recursion and graphic representation on an Argand plane (real vs. imaginary). Anyone?
It depends on the fractal. The pictures of Julia sets you see everywhere are defined by the function Z<sub>n+1</sub> = Z<sub>n</sub><sup>2</sup> + c from complex numbers to complex numbers. c is a complex constant. Points Z<sub>0</sub> on the complex plane are coloured by the minimum <var>m</var> such that |Z<sub><var>m</var></sub>| > 2 (if I recall correctly, all points beyond 2 units from the origin will escape to infinity). Calculating this <var>m</var> is a recursive or iterative process.
The Mandelbrot set uses the same map, but the location of a point on the plane is taken as the value for c for the orbit of that point, and Z<sub>0</sub> = 0 for all points.
There are fractals in other spaces, too. The middle-thirds Cantor set can be defined by taking the closed real unit interval [0, 1] and removing the open interval corresponding to the middle third (leaving the union of [0, 1/3] and [2/3, 1]), then removing the middle third of each of the two remaining intervals, and so on. The three dimensional cross fractal on my website is constructed in a similar manner - starting with a cube, then recursively replacing each cube with the cross-shape (a 3*3*3 cube with the corners and central cube removed) of the same size, constructed out of smaller cubes. You can only let it go so deep before the image becomes unclear or the computer runs out of memory, of course.
