Hammersley sequence

The two-dimensional Hammersley point set of order m is defined by taking all numbers in the range from 0 to 2^m - 1 and interpreting them as binary fractions. Calling these numbers x_i, then the corresponding y_i are obtained by reversing the binary digits of x_i. For example, the x_i for the Hammersley point set of order 2 are given by 0._2, 0.1_2, 0.01_2, and 0.11_2, or (0, 1/2, 1/4, 3/4). Reversing the bits then gives the second component, leading to the set of points (0, 0), (1/2, 1/4), (1/4, 1/2), and (3/4, 3/4).

net | quasirandom sequence | uniform distribution

John Hammersley