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Fractal Dimension

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Book: The Fractal Geometry of Nature
  • Form cannot be studied solely through topology as it requires an additional dimension, the fractal one

    • Essentially, it expresses a non-topological aspect of form; the fractal form
  • The fractal dimension \(D\) is always greater than the topological dimension \(D_T\). i.e. \(D >= D_T\)

  • In the euclidean span \(R^\epsilon\): \(0 < D_T,D < \epsilon\)

  • For all euclidean figures (Ex: circles, squares, triangles etc), \(D=D_T\)