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- W2565646818 abstract "Using the moving frame and invariants, any discrete curve in $R^3$ could be uniquely identified by its centroaffine curvatures and torsions. In this paper, depending on the affine curvatures of the fractal curves, such as Koch curve and Hilbert curve, we can clearly describe their iterative regularities. Interestingly, by the affine curvatures, the fractal curves can be quantified and encoded accordingly to a sequence. Hence, it is more convenient for future reference. Given three starting points, we can directly generate the affine Koch curve and affine Hilbert curve at the step $n, forall nin mathbb{Z}^+$. Certainly, if the initial three points are standard, the curve is the traditional Koch curve or Hilbert curve. By this method, the characteristic of some fractal curves which look like irregular could be quantified, and the regularities would become more obvious." @default.
- W2565646818 created "2017-01-06" @default.
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- W2565646818 date "2016-12-15" @default.
- W2565646818 modified "2023-09-25" @default.
- W2565646818 title "The moving frame on the fractal curves" @default.
- W2565646818 cites W1978397569 @default.
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- W2565646818 doi "https://doi.org/10.48550/arxiv.1612.05341" @default.
- W2565646818 hasPublicationYear "2016" @default.
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