Abstract
Two types of dynamical systems whose domains have fractal boundaries are proposed. The first one is realized as a dynamical system which induces binary expansions of complex numbers and whose domain is shown to be a twindragon. The second one is proposed as a dynamical system which induces revolving expansions of complex numbers and whose domain is shown to be a tetradragon.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Davis and D. E. Knuth, Number representations and dragon curves I. J. Recreational Math.,3 (1970), 66–81.
F. M. Dekking, Recurrent sets. Adv. in Math.,44 (1982), 78–104.
F. M. Dekking, Repricating super figures and endomorphisms of free groups. J. Combin. Theory, A32 (1982), 315–320.
F. M. Dekking, M. Mendes France and A. van der Poorten, Folds. Math. Intelligencer,4 (1982), 131–138, 173–180, 190–195.
M. Gardner, Mathematical games. Scientific American,216 (1967), No. 3, 124–129, No. 4, 116–123.
D. Knuth, The Arts of Computer Programing II. section 4.1. Addison Wesley, Reading, 1969.
B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco 1982.
W. J. Gilbert, Fractal geometry derived from complex bases. Math. Intelligencer,4, No. 2 (1982), 78–86.
J. E. Hutchinson, Fractals and self-similarity. Indiana Univ. Math. J.,30 (1981), 713–747.
M. Hata, On the structure of self-similar sets. Japan J. Appl. Math.,2 (1985), 381–414.
P. Lévy, Les courbes planes ou gauches et les surfaces composées de parties semblables ou tout. J. Ecole Polytech., Ser. III,7–8 (1938), 227–291, Reprinted in “Oeuvres de Paul Lévy” Vol. II, Gauthier Villars, Paris, Bruxelles, Montréal, 1973, 331–394.
Author information
Authors and Affiliations
About this article
Cite this article
Mizutani, M., Ito, S. Dynamical systems on dragon domains. Japan J. Appl. Math. 4, 23–46 (1987). https://doi.org/10.1007/BF03167753
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03167753