Abstract
In this article, we will give a construction of a random fractal in the ring of p-adic integers and examine an extent of the random fractals. Paying attention to an importance in statistical self similarity, we will perform measurement for the extent in terms of the Hausdorff dimension similarly to the typical fractal analysis in the Euclidean space. In our study, we will take a measure theoretic approach combined with the martingale theory based on Falconer’s method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. J. Falconer, “Random fractals,” Math. Proc. Camb. Phil. Soc. 100, 559–582 (1986).
K. J. Falconer, Fractal Geometry — Mathematical Foundations and Applications (John Wiley & Sons Ltd, 1990).
K. J. Falconer, Technique in Fractal Geometry (John Wiley & Sons Ltd, 1997).
U. Zähle of Jena, “Random fractals generated by random cutouts,” Math. Nachr. 116, 27–52 (1984).
Author information
Authors and Affiliations
Corresponding author
Additional information
The text was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Kaneko, H., Nishiwaki, W. A random fractal in the ring of p-adic integers. P-Adic Num Ultrametr Anal Appl 3, 74–80 (2011). https://doi.org/10.1134/S2070046611010067
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2070046611010067