Angular Projections of Fractal Sets

Abstract

We discuss various questions which arise when one considers the central projection of three dimensional fractal sets (galaxy catalogs) onto the celestial globe. The issues are related to how fractal such projections look. First we show that the lacunarity in the projection can be arbitrarily small. Further characteristics of the projected set---in particular scaling---depend sensitively on how the apparent sizes of galaxies are taken into account. Finally, we discuss the influence of opacity of galaxies. Combining these ideas, seemingly contradictory statements about lacunarity and apparent projections can be reconciled.