Non-extensive block entropy statistics of Cantor fractal sets

By using non-extensive block entropy statistics, we demonstrate analytically that the static structures of deterministic Cantor sets with fractal dimension df are characterised by a non-extensive q-exponent q=1/(df-d), for df<d (where d is the embedding dimensions of the fractal set). To calculate the Sq entropy we use the block entropy method based on non-overlapping windows and standard exact enumeration on Cantor sets. This result indicates that fractal structures are formed via dynamical processes which operate “at the edge of chaos”.