Proceedings: GI 1996

Spatial bounding of self-affine iterated function system attractor sets

Jonathan Rice

Proceedings of Graphics Interface '96: Toronto, Ontario, Canada, 22 - 24 May 1996, 107-115

DOI 10.20380/GI1996.13

  • BibTeX

    @inproceedings{Rice-gi96,
     title = {Spatial bounding of self-affine iterated function system attractor sets},
     author = {Jonathan Rice},
     booktitle = {Proceedings of the Graphics Interface 1996 Conference, May 22-24, 1996, Toronto, Ontario, Canada},
     year = {1996},
     month = {May},
     isbn = {0-9695338-5-3},
     publisher = {Canadian Human-Computer Communications Society},
     url = {http://graphicsinterface.org/wp-content/uploads/gi1996-13.pdf},
     pages = {107--115}
    }
    

Abstract

An algorithm is presented which, given the parameters of an Iterated Function System (IFS) which uses affine maps, constructs a closed ball which completely contains the attractor set of the IFS. These bounding balls are almost always smaller than those computed by existing methods, and are sometimes much smaller. The algorithm is numerical in form, involving the optimisation of centre-point and radius relationships between the overall bounding ball and a set of smaller, contained balls which are derived by analysis of the contractive maps of the IFS. The algorithm is well-behaved, in that although it converges toward an optimal ball which it only achieves in the limit, the process may still be stopped after any finite number of steps, with a guarantee that the sub-optimal ball which is returned will still bound the attractor.