Abstract
The well-known self-affine Sierpinski carpets, first studied by McMullen and Bedford independently, are constructed geometrically by repeating a single action according to a given pattern. In this paper, we extend them by randomly choosing a pattern from a set of patterns with different scales in each step of their construction process. The Hausdorff and box dimensions of the resulting limit sets are determined explicitly and the sufficient conditions for the corresponding Hausdorff measures to be positive finite are also obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 495-512 |
| Number of pages | 18 |
| Journal | Nonlinearity |
| Volume | 23 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2010 |