bsamzier曲线和Takagi函数

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2024-11-28 DOI:10.1016/j.bulsci.2024.103543

Lenka Ptáčková , Franco Vivaldi

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引用次数: 0

摘要

考虑具有复参数的bsamzier曲线，明确地确定了与de Casteljau细分算法相对应的仿射迭代函数系统（IFS），以及该系统具有唯一全局连通吸引子的复参数域。对于一类具有虚部消失的复参数族，在适当的标度下，证明了Takagi分形曲线是吸引子。

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Bézier curves and the Takagi function

We consider Bézier curves with complex parameters, and we determine explicitly the affine iterated function system (IFS) corresponding to the de Casteljau subdivision algorithm, together with the complex parametric domain over which such an IFS has a unique global connected attractor. For a specific family of complex parameters having vanishing imaginary part, we prove that the Takagi fractal curve is the attractor, under suitable scaling.

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