Mean diameters of voids have been determined for galaxy and cluster samples of different size, CDM simulated samples and samples of randomly spaced clusters. Two methods have been used to determine diameters of voids. In the first case 'pencil beams' were put through the sample volume and mean distances between consecutive density maxima were determined. In the second case diameters of empty spheres, surrounded on various sides by galaxies at equal distances, were found. Observed samples of galaxies and clusters of galaxies range in size from 1 to 250 h−1 Mpc. In these samples, as well in the CDM simulation, mean void diameters increase with sample size, indicating the self-similarity of the structure on various scales, i.e. the fractal nature of the distribution. In randomly spaced cluster samples void diameters are independent on the sample size which confirms the non-fractal nature of the distribution. This property is closely related to the behaviour of the correlation function: the correlation length of a sample is proportional to the mean void diameter. The lower scale limit of the fractal structure of the Universe as defined by the self-similarity of voids is given by the size of clusters of galaxies, the upper limit cannot be derived from available data. The largest voids observed in galaxy samples studied here have mean diameters of ≃ 30 h−1 Mpc, but voids in cluster and supercluster samples have larger mean diameters, ≃ 100 h−1 Mpc. This suggests that we have not yet reached representative samples of the Universe.
Einasto et al. (Mon,) studied this question.