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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-5,
author = {Michael Keane and K. K\'aroly and Boris Solomyak},
title = {The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {279-292},
zbl = {1099.28005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-5}
}
Michael Keane; K. Károly; Boris Solomyak. The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition. Fundamenta Mathematicae, Tome 177 (2003) pp. 279-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-5/