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Iterated Function Systems Enriched with Symmetry
Constructive Approximation, 2021This paper deals with finite IFSs (iterated function systems) which are contractive on average. ``The average contractivity of an IFS guarantees the asymptotic stability of the Markov operator associated with this IFS. This in turn ensures the existence and uniqueness of the invariant measure.'' One can cite authors' abstract: ``An iterated function ...
Krzysztof Leśniak, Nina Snigireva
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ITERATED FUNCTION SYSTEMS ON FUNCTIONS OF BOUNDED VARIATION
Fractals, 2016We show that under certain hypotheses, an iterated function system on mappings (IFSM) is a contraction on the complete space of functions of bounded variation (BV). It then possesses a unique attractor of BV. Some BV-based inverse problems based on the Collage Theorem for contraction maps are considered.
D. La Torre, F. Mendivil, E. R. Vrscay
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Iterated Function Systems, Capacity and Green’s Functions
Computational Methods and Function Theory, 2004The iterated function system \(f_1, \ldots, f_m: \mathbb C\to\mathbb C\) with Lipschitz bounds \[ a_j | z-w| \leq | f_j(z)-f_j(w)| \leq b_j | z-w| , \] for ...
Baribeau, Line +3 more
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ON (n, m)-ITERATED FUNCTION SYSTEMS
Asian-European Journal of Mathematics, 2013One of the most common way to generate a fractal is by using an iterated function system (IFS). In this paper, we introduce an (n, m)-IFS, which is a collection of n IFSs and discuss the attractor of this system. Also we prove the continuity theorem and collage theorem for (n, m)-IFS.
Balu, Rinju, Mathew, Sunil
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Random iteration for infinite nonexpansive iterated function systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015We prove that the random iteration algorithm works for strict attractors of infinite iterated function systems. The system is assumed to be compactly branching and nonexpansive. The orbit recovering an attractor is generated by a deterministic process and the algorithm is always convergent.
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Affine Mappings in Iterated Function Systems
Results in Mathematics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2009
In the early 1980's, Michael Barnsley introduced the idea of synthesizing a predetermined image as the attractor of a chaotic process. Other researchers had previously shown that chaotic systems were capable of producing fascinating images known as strange attractors.
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In the early 1980's, Michael Barnsley introduced the idea of synthesizing a predetermined image as the attractor of a chaotic process. Other researchers had previously shown that chaotic systems were capable of producing fascinating images known as strange attractors.
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Chaotic fuzzy iterated function systems
Journal of Intelligent & Fuzzy SystemsIt is observed that IFSs are defined based on the concept that the iterates take only an integer number of times. This work studies the dynamics of functions, where a function can iterate r times for every r ∈ R. Utilizing concepts from fuzzy sets, r-times iterates of a function are defined for r ∈ R.
R. Selvy, P. B. Vinod Kumar
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Automatic generation of iterated function systems
Computers & Graphics, 1994Abstract A set of affine mappings with randomly chosen coefficients is repeatedly iterated numerically using the random iteration algorithm to produce an attractor with fractal characteristics. The attractor is tested for boundedness, sensitivity to initial conditions, and correlation dimension. In this way, a computer can generate a large collection
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Iterated function systems for DNA replication
Physical Review E, 2017The kinetic equations of DNA replication are shown to be exactly solved in terms of iterated function systems, running along the template sequence and giving the statistical properties of the copy sequences, as well as the kinetic and thermodynamic properties of the replication process.
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