## The Mandelbulb

Here is a 3200x2000 pixel background picture of the mandelbulb set. It was rendered with the free program "mandelbulber" under linux (apt-get install mandelbulber). The Mandelbulb is the set of points C=(x,y,z) in space for which the iteration of the map T(X)=X^{2}+ C starting at 0=(0,0,0) does not lead to infinity. The square X

^{2}of a point is defined as the point with spherical coordinates (r

^{2},2 t,2s) if (r,t,s) are the spherical coordinates of X. Despite the fact that the set is extremely beautiful, almost nothing is known about it. Is it connected, simply connected?