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Pure states of the quantum spin (we are discussing spin
here) are described by unit vectors in our Hilbert space
. But, as it is standard in quantum theory, proportional
vectors describe the same state  the overall phase of the vector
has no physical significance. Therefore, in geometrical terms, the
set of all pure states is nothing but the projective complex space
which happens to be the same as the sphere
That is why the fractal pattern, in our case, is being drawn on a
spherical canvas. There is, however, another possible
interpretation of the same algorithm. It is well know that there
is an intrinsic relation between Minkowski space and the space of
complex Hermitean matrices. ^{} In
coordinates the map is given by

(18) 
so that
In
particular our projection operators ,
correspond to null directions. In other words our canvas, the
sphere , can be also thought of as the projective light cone
 the space of light directions. Quantum jumps would then
correspond to sudden changes of directions of light or lightlike
entities. The formula () can be easily generalized
for being a generic Hermitean matrix (thus representing
a fourvector of space or timelike character as well.
However there is no such generalization for the formula
(), so that the probabilities would have to be
assigned equal, and a physical interpretation, even tentative one,
is missing in such a case.
Next: 1. Pure states as
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