### 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 |

Publication status | Published - 2003 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Fundamenta Mathematicae*,

*180*(3), 279-292.

**The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition.** / Keane, Michael; Simon, K.; Solomyak, Boris.

Research output: Contribution to journal › Article

*Fundamenta Mathematicae*, vol. 180, no. 3, pp. 279-292.

}

TY - JOUR

T1 - The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition

AU - Keane, Michael

AU - Simon, K.

AU - Solomyak, Boris

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - Fractal image recognition

KW - Fractals with overlapping cylinders

KW - Graph directed IFS

KW - Self-affine fractals

UR - http://www.scopus.com/inward/record.url?scp=1942473916&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1942473916&partnerID=8YFLogxK

M3 - Article

VL - 180

SP - 279

EP - 292

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

SN - 0016-2736

IS - 3

ER -