Notes

Chapter 4: Systems Based on Numbers

Section 2: Elementary Arithmetic


Digit reversal

Sequences of the form

Table[FromDigits[Reverse[IntegerDigits[n,k,m]],k],{n,0,k^m-1}]

shown below appear in algorithms such as the fast Fourier transform and, with different values of k for different coordinates, in certain quasi-Monte Carlo schemes. (See pages 1073 and 1085.) Such sequences were considered by Johannes van der Corput in 1935.


From Stephen Wolfram: A New Kind of Science [citation]