  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 of
fractal geometry (Mandelbrot 1983) and found many applications in non-linear
dynamics, is particularly illuminating in the study of correlations between
morphology and environment. To our knowledge the technique is being applied for
the first time to the study of galaxy morphology and evolution. The PD is the
slope of the curve representing the number of galaxies within some radius,
determined separately for each galaxy in the catalog. Thus the distributions of
PD'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 tendency
for early-type galaxies to cluster more than late-type galaxies; however, there
is considerable overlap between these populations. 2) The PD statistic does not
find a significant relationship between luminosity and clustering in RC3, but
it could be an effective diagnostic in larger 2D catalogs. 3) The majority of
galaxies in RC3 (excluding clusters) are spread out in space much like a random
distribution. A population of objects that traces the distribution of galaxies,
but avoids clusters, would have only small correlations. It is worthwhile to
pursue application of the PD to larger catalogs with a wider range of
luminosities.
