Comparative analysis of topological organization in Metazoa

Topological patterns in Metazoa, using previously elaborated methodology with employment of the genus of the surface (p) as topological invariant are considered. The term "density of the genus of the surface" is introduced. In sponges and in a lesser degree among Cnidaria and, Ctenophoria an increase of genus p up to indefinite high values and the shaping of topologically complicated quasifractal systems (irrigation system in sponges and gastro-vascular system in Radiata) are evident. In most Bilateria a stable topological pattern with open digestive tube is formed and subsequent topological complications of other systems may occur. Complicated topological patterns increasing the genus of the surface are evolved on the base of quasifractal systems: gut pockets in turbellaria, tracheal system in arthropods, bronchial system in birds, gills in bivalve mollusks, etc. Peculiarities of ordered and disordered topological patterns as well as topological origin of the increase of the genus of the surface are considered.