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Book: The Fractal Geometry of Nature
  • Fractals are the set of figures for which the fractal dimension is greater than the topological dimension i.e. \(D > D_T\)

    • Furthermore, every set with a non-integer \(D\) is a fractal
    • Although D may be an integer (Ex: Brownian motion has \(D=2\)
  • Scaling Fractals: Fractals that are invariant to scaling

    • The term scaling signifies a type of order
    • The term fractals excludes lines and planes
  • Fractals that are invariant under geometric similarity are called self-similar fractals.

    • Self-similar fractal curves are theoretically unbounded
    • In reality, cutoffs at the very large and small end are suspected