DNA microarray experiments generate a substantial amount of information about the 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. A number of clustering techniques have been introduced. However, these traditional methods mainly utilize shape-based assumption or some distance metric to cluster the points in multi-dimension linear Euclidean space. Their results shows poor consistence with the functional annotation of genes in previous validation study. From a novel different perspective, we propose fractal clustering method to cluster genes using intrinsic (fractal) dimension from modern geometry. This method clusters points in such a way that points in the same clusters are more self-affine among themselves than to the points in other clusters. We assess this method using annotation-based validation assessment for gene clusters. It shows that this method is superior in identifying functional related gene groups than other traditional methods.