A mantle plume is a rising stream of vigorous thermal convection, which takes a mushroom-like shape and has a finite lifetime. When the plume approaches to the lithosphere the plume head first penetrates it. During the solidification of magma near the plume head a large igneous province (LIP) is formed. Later the plume tail penetrates the moving plate and forms a chain of volcanoes oriented in the direction of plate motion. A hot spot (HS) is the end location of the chain or the place of modern penetration of the plume tail in the form of an active volcano. In existing numerical models of mantle convection the plume tails are continuous streams. The question of why between the volcanic islands there is an interval of several hundred km (which corresponds to the interval between eruptions of several million years) is discussed starting from the time of emergence of the concept of plumes. This work on the numerical models shows that a primary plume originates only at the mantle bottom and dies not by attenuation but by pairwise association of two adjacent plumes. Also the work studies the internal structure of mantle plumes. It is shown that the plume tail is a pulsating jet already in the lower mantle with periods of several million years. When the plume encounters the 660 km phase boundary it flattens out against this surface and transforms into secondary more frequent plumes in the form of the individual thermals (heads detached from tails).