The average velocity magnitude the

self-similar profile described by Eq.

Iterated applications of an IFS Markov operator operating on a probability measure converge to a

self-similar measure which is invariant under the action of the functions in the IFS.

A second-order stationary process X is called exactly second-order

self-similar (ESOSS) with Hurst parameter H=1-[beta]/2, 0<[beta]<1, if the autocorrelation function satisfies

i] is a contractive

self-similar map, then we call (X, [{[w.

A coastline is fractal because it is

self-similar at each degree of magnification.

Let us now consider the sequence of

self-similar graphs depicted in Figure 4.

The experimental sand-carbon dioxide model thus holds the characteristics of a self-organized critical system - a large number of interacting members and degrees of freedom to adapt to higher transport rates, which results in a scale-free and

self-similar behaviour over three orders of magnitude at the length and time scales, inferred from the power law size distribution of the gas batches in the system and volumes escaped, as well as from the 1 /f power spectrum of the gas level fluctuations in the tank.

The mean concentration field, which provide the information of the spread and dilution of jet in the ambient current, show that the cross-section distributions of concentration are

self-similar and appear to be Gaussian in the ZFE;

self-similar measures, orthogonal polynomials, moment matrix

As SuperWaves are intrinsically

self-similar, we can now understand why nature is fractal in form, at all scales.

This property led Barabasi and many other researchers to assume that complex networks cannot be

self-similar.

This method of finding fractal dimensions can be used only for strictly

self-similar fractals.