Avalanches and 1/f noise in evolution and growth models.

We formally establish the relationship between spatial fractal behavior and long-range temporal correlations for a broad range of self-organized (and not self-organized) critical phenomena including directed percolation, interface depinning, and a simple evolution model. The recurrent activity at any particular site forms a fractal in time, with a power spectrum [ital S]([ital f])[similar to]1/[ital f][sup [ital [tilde d]]]. The exponent [ital [tilde d]]=([ital D][minus][ital d])/[ital z], where [ital d] is the spatial dimension, [ital D] is the avalanche dimension, and [ital z] is the usual dynamical exponent. Theoretical results agree with numerical simulations.