FAURE
Faure Datasets
FAURE
is a dataset directory which
contains points generated
by the Mdimensional 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 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.
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:

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 195213, 1992.

Henri Faure,
Discrepance de suites associees a un systeme de numeration
(en dimension s),
Acta Arithmetica,
Volume XLI, 1982, pages 337351, especially page 342.

Bennett Fox,
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,
ACM Transactions on Mathematical Software,
Volume 12, Number 4, pages 362376, 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.
Last revised on 26 September 2005.