This paper presents a study on a family of local hexagonal and multi-scale operators useful for texture analysis. The hexagonal grid shows an attractive rotation symmetry with uniform neighbour distances. The operator depicts a closed connected curve (1D periodic). It is resized within a scale interval during the conversion from the original square grid to the virtual hexagonal grid. Complementary image features, together with their tangential first-order hexagonal derivatives, are calculated. The magnitude/phase information from the Fourier or Fractional Fourier Transform (FFT, FrFT) are accumulated in thirty different Cartesian (polar for visualisation) and multi-scale domains. Simultaneous phase-correlation of a subset of the data gives an estimate of scaling/rotation relative the references. Similarity metrics are used as template matching. The sample, unseen by the system, is classified into the group with the maximum fuzzy rank order. An instantiation of a 12-point hexagonal operator (radius=2) is first successfully evaluated on a set of thirteen Brodatz images (no scaling/rotation). Then it is evaluated on the more challenging KTH-TIPS2b texture dataset (scaling/rotation, varying pose/illumination). A confusion matrix and cumulative fuzzy rank order summaries show, for example, that the correct class is top-ranked 44 - 50% and top-three ranked 68 - 76% of all sample images. A similar evaluation, using a box-like 12-point mask of square grids, gives overall lower accuracies. Finally, the FrFT parameter is an additional tuning parameter influencing the accuracies significantly.