Scaling law

Subscales laws or scaling laws refers to the manifestations of mathematical relations of the type

That is, exponential relationships, or

That is, power or polynomial relationships that are where and are real constants. Power laws are more common than exponential relationships.

Such relationships are common in nature and society so that one can speak of a structuring principle. Partly it is a purely empirical distributions found, partially but these could be put on a sound theoretical basis, so that in a scientific sense, one can speak of "laws". This is due to, among other things, that

The solution of the simplest linear differential equation

Is describing a self-accelerating process, such as the growth of a population without resource constraints.

Scale relationship based on power laws are scale invariant due to the relationship

Ie that is proportional and do not change the characteristics of. Exponential relationships do not show this scale invariance.

Examples

Statistics

Biology

Geoffrey West leads the universality of scaling laws in biology on the following back:

From these principles, the allometries with very simple scaling laws appear ( the exponents tend to be integral multiples of 1 /4) to be derived at least.

Examples are the relationships between

• Metabolic rate and body mass M U, also law of metabolic reduction, law of reduction of specific metabolic rates or allometry called: with
• The mass of the white and gray matter in the mammalian brain
• Tree trunk base diameter and total foliage area
• Tree trunk diameter and frequency of tree specimens in a forest

Chemistry

Physics

Linguistics

Internet

The Internet is a huge network with emergent phenomena such as self-similar scaling in the burst patterns of its traffic and scale-free structure in the connection topology.

Blogs

Other self- link end Internet platforms like weblogs show a particular context: new weblogs left preference - that is, more likely - on already popular weblogs and make them even more popular. This HYPERLINK algorithm is incidentally also the rule for the creation of a scale-free network.

Economics

Main article: Pareto distribution: ...