Order in Randomness
Sub-Systems of Chaos Theory
- Feedback loops
- Repetition
- Self-similarity
- Fractals
- Self organization
Fractals
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Never ending patterns.
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Infinitely repeating patterns.
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Any geometric object with chaotic structure
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Fractals are the geometry of chaos.
\begin{equation} N_{n} = N_{(n 1)}x 4 = 3 x 4^n \end{equation} *n represents for repetition number.
Repetition Number | Total Perimeters |
---|---|
2 | 48 |
3 | 192 |
4 | 768 |
5 | 3072 |
∞ | ∞ |
History
Menger Sponge
References
- The Role Of Chaos And Fractals
- Werner Lauterborn, in Encyclopedia of Physical Science and Technology (Third Edition), 2003
- Order in Randomness: Fractals and Chaotic Systems
- Chaos Theory
- Fractals: The Geometry of Chaos - Christmas Lectures with Ian Stewart
- Fractals are typically not self-similar
- What Is A Fractal (and what are they good for)?
- Benoit Mandelbrot
- Helge von Koch
- Nathan Cohen BIO