Faure Datasets

FAURE is a dataset directory which contains points generated by the M-dimensional Faure sequence.

The datasets are distinguished by the values of the following parameters:

The values of M and N are specified in the dataset file names.

The value of SKIP may be set nonzero to allow the sequence to "warm up". A recommended value is (BASE**4)-1.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

FAURE, a C++ library which computes elements of a Faure quasirandom sequence.

FAURE_DATASET, a FORTRAN90 program which allows the user to define and compute a Faure dataset.

PLOT_POINTS, a FORTRAN90 program which can plot two dimensional datasets, making Encapsulated PostScript images.

TABLE, a file format which is used to store the datasets.

TABLE_TOP, a FORTRAN90 program which can be used to analyze datasets of any dimension, by creating images of pairwise coordinates.

Example dataset:

A typical (but small) dataset looks like this:

#  faure_02_00010.txt
#  created by FAURE_DATASET.
#  File generated on March 19 2003   9:08:24.332 AM
#  Spatial dimension M =      2
#  Number of points N =     10
#  Base:      2
#  Initial values skipped =     15
  0.937500  0.562500
  0.031250  0.531250
  0.531250  0.531250
  0.281250  0.281250
  0.781250  0.281250
  0.156250  0.156250
  0.656250  0.156250
  0.406250  0.906250
  0.906250  0.906250
  0.093750  0.468750


  1. Paul Bratley, Bennett Fox, Harald Niederreiter,
    Implementation and Tests of Low Discrepancy Sequences,
    ACM Transactions on Modeling and Computer Simulation,
    Volume 2, Number 3, pages 195-213, 1992.
  2. Henri Faure,
    Discrepance de suites associees a un systeme de numeration (en dimension s),
    Acta Arithmetica,
    Volume XLI, 1982, pages 337-351, especially page 342.
  3. Bennett Fox,
    Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, pages 362-376, 1986.


Datasets in M = 2 dimensions include:

Datasets in M = 7 dimensions include:

Datasets in M = 16 dimensions include:

You can go up one level to the DATASETS directory.

Last revised on 26 September 2005.