A self-similar object is exactly or approximately similar to a part of itself. A curve is said to be self-similar if, for every piece of the curve, there is a smaller piece that is similar to it. For instance, a side of the Koch snowflake is self-similar; it can be divided into two halves, each of which is similar to the whole.

Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals.

It also has important consequences for the design of computer networks, as typical network traffic has self-similar properties. For example, in telecommunications traffic engineering, packet switched data traffic patterns seem to be statistically self-similar. This property means that simple models using a Poisson distribution are inaccurate, and networks designed without taking self-similarity into account are likely to function in unexpected ways.

See also

• Fractal
• Scale invariance
• Benoît Mandelbrot
• How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
• Self-reference
• Zipfs law

Reference

• Leland et. al. On the self-similar nature of Ethernet traffic IEEE/ACM Transactions on Networking Volume 2, Issue 1 (February 1994)

External links

• "Copperplate Chevrons" - a self-similar fractal zoom movie

Fractals

Selbstähnlichkeit | Autosimilaire | 自己相似 | Självliknande | 自相似