Abstract
We study random recursive constructions with finite "memory" in complete metric spaces and the Hausdorff dimension of the generated random fractals. With each such construction and any positive number β we associate a linear operator V(β) in a finite dimensional space. We prove that under some conditions on the random construction the Hausdorff dimension of the fractal coincides with the value of the parameter β for which the spectral radius of V(β) equals 1.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 99-115 |
| Number of pages | 17 |
| Journal | New York Journal of Mathematics |
| Volume | 7 |
| Publication status | Published - Dec 1 2001 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
Dryakhlov, A. V., & Tempelman, A. A. (2001). On Hausdorff dimension of random fractals. New York Journal of Mathematics, 7, 99-115.