lol, just discovered Simple English Wikipedia: https://simple.wikipedia.org/wiki/Mandelbrot_set Not so complex anymore Also this is easier on the eyes than the wikipedia page and does a better job of explaining what a mendelbrot set really is: http://mathworld.wolfram.com/MandelbrotSet.html
Oh now you're talking! There's a reason my youtube channel is 'FractalJaguar', hah. Some of my old renders: Links to my friend's galleries: https://www.flickr.com/photos/pegasusepsilon/sets/72157638602133966 https://www.flickr.com/photos/pegasusepsilon/sets/72157638597810636 https://www.flickr.com/photos/pegasusepsilon/sets/72157635276921082 I would say that my renderer is better, and my friend's renderer is basically the best (it's on github: https://github.com/pegasusepsilon/threadedfractals), but I haven't ported mine to HTML5 (yet). He has put a lot of time into it, and his understanding is exceptional. He got reddit gold for this explanation of the Mandelbrot & Julia Sets: http://www.reddit.com/r/explainlike...are_the_mandlebrot_and_julia_sets_and/ckq2ft8 You'll want to read that reddit thread It looks neat because MATH! Yeah that's a Julia Set, and a lovely looking one at that. Do you have the seed for it? The palette is lovely as well. I ******* love fractals
Just for your total confusion: There is no fixed dimension for fractals. I guess you are talking about the 4 dimension of this Mandelbrot x Julia configuration space, but that is only the surrounding space itself. Usually you want the "dimensionality" of the embedded thing, some thing like a line is 1D, a square is 2D a cube is 3D regardless of the surrounding space. Such a "dimensionality" is called Hausdorff dimension, and this is the point where things get really interesting, because fractals can have any dimension on this one, and with "any" I don't mean any natural number, but any positive real number. The Cantor set, which consists of points (o dimensions) and is embedded in the real space between [0, 1] (1 dimension) has the dimensionality of ~0.63 The Koch curve, which is a line (1 dimension) that is embedded on a flat plane (2 dimensions) has the dimensionality of ~1.26 Interestingly the border of the Mandelbrot set, which is a line (1 dimension) and is embedded in the complex plane (2 dimensions) has the dimensionalty of 2. Another really interesting fractal is the space filling curve, or Hilbert curve. Hilbert described this curve, which consists of a single line, drawn continuously on a flat plane in 1892. The interesting and revolutionary thing of this curve was, that even this curve consisted of a single line with 1 dimension, it can fill a square (2 dimensions) completely, which means that for every point (of the infinity many points there are in a square), there is a point on the curve. The curve itself has - of course - a dimensionality of 2.
And, by the way ... This is a screen cap from a Mandelbrot renderer I wrote in 2001 (It is still working - sadly I do not own the tools to compile this again. It was written in Borland Pascal, my guess is that the executable was compiled around 2004 and it is still running on Windows 7)
You've no idea how many hours you lot made me sit in front of Wikipedia trying to understand what I was looking at. On the plus side, I now know what an imaginary number is, and a complex one. On the minus side, I had so many more productive things I wanted to get done yesterday.
I remember one of my lecturers at university joking about how only in mathematics would someone come across 'oh, the square root of -1 is impossible' and workaround it by saying "**** it, we'll just call that impossible thing 'i' and move on" - genius I'd be happy to talk to you for hours about fractals if you want mate You should read my friend's explanation of the Mandelbrot and Julia sets that I linked in a previous post (the reddit link) - he talks about how they are four dimensional, as others in this thread have pointed out. They're pretty cool, and the amount of math that goes into calculating and rendering one of those images is insane.
