Fractals
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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 noninteger \(D\) 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 selfsimilar fractals.
 Selfsimilar fractal curves are theoretically unbounded
 In reality, cutoffs at the very large and small end are suspected

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