Probing the Fractal Nature of Long GRBs

摘要

We interrogated Swift Long GRBs using a Fast Wavelet technique to probe the observed variability for fractal (or self-affine) behavior. Self-affine behavior for a time-series implies a statistical similarity after a particular rescaling transformation from the Affine Group, X(jt) velence j~(-(alpha-1)/2)X(t). It is straightforward to associate the slope parameter, alpha, with the Hurst exponent, H, and the fractal dimension, D. These measures may hold a key to a better understanding of GRB variability and provide constraints for theoretical models.