Efficient feature extraction metrics are crucial in many computer vision applications. One such application is texture classification which involves classifying samples as members of one of a preset number of classes. These classes are chosen to correspond with our human intuition of which textures are different from others. In this work we use the wavelet-based fractal signature, a new multichannel texture model introduced previously which characterizes patterns as 2D functions in a Besov space. The wavelet-based fractal signature generates an n-dimensional surface, which is then used for classification by a fuzzy self-organizing feature map as well as two other supervised classification techniques. The feature space has a low dimensionality and as a result is classified in few training epochs. Experimental results are presented for a test set of textures of different types.