The dictionary defines fractals as “a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry.” Indeed, fractals are some of the most beautiful forms produced by dry mathematics. A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.[The following are extracts from the Wikipedia entry for fractal.]
A fractal has the following features:
- It has a fine structure at arbitrarily small scales.
- It is too irregular to be easily described in traditional Euclidean geometric language.
- It is self-similar.
- It has a simple and recursive definition.
Fractals are considered to be infinitely complex.
One way of classifying fractals is according to the way they are generated.
One way of classifying fractals is according to the way they are generated.
- Escape-time fractals: They are defined by a formula or recurrence relation at each point in a space.
- Iterated function systems: They have a fixed geometric replacement rule
- Random fractals: They are determined by probabilistic processes.
- Strange attractors.
Fractals can also be classified according to their self-similarity.
In nature, fractals can be found in clouds, snowflakes, rivers and lightning.
Applications of fractals include
In nature, fractals can be found in clouds, snowflakes, rivers and lightning.
Applications of fractals include
- Fractal landscape or Coastline complexity
- Generation of new music
- Generation of various art forms
- Signal and image compression
- Creation of digital photographic enlargements
- Seismology
- Soil Mechanics
- Computer and video game design
- Fracture mechanics
- Fractal antennas – Small size antennas using fractal shapes
- Small angle scattering theory of fractally rough systems
- Generation of patterns for camouflage
- Digital sundial
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