report.inf

分形维数的估算软件FD3

		A Guide to Reading Reports Output by FD3


Here is a sample output of fd3, with some helpful comments
inserted (COMMENTS ARE IN CAPITAL LETTERS):

******************************************************************
  FRACTAL DIMENSION REPORT -- by fd software (DiFalco/Sarraille)
******************************************************************


Reporting on file named: can1k.3d.
                         ^^^^^^^^ THE USER TYPED "fd3 can1k.3d"
                                  ON THE COMMAND LINE.

Getting the embedding dimension ...
Embedding Dimension taken to be: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ FD3 FOUND THAT THERE WERE
         THREE COORDINATES ON THE FIRST DATA LINE, AND
	 CONCLUDED THAT ALL DATA LINES IN THIS INPUT FILE HAVE
	 THREE COORDINATES ON THEM.

Finding max and min values in data ...
        ^^^^^^^^^^^^^^^^^^^^^^^^^^ FD3 NEEDS THESE IN ORDER TO
                                   RE-SCALE THE DATA.

Minimum value in input file is: 0.000036 ...
Maximum value in input file is: 0.999987 ...

32 different cell sizes will be used ...
Data will be shifted and re-scaled so that minimum coordinate
value is ZERO and maximum coordinate value is: 4294967295 ...

THIS TRANSFORMATION OF THE DATA IS NECESSARY IN ORDER FOR THE
FAST ALGORITHM USED BY FD3 TO WORK.  THE SHAPE OF THE DATA SET
IS *NOT* ALTERED.

Allocating storage ... Done ...
Initializing queues ... Done ...
Loading data ... Done ...
Sorting the data ... Done ... 
Doing sweep to get counts ... Done ...


[log(epsl)]  [CellCount]  [log(CellCount)]  [informtn]  [-log(SumSqrFreqs)]
 = [log(e)]   = [N(e)]      = [logN(e)]      = [I(e)]     = [-logSSF(e)]

        0         1000           9.96578     9.96578              9.96578
        1          999           9.96434     9.96378              9.96290
       ^^^
CELL SIZES OF
1, 2, 4, 8, ETC
ARE USED.  THIS COLUMN
SHOWS THE LOGS OF EACH
CELL SIZE TO THE BASE 2.

        2          998           9.96290     9.96178              9.96003
        3          998           9.96290     9.96178              9.96003
                   ^^^
             THIS FIGURE GIVES THE
             NUMBER OF CELLS REQUIRED
             TO COVER THE SET.  FOR
             EXAMPLE, THIS PARTICULAR
             COUNT APPLIES TO CELLS OF
             SIZE 2^^3 = 8.

        4          998           9.96290     9.96178              9.96003
        5          997           9.96145     9.95978              9.95715
                                 ^^^^^^^
                            THIS FIGURE IS JUST THE
                            LOG TO THE BASE 2 OF THE
                            CORRESPONDING CELL COUNT.

        6          996           9.96000     9.95778              9.95429
        7          994           9.95710     9.95378              9.94857
                                             ^^^^^^^
                                         THIS FIGURE IS OBTAINED
                                         BY SUMMING THE SAMPLE
                                         FREQUENCY OF POINTS IN
                                         EACH OCCUPIED CELL TIMES
                                         THE LOG OF THE FREQUENCY.
					 SUCH NUMBERS ARE USED TO
					 ESTIMATE THE INFORMATION
					 DIMENSION.

        8          992           9.95420     9.94978              9.94288
        9          983           9.94105     9.93178              9.91755
                                                                  ^^^^^^^

						  THIS FIGURE IS OBTAINED BY
						  SUMMING THE SQUARES OF THE
						  SAMPLE FREQUENCIES.  THESE
						  NUMBERS ARE USED TO ESTIMATE
						  THE CORRELATION DIMENSION.

       10          975           9.92926     9.91503              9.89265
       11          964           9.91289     9.89303              9.86279
       12          952           9.89482     9.86752              9.82566
       13          922           9.84862     9.80525              9.74174
       14          885           9.78953     9.72824              9.64386
       15          840           9.71425     9.63295              9.52856
       16          772           9.59246     9.47789              9.33911
       17          681           9.41151     9.26276              9.10026
       18          560           9.12928     8.92970              8.73190
       19          448           8.80735     8.58118              8.38275
       20          319           8.31741     8.08084              7.88991
       21          229           7.83920     7.58426              7.39338
****************************************************************************

THE INFORMATION BETWEEN THE "STAR BARS" HERE, IS WHAT THE
PROGRAM TAKES TO BE THE MOST SIGNIFICANT.  FIGURES ABOVE THE
STAR BARS ARE ASSUMED TO BE IN OR NEAR SATURATION, AND FIGURES
BELOW THE STAR BARS ARE ASSUMED TO BE TOO COARSE GRAINED.

       22          148           7.20945     7.02644              6.89815
       23           99           6.62936     6.45337              6.32516
       24           67           6.06609     5.78224              5.62010
       25           42           5.39232     5.25480              5.17741
       26           28           4.80735     4.65834              4.55823
       27           16           4.00000     3.90607              3.83650
       28           10           3.32193     3.27427              3.23208
       29            6           2.58496     2.47251              2.37646
       30            4           2.00000     1.89188              1.80330
****************************************************************************
       31            2           1.00000      1.0000              0.99999
       32            1           0.00000    -0.00000             -0.00000



Two-Point Estimates of FD's:

[log(e)]  [logN(e)-logN(2e)]  [I(e)-I(2e)]  [logSSF(2e)-logSSF(e)]

       0             0.00144       0.00200                 0.00288
       1             0.00144       0.00200                 0.00288
                     ^^^^^^^       ^^^^^^^                 ^^^^^^^
                THE FIGURES IN THE LAST THREE COLUMNS HERE ARE OBTAINED BY
                SIMPLY TAKING DIFFERENCES BETWEEN SUCCESSIVE ENTRIES IN THE
                CORRESPONDING COLUMNS OF THE TABLES ABOVE.  THEY GIVE
		"TWO-POINT ESTIMATES" OF RESPECTIVELY, THE CAPACITY
		DIMENSION, THE INFORMATION DIMENSION, AND THE CORRELATION
		DIMENSION.

       2             0.00000       0.00000                 0.00000
       3             0.00000       0.00000                 0.00000
       4             0.00145       0.00200                 0.00287
       5             0.00145       0.00200                 0.00287
       6             0.00290       0.00400                 0.00571
       7             0.00291       0.00400                 0.00569
       8             0.01315       0.01800                 0.02534
       9             0.01179       0.01675                 0.02490
      10             0.01637       0.02200                 0.02986
      11             0.01807       0.02551                 0.03713
      12             0.04619       0.06226                 0.08392
      13             0.05909       0.07702                 0.09789
      14             0.07529       0.09528                 0.11530
      15             0.12179       0.15506                 0.18945
      16             0.18095       0.21514                 0.23885
      17             0.28223       0.33306                 0.36837
      18             0.32193       0.34852                 0.34915
      19             0.48994       0.50034                 0.49284
      20             0.47821       0.49658                 0.49653
      21             0.62975       0.55783                 0.49523
****************************************************************************
      22             0.58010       0.57306                 0.57298
      23             0.56327       0.67113                 0.70506
      24             0.67377       0.52744                 0.44269
                     ^^^^^^^
                  THE MEANING OF THIS FIGURE IS THAT
                  AT THE SCALE OF CELL SIZES OF 2^^24,
                  THE SET APPEARS TO HAVE A CAPACITY
                  DIMENSION OF 0.67377

      25             0.58496       0.59645                 0.61918
      26             0.80735       0.75227                 0.72173
                                   ^^^^^^^                 ^^^^^^^
				SIMILARLY, THESE FIGURES ESTIMATE
				INFORMATION AND CORRELATION DIMENSION
				AT SPECIFIC SCALES.

      27             0.67807       0.63180                 0.60442
      28             0.73697       0.80177                 0.85562
      29             0.58496       0.58063                 0.57315
****************************************************************************
      30             1.00000       0.89188                 0.80331
      31             1.00000        1.0000                 0.99999


22 is the smallest cell size used in the overall dimension estimates
below.  The largest cell size is 30.  Data above corresponding to
this range is between rows of asterisks.



Least-Square Estimates based on Indicated Cell Range:

Fractal Dimension  (Capacity)   =  0.66419
Fractal Dimension (Information) =  0.64743
Fractal Dimension (Correlation) =  0.63904

EACH ESTIMATE ABOVE IS OBTAINED BY FITTING A LINE TO A GRAPH OF
THE LOG(EPSILON) COLUMN VERSUS ANOTHER COLUMN.  THE LAST THREE
COLUMNS OF THE FIRST TABLE ABOVE ARE USED TO GET, RESPECTIVELY,
THE CAPACITY DIMENSION, THE INFORMATION DIMENSION, AND THE
CORRELATION DIMENSION.  ONLY THE DATA BETWEEN THE STAR BARS IS
USED IN THE FITTING OF THE LINE, SINCE IT IS PRESUMED THAT THE
GRAPH IS DISTORTED OUTSIDE THIS REGION.

****************************************

/* BEGIN NOTICE

Copyright (c) 1992 by John Sarraille and Peter DiFalco
([e-mail])

Permission to use, copy, modify, and distribute this software
and its documentation for any purpose and without fee is hereby
granted, provided that the above copyright notice appear in all
copies and that both that copyright notice and this permission
notice appear in supporting documentation.

The algorithm used in this program was inspired by the paper
entitled "A Fast Algorithm To Determine Fractal Dimensions By
Box Counting", which was written by Liebovitch and Toth, and
which appeared in the journal "Physics Letters A", volume 141,
pp 386-390, (1989).

This program is not warranteed: use at your own risk.

END NOTICE */