Browsing by Author "Igudesman K."

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  • A certain family of self-similar sets 
    Igudesman K. (2011)
    In this paper we consider an one-parameter family of iterated function systems. For every value of the parameter we find the set of top addresses. We prove that this set is a countable disjoint union of self-similar sets ...
  • Attractor decompositions for closed binary relations on compact Hausdorff spaces 
    Igudesman K. (2013)
    One of the main methods for studying iterated function systems is the attractor decomposition by a code map. In this paper we obtain an analog of such a decomposition for closed binary relations on compact Hausdorff spaces. ...
  • Dynamics of finite-multivalued transformations 
    Igudesman K. (2005)
    We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such a transformation an m-transformation. In this case the orbit of any point looks like a tree. In the ...
  • Fractal approximation of vector functions 
    Davletbaev M.; Igudesman K. (2013)
    We present a new approach to the approximation of continuous vector-valued functions by fractal interpolative vector-valued ones and find optimal values of their parameters. We illustrate the obtained results with examples. ...
  • How to transform and filter images using iterated function systems 
    Barnsley M.; Harding B.; Igudesman K. (2011)
    We generalize the mathematics of fractal transformations and illustrate how it leads to a new approach to the representation and processing of digital images, and consequent novel methods for filtering, watermarking, and ...
  • Lacunary self-similar fractal sets and intersection of cantor sets 
    Igudesman K. (2003)
    The problem on intersection of Cantor sets was examined in many papers. To solve this problem, we introduce the notion of lacunary self-similar set. The main difference to the standard (Hutchinson) notion of self-similarity ...
  • Least-squares fitting of a three-dimensional ellipsoid to noisy data 
    Malyugina A.; Igudesman K.; Chickrin D. (2014)
    © 2014 Alexandra Malyugina, Konstantin Igudesman and Dmitry Chickrin. This paper deals with the problem of fitting a three-dimensional ellipsoid to a noisy data point set in the context of three-axis magnit-ometer calibration. ...
  • Matrices over a semiring of binary relations and V -variable fractals 
    Biserov D.; Igudesman K. (2011)
    In this paper we prove that V -variable fractal sets are limits of infinite products of matrices over the semiring of binary relations on a compact metric space. © Allerton Press, Inc., 2011.
  • New approach to fractal approximation of vector-functions 
    Igudesman K.; Davletbaev M.; Shabernev G. (2015)
    © 2015 Konstantin Igudesman et al. This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization ...
  • Novel approach to calculation of box dimension of fractal functions 
    Igudesman K.; Lavrenov R.; Klassen V. (2014)
    © 2014 Konstantin Igudesman, Roman Lavrenov and Victor Klassen. We introduce new method of calculation of box dimension of fractal functions' graphs, which are based on fractal interpolation functions. Provide a comparison ...
  • Overlapping iterated function systems on a segment 
    Barnsley M.; Igudesman K. (2012)
    Overlapping iterated function systems generate families of injective mappings from the attractor onto shift-invariant subsets of the code space. In this paper we consider an example of such a family for the uniformly linear ...
  • Peculiarities of elastic wave refraction from the layer with fractal distribution of density 
    Anufrieva A.; Igudesman K.; Tumakov D. (2014)
    In this study, we underline the peculiarities of the refraction problem of elastic waves from a layer with a fractal density distribution. The refraction problem is reduced to the system of ordinary di erential equations ...

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