New demonstrations give some insight to comprehend subsets of qubit and qutrit states in the probability space. Demonstrations enable you to change parameters and trace the change of the investegated object. Current demonstrations give you an opportunity to choose directions in space and see how it effects the subset of qudit states in the probability simplex. Moreover, there is presented a direct indicator of the condition number of the problem which shows immediately whether the problem is well- or ill-conditioned. Observation of limitations of differrent order and alternative cut sets by your own eyes is surely an advantage of the Wolfram Demonstrations Project. A short theoretical explanation is also provided.
Qubits (spin = 1/2): http://demonstrations.wolfram.com/RepresentationOfQubitStatesByProbabilityVectors/
Qutrits (spin = 1): http://demonstrations.wolfram.com/QutritStatesAsProbabilityVectors/