FAURE
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:

• M, the spatial dimension;
• N, the number of points to generate;
• BASE, a base, default value is the smallest prime greater than or equal to M;
• SKIP, the initial number of points to skip over;

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

Licensing:

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
      

Reference:

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:

Datasets in M = 2 dimensions include:

• faure_02_00010.txt, M = 2, N = 10, BASE = 2, SKIP = 15;
• faure_02_00010.png, an image of the dataset;
• faure_02_00100.txt, M = 2, N = 100, BASE = 2, SKIP = 15;
• faure_02_00100.png, an image of the dataset;
• faure_02_01000.txt, M = 2, N = 1000, BASE = 2, SKIP = 15;
• faure_02_01000.png, an image of the dataset;
• faure_02_10000.txt, M = 2, N = 10000, BASE = 2, SKIP = 15;

Datasets in M = 7 dimensions include:

• faure_07_00010.txt, M = 7, N = 10, BASE = 7, SKIP = 2400;
• faure_07_00100.txt, M = 7, N = 100, BASE = 7, SKIP = 2400;
• faure_07_01000.txt, M = 7, N = 1000, BASE = 7, SKIP = 2400;
• faure_07_10000.txt, M = 7, N = 10000, BASE = 7, SKIP = 2400;

Datasets in M = 16 dimensions include:

• faure_16_00010.txt, M = 16, N = 10, BASE = 17, SKIP = 83520;
• faure_16_00100.txt, M = 16, N = 100, BASE = 17, SKIP = 83520;
• faure_16_01000.txt, M = 16, N = 1000, BASE = 17, SKIP = 83520;
• faure_16_10000.txt, M = 16, N = 10000, BASE = 17, SKIP = 83520;

You can go up one level to the DATASETS directory.