If the replication is exactly the same at every scale, it is called a

self-similar pattern.

A fractal is a geometric object which is constructed from a "simple" initial shape and arranged to form

self-similar patterns across different scales and with fractal dimensions.

After a brief biography of Russian mathematician Cantor (1845-1918) he considers such topics as basics, Cantor sets and continued fractions,

self-similar objects, porosity and thickness-looking at the gaps, and generalizations and applications.

This assumption of proportionality holds true for flows with a

self-similar velocity profile.

They are related to fractals, in that they have

self-similar patterns.

An example of this nested,

self-similar organization is the Russian Matryoshka doll.

They are

self-similar porous clusters in which the nanoparticles, smaller porous clusters, and larger aggregates of clusters all have the same rough geometry.

As Garrett sums up, the Thanksgiving Ode volume aspires to a "'prospect-view' or grand imperial vision" of the nation as "an abstract unified whole, the self-contained and

self-similar island nation united in purpose by the war with France" (10), but the poems in it are characterized by anxious self-consciousness and a nearly debilitating ambivalence; "when referred to at all, [they are] usually held up as the nadir of Wordsworth's career.

In the second part we introduce a definition of

self-similar multimeasure based on a Markov operator.

The most complicated type of encoding is indirect (usually growth) encoding, which enables the creation of complex modular networks with

self-similar parts, that are bigger and more complex than the genotype in which they are encoded.

Seven chapters cover hyperbolic systems of conservation laws, scalar hyperbolic equations in one dimension, hyperbolic systems in one space dimension, evolution of weak waves in hyperbolic systems, asymptotic waves for quasilinear systems,

self-similar solutions involving discontinuities, and kinematics of a shock of arbitrary strength.

first found that the network traffic is

self-similar and this attribute is one of the basic natures of the network traffic.