Schematic showing the computation ofk-space information. The scanning light sheet imaging data from the developing zebrafish embryo at each time point was reduced to a collection of xyz coordinates (Keller et al., 2008). These data were scaled to construct an image of the embryo in a 512³ voxel volume, where the position of each nucleus is marked by a voxel value of 1 (all other voxels being 0). At this point there are two branches in the analysis, a discrete Fourier transform (F(x)) for the embryo is computed using the fast Fourier transform (FFT), and Parseval′s theorem is used to compute a probability distribution for the Fourier coefficients a and b. For presentation purposes the Fourier transform shown is one-dimensional, but the actual computation involves a three-dimensional FFT. The Fourier transform shown is summed over all voxels (N_V) in the image, and the x coordinate is normalized to the dimensions of the volume (L). The Parseval′s based probability distribution represents how likely any particular coefficient would be if the cell positions in the embryo were established by a random process (note that the distribution is identical for both a and b). An information (I_kS) is then computed using the probabilities (P_a and P_b) for the Fourier coefficients from the FFT of the embryo image, by summing log₂P for all N_V coefficients of each type (note that n=0 represents the zeroth order term which is omitted). An entropy (H_kS) is computed from the probability distribution by summing Plog₂P for all probabilities of each type (here a bin size for the probabilities is set to 1% of the standard deviation). The kSI was then computed by subtracting the information from the entropy. This last step has the effect of making the point of reference the maximally uncorrelated distribution of cells in the volume (as reflected by the k-space entropy). Thus the kSI provides a measure of how correlated the positions of the cells in the embryo are relative to the case where the cell positions are randomly determined. Alternatively, the kSI can also be viewed as a measure of how likely that the organization of cells observed was the result of a random process (the higher the kSI the less likely). For additional details see Heinz et al. (2011).