Mathematical approach to the problem of clustering

Extract

The mathematical theory of the description of the structure of point-sets in a plane or in space can be applied to the investigation of the distribution of different extragalactic objects. Mathematically we can define rigorously such ideas as cluster, nucleus of cluster, monoor polynuclear structure, background and so on. First we choose a critical distance that determines the scale on which we investigate the distribution of objects. the critical distance plays a similar role to the wavelength of radiation by means of which we investigate the internal structure of matter. It is obvious that the description is different for different critical distances. To obtain a complete picture we have to analyse the evolution of this description as the critical distance changes.