# self-similar

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## self-sim·i·lar

(sĕlf′sĭm′ə-lər)
Having a substructure analogous or identical to an overall structure. In mathematics, certain geometrical objects such as line segments and fractals are self-similar to an arbitrary level of magnification; many natural phenomena, such as clouds and plants, are self-similar to some degree.

self′-sim′i·lar′i·ty n.
References in periodicals archive ?
The stages of the city of Cologne are a self-similar institution of the city of Cologne and operate the opera, the drama, the children's opera and two other venues.
When we look at landscapes that have a natural fractal pattern [fractals are infinitely complex patterns that are self-similar across different scales]--natural shapes like tree limbs, clouds, ripples on the water, or coastlines--our brains produce more alpha waves, which signify a wakefully relaxed state.
D = log (number of self-similar pieces)/log (scale factor)
The layout of the paper is as follows: Section 2 estimates brain plasma parameters and set up a set of two-fluid Vlasov-Maxwell equations; Section 3 derives a set of nonlinear, self-similar differential equations for the excitation and propagation of EEG waves; Section 4 exposes the data-fit modeling of the solitary EEG waves under different conditions.
Fractals considered as self-similar when an object is exactly or approximately similar to a part of itself or self-affine or self-affine when objects are scaled by different amounts in the x- and y-directions.
But, since not all SFCs are exact self-similar, in this paper, we propose a method to determine whether a discrete approximation of Space Filling Curve is exact self-similar.
Traffic anomaly based detection: Anomaly detection by self-similar analysis.
Finally we describe the Lagrangian self-similar solutions of the Mean Curvature Flow which are SO(n)-equivariant.
These discrepancies have major impacts on the position of the virtual origin, the core length, the position where self-similarity is achieved, but have minor effects on the self-similar profiles.
The proceedings of first gathering contains 11 papers on such topics as min-max theory of minimal surfaces and applications, Lagrangian cobordism: rigidity and flexibility aspects, biochemical reaction networks: an invitation for algebraic geometers, entrance laws for positive self-similar Markov processes, and geometric regularity estimates for elliptic equations.
If the replication is exactly the same at every scale, it is called a self-similar pattern.
Hence microseismic events spectra of different magnitudes from similar locations are self-similar as observed.
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