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The box-counting dimension of the sine-curve. (English) Zbl 0957.54016
It is shown that the celebrated sine-curve provides a simple example of a smooth function on an interval whose graph has box-counting dimension exceeding one.
MSC:
54F45 Dimension theory in general topology
26A09 Elementary functions
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References:
[1] FALCONER K. J.: Dimensions-their determination and properties. Fractal Geometry and Analysis (J. Belair, S. Dubuc, Kluwer Academic Publishers, Dordrecht, 1991, pp. 221-254. · Zbl 0734.28008
[2] FALCONER K. J.: Fractal Geometry. Mathematical Foundations and Applications. John Wiley & Sons, Chichester, 1990. · Zbl 0689.28003
[3] BARNSLEY M.: Fractals Everywhere. Academic Press, Boston, MA, 1988. · Zbl 0691.58001
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