Zapp wrote:I've been meaning to ask this question for a long time...
is the circumference of the mandelbrot shape finite or infinite?
The perimeter of the Mandelbrot set is infinite. As you "zoom in" on the boundary of the set, you will continue to find increasing details (i.e. additional "bays" and "peninsula" along the boundary, if you assume that the Mandelbrot set itself is a kind of lake or ocean). As you measure these details with a finer and finer measuring stick, the length of the perimeter will increase without bound.
Zapp wrote:it took me 5 minutes (and the post on your website) to realise, just how awesome that mosaic is. I first thought you just changed the colorschemes in a way that it would represent the mandelbrot set, but now I realise, that you didn't and that the mandelbrot set and the julia sets are connected with each other. amazing o_o
In fact, when Mandelbrot "discovered" (invented?) the set, he was actually interested in Julia sets. The Mandelbrot set is a kind of "map" of the Julia sets. Julia sets generated with a constant from within the Mandelbrot set will be connected, while Julia sets generated with a constant from outside of the Mandelbrot set will consist of disconnected components (or can be empty, I believe---my knowledge is not that deep). If you want to get some idea of how a Julia set will behave, it is helpful to see where that set is in relation to the Mandelbrot set.