Abstract: In this paper, we discuss the fractal images of M-set and design its aigorithms. The programs are written in Ms-C language. Several illustrative images are included. It is generated on the GW-386,286 at HUST and NCC.Further more, in order to develop the application of fiactal geometry, we have studied tne M-Euler algorithrn and ussd it to simulate the non-linear systems such as Riccati otdinary non-linear differential equa tion, which can be used to visualize ths Duffing and Van dd Pol non-linear vibration systems.This work is supported by NSFC(No. 6883019) and CAD Lab. of Institute of Computing Technology, Academia Sinica.