Correlation functions in 2D and 3D as descriptors of the cosmic web

Aims. Our goal is to find the relation between two-point correlation functions (CFs) of projected and spatial density fields galaxies in context cosmic web. Methods. To investigate relations (3D) (2D) CFs we used two simulations: a $\Lambda$-dominated cold dark matter (LCDM) model with known particle data, Millennium simulation know data on simulated galaxies. We compare 3D 2D functions. In case, use samples various thickness dependence samples. also real redshift space. Results. The dominant elements web are clusters filaments, separated by voids filling most volume. individual sheets, positions filaments do not coincide. As result, projection, fill voids. This leads decrease amplitudes (and power spectra) projection. For this reason, lower than functions: thicker sample, greater difference. Conclusions. Spatial contain valuable information about geometrical properties that cannot be found from CFs.