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 S(f) similar to 1/f((d) over bar) . The exponent (d) over tilde = to (D - d)/z, where d is the spatial dimension, D is the avalanche dimension, and z is the usual dynamical exponent. Theoretical results agree with numerical simulations.