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Midpoint Displacement
In mathematics, the blancmange curve is a self-affinity, self-affine 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 Blancmange, Blancmange pudding. It is a special case of the more general de Rham curve; see also fractal 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_, x-n, , that is, s(x) is the distance from ''x'' to the nearest integer. The Takagi–Landsberg curve is a slight generalization, given by : T_w(x) = \sum_^\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 definitio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blancmange
Blancmange (, from french: blanc-manger ) is a sweet dessert popular throughout Europe commonly made with milk or cream and sugar thickened with rice flour, gelatin, corn starch, or Irish moss (a source of carrageenan), and often flavoured with almonds. It is usually set in a mould and served cold. Although traditionally white (hence the name, in English literally "white eating"), blancmanges are frequently given alternative colours. Some similar desserts are French chef 's Bavarian cream, Italian , the Middle Eastern , Chinese ''annin tofu,'' Hawai'ian and Puerto Rican . The historical blancmange originated at some time during the Middle Ages and usually consisted of capon or chicken, milk or almond milk, rice, and sugar and was considered to be ideal for the sick. is a sweet contemporary Turkish pudding made with shredded chicken, similar to the medieval European dish. History The origins of the blancmange have long been believed to lie in the introduction of r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
