The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition

Tom 180 / 2003

Michael Keane, K. Károly, Boris Solomyak Fundamenta Mathematicae 180 (2003), 279-292 MSC: Primary 28A78, 28A80, 94A08; Secondary 37C45. DOI: 10.4064/fm180-3-5


Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.


  • Michael KeaneMathematics Department
    Wesleyan University
    Middletown, CT 06459, U.S.A.
    University of Amsterdam
    Amsterdam, The Netherlands
  • K. KárolyInstitute of Mathematics
    Technical University of Budapest
    P.O. Box 91
    H-1529 Budapest, Hungary
  • Boris SolomyakDepartment of Mathematics
    University of Washington
    Box 354350
    Seattle, WA 98195-4350, U.S.A.

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