2.4 Fractals and other information theoretic models

Alfred Renyi (Renyi, 1961) further generalized this idea and presents a model that relates a number of different
measures (or dimensions) such as Hausdorff dimension and Shannon Uncertainty. This relationship is interesting
because it allows for a conceptual model that coordinates spatial measures of complexity with information theoretic
ones. Takayasu and Schroeder describe the relation between fractal dimension and Shannon Uncertainty through
Renyi’s generalization of entropy (Takayasu, 1990) (Schroeder, 1991). The mathematical relationship between
Shannon entropy/ information and fractal dimension will be discussed more in section 5.0 of this dissertation and in
section 7.1 in the appendix.

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