# 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 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