References
Bedford, T. 1989. Hölder exponents and Box dimension for self-affine fractal functions,J. Construct. Approx. 5, 33–48.
Billingsley, P. 1967.Ergodic Theory and Information. New York: Wiley.
Jaffard, S. and Mandelbrot, B. B. 1996. Local regularity of nonsmooth wavelet expansions and application to the Pólya function,Adv. Math. 120, 265–282.
Lax, P.D. 1973. The differentiability of Pólya’s function,Adv. Math. 10, 456–464.
Mandelbrot, B. B. 1982.The Fractal Geometry of Nature. New York: W. H. Freeman and Company.
Mandelbrot, B. B. 1995. Negative dimensions and Hölders, multifractals and their Hölder spectra, and the role of lateral preasymptotics in science.J. P. Kahane meeting (Paris, 1993),J. of Fourier Anal. Appl. 409-432, special issue edited by J. Peyrière and A. Bonami
Pólya, G. 1913. Über eine Peanosche Kurve.Bull. Acad. Sci. Cracovie, Série A, 305-313.
Volkmann, B. 1958. Über Hausdorffsche Dimensionen von Mengen, die durch Zifferneigenschaften definiert sind, VI.Math. Zeitschr. 68, 439–449.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mandelbrot, B.B., Jaffard, S. Peano-pólya motions, when time is intrinsic or binomial (uniform or multifractal). The Mathematical Intelligencer 19, 21–26 (1997). https://doi.org/10.1007/BF03024410
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03024410