the data gathered for each formula_4 are manipulated to calculate lacunarity. one measure, denoted here as formula_9, is found from the coefficient of variation (formula_10), calculated as the standard deviation (formula_11) divided by the mean (formula_12), for pixels per box. because the way an image is sampled will depend on the arbitrary starting location, for any image sampled at any formula_4 there will be some number (formula_14) of possible orientations, each denoted here by formula_15, that the data can be gathered over, which can have varying effects on the measured distribution of pixels. equation shows the basic method of calculating formula_16: