The fixed point or fixed set (set or point A) in Theorem 3 is called the attractor of this

iterated function system. The attractors of the

iterated function system are generally fractal or have basic properties of fractal.

Fractal image coding is based on the theory of the partitioned

iterated function system (PIFS) [2].

Hence we obtained the set [C.sub.[delta]] as the attractor of the graph directed

iterated function systems, defined by the graph, shown in Figure 8.

Igudesman, "Top addresses for a certain family of

iterated function system on a segment," Russian Mathematics (Izvestiya VUZ.

The method of

iterated function systems with greyscale maps (IFSM), as formulated by Forte and Vrscay (1995), can be used to approximate a given element u of [L.sup.2]([0,1]).

If each [w.sub.i] (1 [less than or equal to] i [less than or equal to] m) is a contractive map from X to X, then we call (X, [{[w.sub.i]}.sup.m.sub.i=1]) the contractive

iterated function systems (IFS).

In (KigLap93), the authors prove that for a nested fractal the exponent [d.sub.S] of the leading term in the eigenvalue counting function of this Laplacian satisfies [d.sub.S]/2 = ln M/ln(M[??]), where M denotes the number of similitudes in the

iterated function system and [??] the energy scaling factor introduced above.

singular measures, Fourier transform, orthogonal polynomials, almost periodic Jacobi matrices, Fourier-Bessel functions, quantum intermittency, Julia sets,

iterated function systems, generalized dimensions, potential theory

For an infinite

iterated function system, by assuming the open set condition, BDP, and that the maps of the IFS are [C.sup.1+[epsilon]] smooth, Mauldin and Urbanski [4] proved that the Hausdorff dimension of the limit set is given by the zero of some topological pressure function.

We give in this paper an expression for the moment matrix associated to a self-similar measure given by an

Iterated Function Systems (IFS).

In Section "

Iterated function systems" the main results from the IFS theory are briefly recalled.

iterated function systems, fractal interpolation functions, trigonometric approximation