AVALANCHES AND 1 F NOISE IN EVOLUTION AND GROWTH-MODELS/

We formally establish the relationship between spatial fractal behavio r and long-range temporal correlations for a broad range of self-organ ized (and not self-organized) critical phenomena including directed pe rcolation, interface depinning, and a simple evolution model. The recu rrent activity at any particular site forms a fractal in time, with a power spectrum S(f) similar to 1/f((d) over bar) . The exponent (d) ov er tilde = to (D - d)/z, where d is the spatial dimension, D is the av alanche dimension, and z is the usual dynamical exponent. Theoretical results agree with numerical simulations.