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Estimating Fractal Dimensions in an Evolving System
  • Subhash Kak
Subhash Kak
Oklahoma State University

Corresponding Author:[email protected]

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Abstract

It is shown that fractal dimensions may be reasonably estimated in an evolving system when further information is not available by considering the growth in the number of cells in two steps. This may be of use in the estimation of the dimensionality of metamaterials as well as in other natural phenomena. In contrast to algorithm-generated patterns for which a time step is well defined, natural systems evolve in an active space that leads one to the optimal information dimension of e, and this provides a novel perspective on self-similar behavior in natural systems.