Self-Similar Structure in Hilbert's Space Filling Curve
نویسنده
چکیده
Hilbert's spacelling curve is a continuous function that maps the unit interval onto the unit square. The construction of such curves in the 1890s surprised mathematicians of the time and led, in part, to the development of dimension theory. In this paper, we discuss how modern notions of selfsimilarity illuminate the structure of this curve. In particular, we show that Hilbert's curve has a basic self-similar structure and its coordinate function display a mixed self-a ne structure. The notions of self-similarity which we use are described in [1]. General information on spacelling curves may be found in [4].
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