What is self-similarity?
What is self-similarity?
A self-similar object is exactly or approximately similar to a part of itself (Wikipedia 2006).
Examples:
- 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 (Wikipedia 2006).
- Coastlines are statistically self-similar as parts of them show the same statistical properties at many scales (Wikipedia 2006).
Self-similarity is an important aspect of the design of computer networks, as typical network traffic has self-similar properties (Wikipedia 2006).
Example: In teletraffic engineering, packet switched data traffic patterns are statistically self-similar (Wikipedia 2006). This property emphasises that simple models using the Poisson distribution are inaccurate (Wikipedia 2006). Networks that are designed using the Poisson distribution without taking self-similarity into account are likely to function in unexpected ways.
Self-similarity is a typical property of fractals.
Exercise: In the following diagrams, say whether they are self-similar or not. Answer
References:
Wikipedia. "Self-similarity", Wikimedia Foundation Inc, http://en.wikipedia.org/wiki/Self-similarity, Last accessed 11 February 2006.
Brandon Hodgson
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Last edited by Brandon Hodgson on Feb 15, 2006 8:50 am US/Central.