# Self-Similar

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## Self-Similar

When small parts of an object are qualitatively the same, or similar to the whole object. In certain deterministic fractals, like the Sierpinski Triangle, small pieces look the same as the entire object. In random fractals, small increments of time will be statistically similar to larger increments of time. See: Fractal.

## Self-Similar

In mathematics, describing a condition in which the parts of an object are substantially the same as its whole. See also: Fractals.
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The financial trader and analyst Bill Williams  believes that this complexity is built up from self-similar patterns of trader behavior.
In our case, self-similar objects are convex bodies in n-dimensional spaces, for example, in the three-dimensional Euclidean space.
There exists a unique solution of Cauchy problem (1) in the self-similar form [v.sub.m](t, x) = [t.sup.-1/3] [f.sub.m]([xt.sup.-1/3]), such that
In this experiment, we have considered the azimuthal angles of the shower tracks belonging to four overlapping pseudorapidity intervals centered around [c.sub.r], from the same interaction to analyse the fluctuation and to identify the clustering pattern from a complex network perspective, and attempted to detect whether the azimuthal fluctuation is also self-similar in nature and follows scaling laws.
Besides isometries, there are symmetries called the self-similar solutions of space-time which are more restrictive.
The spreading rate is given by the gradient of the best-fit line for the [r.sub.1/2] plot in the self-similar region.
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.
First, we recall that Carrillo and Ferreira  considered self-similar solutions for equation (1.1).
Following the self-similar model, at a distance exceeding several diameters of the thruster's nozzle, the plume has Gaussian density profile, a constant axial velocity, and a linearly increasing radial velocity .
(i) The Q-sequence is built out of apparently self-similar "sausages."
The mathematical models of self-similar hierarchies of cities can be expressed as a set of exponential functions and power functions.

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