Random Fractal Measures via the Contraction Method

Indiana University Mathematics Journal

Volumn 47, Issue 2, 1998, Pages 471-487

  Hutchinson, John E ^a   Rüschendorf, Ludger ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000150478     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1998.47.1461     Document Type: Article

References (14)

1. ARBEITER, M.A., Random recursive constructions of self-similar fractal measures. The noncompact case. Prob. Th. Rel. Fields 88, 497-520 (1991).
2. BARNSLEY, M.F., Fractals Everywhere. Academic Press, New York, 1988.
3. BARNSLEY, M.F., DEMKO, S., Iterated function systems and the global construction of fractals. Proc. Roy. Soc. London A399 (1985), 243-275.
4. CAWLEY, R. AND MAULDIN R., Multifractal Decompositions of Moran fractals. Adv. Math. 92 (1992), 196-236.
5. DIACONIS, P ., SHAHSHAHANI, M., Products of random matrices and computer image generation. Contemp. Math. 50 (1986), 173-182.
6. FALCONER, K.J., Random Fractals. Math. Proc. Camb. Phil. Soc. 100 (1986), 559-582.
7. GRAF, S., Statistically self-similar fractals. Prob. Th. Rel. Fields 74 (1987), 357-392.
8. HUTCHINSON, J.E., Fractals and self similarity. Indiana. Univ. Math. J. 30 (1981), 713-747.
9. HUTCHINSON, J.E., Deterministic and random fractals. Complex Systems. Cambridge Univ. Press (T.R.J. Bossomaier and D.G. Green, eds.) (to appear).
10. MAULDIN, R.D., WILLIAMS, S.C., Random recrusive constructions: Asymptotic geometric and topological properties. Trans. Amer. Math. Soc. 295 (1986), 325-346.
11. OLSEN, R., Random Geometrically Graph Directed Self-similar Multifractals. Pitman Research Notes 307, Longman, 1994.
12. PATZSCHKE, N., ZÄHLE, U., Self-similar random measures. IV. The recursive construction model of Falconer, Graf, and Mauldin and Williams. Math. Nachr. 149 (1990), 285-302.
13. PEITGEN, H.O., SAUPE, D., The Science of Fractal Images. Springer-Verlag, New York, 1988.
14. ZÄHLE, U., Self-similar random measures. I - Notion, carrying Hausdorff dimension, and hyperbolic distribution. Prob. Th. Rel. Fields 80 (1988), 79-100.