Abstract
We extend the finite type condition to graph-directed iterated function systems with overlaps. Under this condition, we describe algorithms to compute the box dimension and Hausdorff dimension of the corresponding graph self-similar sets and show that these dimensions agree; moreover, the Hausdorff measure of these sets is shown to be strictly positive.
| Original language | American English |
|---|---|
| Pages (from-to) | 109-134 |
| Number of pages | 26 |
| Journal | Indiana University Mathematics Journal |
| Volume | 53 |
| Issue number | 1 |
| State | Published - Jan 1 2004 |
Scopus Subject Areas
- General Mathematics
Keywords
- Box dimension
- Finite type condition
- Graph self-similar set
- Graph-directed iterated function system
- Hausdorff dimension
- Hausdorff measure