Summary
The canonical distance of points on the Sierpiński gasket is considered and its expectation deduced. The solution is surprising, both for the value and for the method derived from an analysis of graphs connected with the Tower of Hanoi problem.
Article PDF
Similar content being viewed by others
References
Barlow, M.T., Perkins, E.A.: Brownian motion on the Sierpinski gasket. Probab. Th. Rel. Fields79, 543–623 (1988)
Breiman, L.: Probability. Reading, Mass.: Addison-Wesley 1968
Chan, Tat-Hung: A statistical analysis of the Towers of Hanoi problem. Intern. J. Comput. Math.28, 57–65 (1989)
Er, M.C.: An analysis of the generalized Towers of Hanoi problem. BIT23, 429–435 (1983)
Hinz, A.M.: The Tower of Hanoi. Enseign. Math. (2),35, 289–321 (1989)
Lévy, P.: Sur les séries dont les termes sont des variables éventuelles indépendantes. Studia Math.3, 119–155 (1931)
Lu, Xuemiao: Towers of Hanoi graphs. Intern. J. Comput. Math.19, 23–38 (1986)
Mandelbrot, B.B.: The fractal geometry of nature. San Francisco: Freeman 1982
Scarioni, F., Speranza, H.G.: A probabilistic analysis of an error-correcting algorithm for the Towers of Hanoi puzzle. Inform. Process. Lett.18, 99–103 (1984)
Scorer, R.S., Grundy, P.M., Smith, C.A.B.: Some binary games. Math. Gaz.280, 96–103 (1944)
Sierpiński, W.: Sur une courbe dont tout point est un point de ramification. C. R. Acad. Sci. Paris160, 302–305 (1915)
Stewart, I.: Le lion, le lama et la laitue. Pour la Science142, 102–107 (1989)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hinz, A.M., Schief, A. The average distance on the Sierpiński gasket. Probab. Th. Rel. Fields 87, 129–138 (1990). https://doi.org/10.1007/BF01217750
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01217750