Abstract:By useing of the Mathematica’s advantages in programming, numerical computation and drawing, and in combination with the theory of fractal geometry, the Mathematica was adopted to write the recursive program, the Iterated Func- tion System program, LS-System program of the fractal graphs, and the typical fractal graphs in two dimensions or three di- mensions and the corresponding random algorithms are discussed and the simulation of the natural plants were conducted and by modification of the corresponding parts of the programs the desired fractal graphs can be obtained which is a reflection of the advantages in drawing thefractal graphs. .