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Blancmange curve : ウィキペディア英語版
Blancmange curve

In mathematics, the blancmange curve is a fractal curve constructible by midpoint subdivision. It is also known as the Takagi curve, after Teiji Takagi who described it in 1901, or as the Takagi–Landsberg curve, a generalization of the curve named after Takagi and Georg Landsberg. The name ''blancmange'' comes from its resemblance to a pudding of the same name. It is a special case of the more general de Rham curve.
==Definition==
The blancmange function is defined on the unit interval by
:(x) = \sum_^\infty ,
where s(x) is the triangle wave, defined by s(x)=\min_^\infty w^n s(2^x)
for a parameter ''w''; thus the blancmange curve is the case w=1/2. The value H=-\log_2 w is known as the Hurst parameter.
The function can be extended to all of the real line: applying the definition given above shows that the function repeats on each unit interval.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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