This thesis is theoretical study of spatial behavior of spin from two dimensions to quasi-one dimension subject to the Rashba spin-orbital coupling. The theoretical method is Non-Equilibrium Green’s Function (NEGF) in tightbinding model and lead self-energy model. The result of NEGF in 2D simple tight-binding square-lattice Hamiltonian and two normal metal leads is studied. The Spin Hall effect presents in the distribution of spin density. We tune the two-dimensional square-lattice into quasi-one dimensional fractal shape by taking off the element of matrix of Hamiltonian. In the different shape we produced, the local spin density and transmission are discussed and compared with linear shape in each cases.