Van der Corput Sequence
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High Quality Content by WIKIPEDIA articles! A van der Corput sequence is a low-discrepancy sequence over the unit interval first published in 1935 by the Dutch mathematician J. G. van der Corput. It is constructed by reversing the base n representation of the sequence of natural numbers (1, 2, 3, ). For example, the decimal van der Corput sequence begins: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.01, 0.11, 0.21, 0.31, 0.41, 0.51, 0.61, 0.71, 0.81, 0.91, 0.02, 0.12, 0.22, 0.32, whereas the binary van der Corput sequence can be written as: 0.12, 0.012, 0.112, 0.0012, 0.1012, 0.0112, 0.1112,...
High Quality Content by WIKIPEDIA articles! A van der Corput sequence is a low-discrepancy sequence over the unit interval first published in 1935 by the Dutch mathematician J. G. van der Corput. It is constructed by reversing the base n representation of the sequence of natural numbers (1, 2, 3, ). For example, the decimal van der Corput sequence begins: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.01, 0.11, 0.21, 0.31, 0.41, 0.51, 0.61, 0.71, 0.81, 0.91, 0.02, 0.12, 0.22, 0.32, whereas the binary van der Corput sequence can be written as: 0.12, 0.012, 0.112, 0.0012, 0.1012, 0.0112, 0.1112, 0.00012, 0.10012, 0.01012, 0.11012, 0.00112, 0.10112, 0.01112, 0.11112, or, equivalently, as: frac{1}{2}, frac{1}{4}, frac{3}{4}, frac{1}{8}, frac{5}{8}, frac{3}{8}, frac{7}{8}, frac{1}{16}, frac{9}{16}, frac{5}{16}, frac{13}{16}, frac{3}{16}, frac{11}{16}, frac{7}{16}, frac{15}{16}, ldots The elements of the van der Corput sequence (in any base) form a dense set in the unit interval: for any real number in [0, 1] there exists a subsequence of the van der Corput sequence that converges towards that number. They are also uniformly distributed over the unit interval.
