Self-dissimilarity is a measure of
complexity
Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence.
The term is generally used to c ...
defined in a series of papers by
David Wolpert 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
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...
observed at various
scales (e.g. the average
matter density
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic parti ...
of a physical body for
volume
Volume is a measure of regions in 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) ...
s at different
orders of magnitude
In a ratio scale based on powers of ten, the order of magnitude is a measure of the nearness of two figures. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are wi ...
) constitute a complexity "signature" of that system.
See also
*
Diversity index
*
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, named after Johan Jensen and Claude Shannon, is a method of measuring the similarity between two probability distributions. It is also known as information radius (IRad) or to ...
*
Self-similarity
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 self-similar ...
*
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 mea ...
*
Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...
References
Information theory
Complex systems theory
Measures of complexity
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