Basins of Attraction and Julia Set with Newton's Iteration Method

Newton's Iteration method is applied to f(z)=z α-1 in the complex plane And its basins of attraction for zero points and its Julia set are discussed With the α change, the basins of attraction and Julia set change If α is integer,the basins of attraction and Julia set is α spin symmetry If α is non-integer, it has not spin symmetry It is a transitional state The transitional state for α change from odd to even is different to from even to odd, it is more complicated If α is with in a certain range there is a set containing open region of starting points, the Newton's method does not converge to any fixed points Therefore, even the simple complex iterated systems, there are much complicated and unknown phenomena to be discussed