Sierpinski's Triangle is obviously only a representation, as stated, of the fractal set, adequate, but far from the "real" thing.  The best representation would have to be a solid with the naught of godhead at the center of a burgeoning sphere.  
     Also, the dynamics of the fractals are not represented.
     There is a German animated short film which is a far better approximation of the nature of a fractal system, though l regret not to have the name of the visual device, seen on educational television.  The short involved three dimensional
triangles, tetrahedrons, the sides of which would allow animated stick figures to dance and to cavort through them into adjacent tetrahedrons in various manners not easy for someone not smart enough to NOT eat crackers in bed to explain here.
At the end of the short, an exit is made onto the surface of the solid comprised of the solid forms and then up a plane onto the surface of the planet.  If anyone has seen or can identify this visual exercise, please come forward.