Self-dissimilarity is a measure of
complexity defined in a series of papers by
David Wolpert
David Hilton Wolpert is an American mathematician, physicist and computer scientist. He is a professor at Santa Fe Institute. He is the author of three books, three patents, over one hundred refereed papers, and has received numerous awards. His ...
and
William G. Macready.
The degrees of self-dissimilarity between the
patterns
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated li ...
of a
system observed at various
scales (e.g. the average
matter density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
of a physical body for
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...
s at different
orders of magnitude
An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic dis ...
) constitute a complexity "signature" of that system.
See also
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Diversity index
A diversity index is a quantitative measure that reflects how many different types (such as species) there are in a dataset (a community), and that can simultaneously take into account the phylogenetic relations among the individuals distributed a ...
*
Index of dissimilarity
The index of dissimilarity is a demographic measure of the evenness with which two groups are distributed across component geographic areas that make up a larger area. A group is evenly distributed when each geographic unit has the same percentage ...
*
Jensen–Shannon divergence
In probability theory and statistics, the Jensen– Shannon divergence is a method of measuring the similarity between two probability distributions. It is also known as information radius (IRad) or total divergence to the average. It is based o ...
*
Self-similarity
__NOTOC__
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically se ...
*
Similarity measure
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such meas ...
*
Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbe ...
References
Information theory
Complex systems theory
Measures of complexity
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