Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T14:16:29.189Z Has data issue: false hasContentIssue false

Random fractals

Published online by Cambridge University Press:  24 October 2008

K. J. Falconer
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW

Extract

There has been considerable interest of late in fractals, both in their occurrence in the sciences, and in their mathematical theory. A general account of fractals is given by Mandelbrot [10], whilst a more mathematical approach may be found in Falconer [5].

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Athreya, K. B. and Ney, P. E.. Branching Processes (Springer-Verlag, 1972).CrossRefGoogle Scholar
[2]Bedford, T.. Ph.D. thesis (University of Warwick, 1984).Google Scholar
[3]Bollobás, B.. Graph Theory, an Introductory Course (Springer-Verlag, 1979).Google Scholar
[4]Dekking, F. M.. Recurrent sets. Advances in Mathematics 44 (1982), 78104.CrossRefGoogle Scholar
[5]Falconer, K. J.. The Geometry of Fractal Sets (Cambridge University Press, 1985).CrossRefGoogle Scholar
[6]Ford, L. R. and Fulkerson, D. R.. Flows in Networks (Princeton University Press, 1962).Google Scholar
[7]Grimmett, G. R.. Random flows: network flows and electrical flows through random media. Surveys in Combinatorics 1985 (ed. Anderson, I.) (Cambridge University Press, 1985), 5995.Google Scholar
[8]Hall, P. and Heyde, C. C.. Martingale Limit Theory and its Application (Academic Press, 1980).Google Scholar
[9]Hutchinson, J. E.. Fractals and self-similarity. Indiana University Math. J. 30 (1981), 713–47.CrossRefGoogle Scholar
[10]Mandelbrot, B. B.. The Fractal Geometry of Nature (W. H. Freeman, 1982).Google Scholar
[11]Moran, P. A. P.. Additive functions of intervals and Hausdorff measure. Proc. Cambridge Philos. Soc. 42 (1946), 1523.CrossRefGoogle Scholar
[12]Rogers, C. A.. Hausdorff Measures (Cambridge University Press, 1970).Google Scholar
[13]Mauldin, R. D. and Williams, S. C.. Random constructions: asymptotic geometric and topological properties. Trans. Amer. Math. Soc. 295 (1986), 325346.CrossRefGoogle Scholar
[14]Graf, S.. Statistically self-similar fractals (to appear).Google Scholar
[15]Falconer, K. J.. Cut-set sums and tree processes (to appear).Google Scholar