Examples of fractal in the following topics:
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- Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals.
- Logarithms occur in definitions of the dimension of fractals.
- Fractals are geometric objects that are self-similar: small parts reproduce, at least roughly, the entire global structure.
- Another logarithm-based notion of dimension is obtained by counting the number of boxes needed to cover the fractal in question.
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- The Koch snowflake is a fractal shape with an interior comprised of an infinite amount of triangles.
- In the study of fractals, geometric series often arise as the perimeter, area, or volume of a self-similar figure.
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- Some, such as plant structures and coastlines, may be so arbitrary as to defy traditional mathematical description – in which case they may be analyzed by differential geometry, or as fractals.
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- One common theme in a great deal of traditional African architecture is the use of fractal scaling: small parts of the structure tend to look similar to larger parts, such as a circular village made of circular houses.