Summary: A fixed point exclusive algorithm and a “repeated point” exclusive algorithm for the approximation of fractal sets are proposed in this paper. Five approximations of fractal sets are compared. The first three were described by Hutchinson, Barnsley-Demko and Dubuc-Elqortobi, respectively. The two new methods are more efficient. Stopping criteria of the algorithms are also given. Numerical comparison is done through classical examples of attractors in the plane.