# self-similarity

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## self-similarity

[¦self ‚sim·ə′lar·əd·ē]
(mathematics)
The property whereby an object or mathematical function preserves its structure when multiplied by a certain scale factor.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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In this section we prove the existence of a unique selfsimilar solution [v.sub.m](t, x) [equivalent to] [t.sup.-1/3] [f.sub.m]([xt.sup.-1/3]) for (1), which is uniquely determined by the total mass condition m = (1/[square root of 2[pi]]) [[integral].sub.R] [v.sub.m](t, x)dx [not equal to] 0.
To do this, we will resort to the properties of selfsimilar sets, in such manner that each property will help us discard those partitions of P(X) that do not comply with it.
For fractal processes (selfsimilar), F(n) increases with n by the power law, as shown in Equation 4:
The ideal Sierpinski gasket is a selfsimilar structure and each one of its three main parts has exactly the same shape as that of the whole object but reduced by a factor of two [13].
The selfsimilar nature of the present-day aggregated multimedia traffic is highly restricting traffic forecasting effectiveness, especially in the short time forecasting periods [5].
Since this observer exists at the selfsimilar singular ontological level of Suchness, it is again self-singular without parallel and indeed without any logical extraneous qualifier (and quantifier), thereby encompassing the Real, the Mirror, the Image, and the Shadow, in the manner of Reality.
Nonnenmacher, A fractional calculus approach of selfsimilar protein dynamics, Biophys.
We have shown that every cellular automaton inducing a morphism of abelian groups produces a selfsimilar spacetime diagram.
In this article, we consider the construction of so-called selfsimilar solutions to discrete versions of basic diffusion equations.
We first give a short review on supermodels in quantum mechanics where the main focus will be on selfsimilar supermodels, showing a point spectrum which consists of basic q-versions of the natural numbers.
The calculated object appears to be fractal, in that (a) there are selfsimilar features (lobe structures), and (b) there is lace-like detail at increasing magnification (see inset detailed views).

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