Context. Extragalactic radio sources have been classified into two classes, Fanaroff-Riley I and II, which differ in morphology and radio power. Strongly emitting sources belong to the edge-brightened FR II class, and weakly emitting sources to the edge-darkened FR I class. The origin of this dichotomy is not yet fully understood. Numerical simulations are successful in generating FR II morphologies, but they fail to reproduce the diffuse structure of FR Is. Aims. By means of hydro-dynamical 3D simulations of supersonic jets, we investigate how the displayed morphologies depend on the jet parameters. Bow shocks and Mach disks at the jet head, which are probably responsible for the hot spots in the FR II sources, disappear for a jet kinetic power L sub(kin)< or = 10 super(43) ergs super(-1). This threshold compares favorably with the luminosity at which the FR I/FR II transition is observed. Methods. The problem is addressed by numerical means carrying out 3D HD simulations of supersonic jets that propagate in a non-homogeneous medium with the ambient temperature that increases with distance from the jet origin, which maintains constant pressure. Results. The jet energy in the lower power sources, instead of being deposited at the terminal shock, is gradually dissipated by the turbulence. The jets spread out while propagating, and they smoothly decelerate while mixing with the ambient medium and produce the plumes characteristic of FR I objects. Conclusions. Three-dimensionality is an essential ingredient to explore the FR I evolution becausethe properties of turbulence in two and three dimensions are very different, since there is no energy cascade to small scales in two dimensions, and two-dimensional simulations with the same parameters lead to FRII-like behavior.