A. The discovery of power-law clustering
The pioneering work of Rubin and Limber has already been mentioned. These early authors were limited by the nature of the catalogs that existed at the time and the means to analyze the data - there were no computers!
It was Totsuji and Kihara (1969) and, independently, Peebles (1974b) who were first to present a computer-based analysis of a complete catalog of galaxies. Totsuji and Kihara used the published Lick counts in cells from Shane and Wirtanen (1967), while Peebles and coworkers analysed a number of catalogs: the Reference catalog of Bright Galaxies, the Zwicky catalog, the Lick catalog and later on the very deep Jagellonian field (Peebles and Hauser, 1974; Peebles, 1975; Peebles and Groth, 1975). All this work was done on the projected distribution of galaxies since little or no redshift information was available.
The central discovery was that the two-point correlation function describing the deviation of the galaxy distribution from homogeneity scales like a simple power law over a substantial range of distances. This result has stood firm through numerous analyses of diverse catalogs over the subsequent decades.
The amplitudes of the correlation functions calculated from the different catalogs were found to scale in accordance with the nominal depth of the catalog. This was one of the first direct proofs that the Universe is homogeneous. Before that we knew about the isotropy of the galaxy distribution at different depths and could only infer homogeneity by arguing that we were not at the center of the Universe.