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In this paper we explore the application of the pointwise dimension (PD)analysis as a large-scale structure descriptor to the RC3 catalog of galaxies(de Vaucouleurs et al. 1991). This technique, which originated in the field offractal geometry (Mandelbrot 1983) and found many applications in non-lineardynamics, is particularly illuminating in the study of correlations betweenmorphology and environment. To our knowledge the technique is being applied forthe first time to the study of galaxy morphology and evolution. The PD is theslope of the curve representing the number of galaxies within some radius,determined separately for each galaxy in the catalog. Thus the distributions ofPD's can be compared for subsamples based on morphological type or luminosity.The conclusions of this analysis of RC3 are: 1) The PD elucidates the tendencyfor early-type galaxies to cluster more than late-type galaxies; however, thereis considerable overlap between these populations. 2) The PD statistic does notfind a significant relationship between luminosity and clustering in RC3, butit could be an effective diagnostic in larger 2D catalogs. 3) The majority ofgalaxies in RC3 (excluding clusters) are spread out in space much like a randomdistribution. A population of objects that traces the distribution of galaxies,but avoids clusters, would have only small correlations. It is worthwhile topursue application of the PD to larger catalogs with a wider range ofluminosities.

Analysis of Galaxy Morphology and Evolution Using the Pointwise Dimension