This paper analyzes the numerical simulation of recurrent affine fractal interpolation in M.F.Barnsley’s classical literature［1］, Recurrent Iterated Function Systems.By using MATLAB and random iterative algorithm, the random iterative algorithm of recurrent affine fractal interpolation example is given, and the corresponding fractal interpolation curve is obtained.When the recurrent affine fractal interpolation maps the longer original image range Ji′=［xl,xm］ compression to the shorter image range Ji=［xi-1,xi］,there are three situations:(1)JiJi′， (2)JiJi′ and Ji∩Ji′=Φ,(3)JiJi′andJi∩Ji′≠Φ。According to the recurrent affine fractal interpolation and piecewise fractal interpolation, the random iterative numerical simulation of the above three cases is carried out, and the algorithm process and detailed program codes are given.The numerical analysis is a supplement to the fractal interpolation theory.Finally, the optimal solution of box dimension of affine fractal interpolation function is given by particle swarm optimization algorithm.