This paper analyzes the model for the evolution of sunspots considered as fractal clusters of magnetic flux tubes. Formation of sunspots is regarded as a result of magnetic tubes aggregation to the cluster. It is proved that magnetic field dissipation in the tubes results in effective sunspot decay. Sunspot formation and decay times deduced by the model as well as the rate of magnetic flux loss are in a good agreement with the observational data. The diffusion of magnetic flux tubes in sunspot penumbra is considered as a random walk on a fractal geometry. Disappearance of umbra in decaying sunspots is interpreted as a phase transition. ¿ American Geophysical Union 1992