Abstract
By using non-extensive block entropy statistics, we demonstrate analytically that the static structures of deterministic Cantor sets with fractal dimension d f are characterised by a non-extensive q -exponent q = 1 / ( d f - d ) , for d f < d (where d is the embedding dimensions of the fractal set). To calculate the S q 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”.
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