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Van Der Corput Sequence
  CATEGORIES ABOUT VAN DER CORPUT SEQUENCE
   
quasirandomness
   
diophantine approximation
   
sequences
   
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: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:

: rac{1}{2}, rac{1}{4}, rac{3}{4}, rac{1}{8}, rac{5}{8}, rac{3}{8}, rac{7}{8}, rac{1}{16}, rac{9}{16}, rac{5}{16}, rac{13}{16}, rac{3}{16}, rac{11}{16}, rac{7}{16}, rac{15}{16}, ….

The elements of the van der Corput sequence (in any base) form a of the van der Corput sequence that Converges towards that number. They are also Uniformly Distributed over the unit interval.


SEE ALSO



REFERENCES

  • J. G. van der Corput, ''Verteilungsfunktionen''. Proc. Ned. Akad. v. Wet., 38:813–821, 1935.



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