The Sierpinski is not really just one egression, it is an 
infinite number of original triangles with their apices all 
pointing to a central point in space.  It is a solid geometry 
not just in the shape of the triangle being a pyramid, but it 
a lot of them filling a spherical space.

If one were to slice through this globe of Sierpinski, one 
would have the Mandelsun fractal.  I believe that these two 
fractal "types" are actually the same.  I believe that the 
others may converge also.   Moving pictures of the mandelsun 
fractal are quite beautiful and they make the ordinary 
kaleidoscope look vapid and cheap.  The mandelsun fractal, 
growing away from a central point in a circular plane, is 
what one would see if he were able to visualize the goings on 
in an operating saucer's flat surface.  The mandelsuns or 
mandelbrot are actually triads,  triangular shaped vessels 
use their configuration,  several sets of wheels of different 
sizes stacked on the planar surface of the plane of the craft 
to give the triangular appearance which is two dimensional 
(ordinary use of the words "two dimensional") shape of the 
cosmos.