Continuously measure quantum states with different orthonormal bases

Quantum entanglement plays an important role in Bell's theorem and the quantum key distribution protocol Ekert. But there is one more important thing. It is to successively measure the quantum state with different orthonormal bases. Both Fig.1 and Fig.2 give information about it, but isn't the graphical Fig.1 clearer than the mathematical representation of Fig.2?

Suppose we apply the following replacement rules:

|0> ⇒ 0,  |1> ⇒ 1

The probability that the measurement result by the current Basis becomes |0> can be get by the function below. This function is equivalent to Fig.1.