DNA microarray experiments generate a substantial amount of information about global gene expression. Gene expression profiles can be represented as points in multi-dimensional space. It is essential to identify relevant groups of genes in biomedical research. Clustering is helpful in pattern recognition in gene expression profiles. Some clustering techniques have been introduced. However, these traditional methods mainly utilize shape-based assumption or distance metric to cluster the points in multi-dimension linear Euclidean space. Poor consistence with the functional annotation of genes is shown in their validation study. We propose fractal clustering method to cluster genes using intrinsic (fractal) dimension from modern geometry. Fractal dimension is used to characterize the degree of self-similarity among the points in the clusters. The main idea of fractal clustering is to group points in a cluster in such a way that none of the points in the cluster changes the cluster’s in...