The research discussed in this paper is a continuation of the author's previous research published in SPIE's Visual Information Processing Proceedings of 2003  entitled "Improving the Performance of Content-Based Image Retrieval Systems". The SPIE article discussed a new method for clustering an image database based on level one similarity using a new technique called the "enumeration of gradient states". This technique is based on the direction of the gradient (converting the gradient into pixel moments and computing a value known as the "gradient spin excess" for determining the complexity level of an image). This complexity level was used for clustering images into similarity groupings. From this similarity grouping or clustering, level one similarity retrieval was improved by searching each cluster for the proper membership in a cluster rather than searching the whole database. This article expands the previous study with a theoretical discussion showing that complexity based clustering using gradient spin excess is directly related to the degree of randomness (entropy) of pixel moments. In addition, we propose an improved gradient states methodology by calculating the pixel moments of an image at various sub-block sizes and clustering the image database based on hierarchical clustering using level one similarity. Finally it is shown theoretically as well as experimentally that the speed of similarity retrieval is of complexity O(n), a definite improvement over the traditional color histogram (L1-norm) similarity retrieval method.