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

Michael Keane; Károly Simon; Boris Solomyak

doi:10.4064/fm180-3-5

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

Michael Keane
, Károly Simon
, Boris Solomyak

Wesleyan University
University of Amsterdam
Budapest University of Technology and Economics
University of Washington

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	279-292
Number of pages	14
Journal	Fundamenta Mathematicae
Volume	180
Issue number	3
DOIs	https://doi.org/10.4064/fm180-3-5
State	Published - 2003
Externally published	Yes

Keywords

Fractal image recognition
Fractals with overlapping cylinders
Graph directed IFS
Self-affine fractals

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10.4064/fm180-3-5

Cite this

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KW - Self-affine fractals

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

Abstract

Keywords

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