The effects of iterations of the RANK filter are studied experimentally. The RANK filters are a new family of nonlinear filters. The effects of the RANK filters are significant because of their local adaptivity, i.e. flexibility of the shape of the filter window. Images of random values that are uniformly independently distributed are processed by the RANK filters iteratively, and the fixed points, which are defined as the images invariant to additional filtering, are observed. It is found that various RANK filters generate some structures in the fixed point images and distinct modes in their histograms. The generation of these modes is dependent upon the filter parameters.