Why can't we implement a Sierpinski pattern in povray?

As I understand povray, for some of the more mathematically complicated
thingies,  such as isosurfaces of complex equations and the bozo or
Mandelbrot patterns,  the complexity of the feature depends on the
density of rays hitting it.  For example, the computer doesn't have
stored the "entire" Mandelbrot set at all magnifications, but merely
calculates the pattern at the place where a traced ray hits the object.
Thus, there are few practical limits to zooming in (reducing camera
angle) to see smaller and smaller regions of the Mandelbrot pattern.  Am
I right so far?

It's pretty hard for me to construct a Sierpinski object beyond a half
dozen orders of scale. Isn't this just another mathematically
complicated thingy that povray can solve procedurally?

So why can't we put a Sierpinski pattern in povray?

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