Abstract
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 . The exponent , where is the spatial dimension, is the avalanche dimension, and is the usual dynamical exponent. Theoretical results agree with numerical simulations.
- Received 19 July 1994
DOI:https://doi.org/10.1103/PhysRevLett.73.2162
©1994 American Physical Society