Scale invariance
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In physics, scale invariance is the feature of physical objects or laws that do not change if the space is magnified, i.e. length scales (or energies) are multiplied by a common factor. To give a trivial example for the object feature, the mass of the ball divided by the third power of its radius is independent of the radius i.e. scale invariant. An example of the law is self-similarity in fluid mechanics: all properties of the flow due to a moving body are the same if the size of the body is increased by the same factor as its velocity is decreased by - this is because the fluid flow in a given geometry is completely characterized by the dimensionless Reynolds number which is the product of size and velocity divided by kinematic viscosity.
In mathematics, scale invariance leads to results such as Benford's law, fractals and logarithmic spirals.
In cosmology, scale invariance is usually used to describe the near-scale-invariant energy spectrum of the cosmic microwave background - a pattern that is reasonably well explained by the paradigm of cosmic inflation.