We introduce a harmonic analysis for a class of affine iteration models in R d. Using Hilbert space geometry, and certain complex Hadamard matrices, we develop a new Fourier duality notion for affine and contractive iterated function systems (IFSs). It is known that not all such affine systems admit orthogonal Fourier bases. As a result, our duality is more general than earlier related construc...

An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated function system (IFS) is one type of fractals that maintains a similarity characteristic. By introducing the IFS into the crossover operation, the RCGA performs better searching solution with a faster convergence in a set of benchmark test functions.

We survey some of the topological properties of the attractors of iterated function systems such as connectedness, arcwise connectedness and locally arcwise connectedness. We give necessary and sufficient conditions for the attractors of finite iterated function system (IFS) to be a connected sets and in the case when infinite iterated function systems (IIFS) are considered we give only some su...

It is shown that the discriminant of a discriminant has the same irreducible factors as the product of seven polynomials which are defined as the GCD of the generators of an elimination ideal. Under tame conditions of genericity, three of these polynomials are irreducible and generate the corresponding elimination ideal, while the four other are equal to one. Moreover the factors of two of thes...

We present a general method of generating continuous fractal interpolation surfaces by iterated function systems on an arbitrary data set over rectangular grids and estimate their Box-counting dimension.

We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in R with arbitrary dimension H. Each IFS defines a probability distribution on R , so that the fractal inverse problem can b...

fn = (k −mod(n, k))fbn/kc +mod(n, k)fdn/ke + an, n ≥ k, there is a unique continuous periodic function f∗ : R→ R with period 1 such that fn = nf(logk n)+o(n). If (an) is periodic with period k, ak = 0, and the initial conditions (fi : 1 ≤ i ≤ k − 1) are all zero, we obtain a specific iterated function system S, consisting of k continuous functions from [0, 1] × R into itself, such that the attr...

We investigate when the Hutchinson operator associated with an iterated function system is continuous. The continuity with respect to both the Hausdorff metric and Vietoris topology is carefully considered. An example showing that the Hutchinson operator on the hyperspace of nonempty closed bounded sets need not be Hausdorff continuous is given. Infinite systems are also discussed. The work cla...

In this paper, two new paradigms are proposed with fractal collage and reconstruction residuals to enhance FIC. In the first new paradigm, FIC is optimized using the reconstruction residuals. In the second paradigm, the selected collage residuals are used to correct the iterated function system (IFS) of FIC, and an effective technique for coding the selected collage residuals is applied based o...

LRIFS's (Language-Restricted Iterated Function Systems) generalize the original de nition of IFS's (Iterated Function Systems) by providing tools for restricting the sequences of applicable transformations.In this paper, we study an approach of LRIFS's based on matrices and graph theory. This enables us to generate a matrix which elements are attractors.