is it possible to find the center of the big black spot(the area which with the set?) I've tried to loop through all points which are in the set, sum their locationד and eventually divided by the num of points which are in the set.
it didn't work as expected because the the set isn't formed, e.g its not a perfect sphere or a square therefore the center always changes. is there another way of finding the center?
thanks!
That shape is a perfect cardioid (no other similar shapes in the Mandelbrot set are perfect cardioids, they are somewhat distorted).
Check Wikipedia, you'll find the equation for calculating the cardioid itself: http://en.wikipedia.org/wiki/Cardioid
Note, however that at the borders of the Mandelbrot map (where the black and non-black area meets) deciding whether a point belongs to the map or not, heavily depends on how many times you iterate z = z^2 + c. If you iterate it 50 times, the main cardioid will be smaller than if you iterate it 500 times because with 500 iteration more points at the border will go to infinity.