文件列表:

BRITAIN.DAT (23261, 1995-05-25)
BRITAIN.REP (6329, 1995-05-25)
CAN3D.DAT (39005, 1995-05-25)
CAN3D.REP (6326, 1995-05-25)
COPYRIGH (731, 1995-05-25)
FD.H (1993, 1995-05-25)
FDDRIVER.C (12077, 1995-05-25)
FDQUEUE.C (6888, 1995-05-25)
FDUTIL.C (18709, 1995-05-25)
HENON.DAT (65005, 1995-05-25)
HENON.REP (6327, 1995-05-25)
INDEX (2894, 1995-05-25)
KOCH.DAT (79903, 1995-05-25)
KOCH.REP (6326, 1995-05-25)
LOGISTIC.DAT (26005, 1995-05-25)
LOGISTIC.REP (6329, 1995-05-25)
NOTES (17980, 1995-05-25)
PERF.DAT (50306, 1995-05-25)
PERF.REP (6325, 1995-05-25)
REPORT.INF (10524, 1995-05-25)

HOW TO USE FD3, VERSION 0.3. A PROGRAM FOR CALCULATING FRACTAL DIMENSION. What follows is a fairly detailed set of directions for using the fractal dimension (FD3) program. We are aware that many of the potential users are not well-aquainted with computing systems, and we have made an effort to make this document somewhat accessible to them. We hope that the more sophisticated readers will bear with us. To use the FD3 program, a directory should be created and the source files fdqueue.c, fdutil.c, and fddriver.c should be copied to it. The include file fd.h should also be copied to the same directory. The sample inputs and outputs, and the files containing documentation of the program probably ought to be placed in this directory too. (To you Unix savants: sorry, no man page yet.) If you are getting an update of a previous release of the software, you should put it into a DIFFERENT directory from all other versions. The source files should then be compiled, using the C compiler on the host computer. Compilation is the act of translating the (english-like) source version of the program into the machine-executable binary version of the program. Typically, compilation is carried out by a special program that runs on the host machine -- a compiler. We can't send you our BINARY form of the program because different machines have different machine languages, and thus the binary version that runs on our machine would probably not run on your machine. Since the FD3 you are getting is written in a source language called "C", a "C compiler" is required. When WE compile the program in a Unix environment, we sometimes use the following command: cc -o fd3 fdqueue.c fdutil.c fddriver.c -lm This has the effect of compiling all three source files, linking them to the mathematics libraries, and naming the compiled version of the program "fd3". You should consult your C compiler's documentation or ask your system administrator for help if you are uncertain about this step. (Again, apologies to Unix and C savants -- no makefiles yet.) Once the program has been compiled, the executable version of the program will exist, and will be a named binary file. We assume that you will have given it the name "fd3", but obviously, you can give it any name you like, and if the name you use is different from ours, you should substitute it below where we use "fd3" -- especially where we use it in commands that are to be given to the computer! The simplest way to run the program is to do so while attached to a directory containing the executable code, and an input file. In a Unix environment, one then types fd3 inputfilename to execute the program with the input taken from the file "inputfilename" (instead of literally typing "inputfilename", you type the name of the file that you want the program to use as input.) If this does not work in your environment, you may have to check with your system administrator to find out the conventions for executing a program. The input file must be of the following form: Line 1: Number, N, of data lines (POINTS) in the input file. Line 2: Coordinates of 1st POINT, separated by at least one space or tab. Line 3: Coordinates of 2nd POINT, separated by at least one space or tab. Line 4: Coordinates of 3rd POINT, separated by at least one space or tab. ... ... ... Line n: Coordinates of (N-1)st POINT, separated by at least one space or tab. Line n+1: Coordinates of Nth POINT, separated by at least one space or tab. ------------------------------------------ Example* of a 1-DIMENSIONAL input file: ------------------------------------------ 10 5.56 4.561 111145 34.55 2.2245 324.55555 432 689.9756 546.9***74 76.0*** ------------------------------------------ Example* of a 2-DIMENSIONAL input file: ------------------------------------------ 10 3.34 5.56 66***.9 4.561 111145 .776 234 34.55 2.2245 0 2556.3 324.55555 432 333.0001 334.***7 689.9756 8765.567 546.9***74 345.45 76.0*** ------------------------------------------ Example* of a 3-DIMENSIONAL input file: ------------------------------------------ 10 2.47 3.34 5.56 -3.123 66***.9 4.561 0.334231 111145 0.776 497650 234 34.55 217 2.2245 0 1.23 2556.3 324.55555 10548 432 333.0001 2815 334.***7 689.9756 219.85 8765.567 546.9***74 0.0042***7 345.45 76.0*** ################################################## * Real data sets ought to be larger than the sample above. It is not possible for us to say precisely what the requirements for a good sample are. We have found empirically that we get less than a 5% error in the calculated value of certain fractal dimensions if we use a uniform sample of 200 or more distinct 2-D points. ("Distinct" means the 200 points all have to be different from one another.) In general, there is good reason to think that you will need at least around 2^(4*Fd) DISTINCT points, where Fd is the "true" fractal dimension of the underlying set. ("^" is a symbol for exponentiation and "*" is a symbol for multiplication.) Since you don't KNOW Fd (that's what the program is supposed to be telling you!) you can substitute your best guess as to an upper bound in the formula. Certainly the Fd of your data set is no more than the "embedding dimension", which is the number of coordinates each of your points has. You will most likely need more than what the formula calls for when Fd = 1 or less. In fact, I would recommend 200 as a minimum if you can possibly get that many points. That gives us the following numbers: Fd value minimal # of points 1 200 2 256 3 4,096 4 65,536 5 1,048,576 ON EACH LINE OF THE INPUT FILE, EXCEPT THE FIRST, YOU SHOULD HAVE *ALL* THE COORDINATES OF *EXACTLY ONE* OF THE DATA POINTS. This is important because the program looks at the second line of the input file to determine the embedding dimension. The NUMBER OF NUMBERS ON THAT LINE is taken to be the dimension. ------------------------------ When fd3 executes, it will write it's output to the default output device (usually the screen in front of you). On different systems, different methods exist to "deflect" the output to a printer or file. In our environment, we use such command lines as: fd3 can1K.1D > can1K-1D.rep which has the effect of redirecting the output to a file called "can1K-1D.rep". We can then use the facilities of our system to view "can1K-1D.rep" or print a copy of it if we like. This program is relatively fast. (Basically O(NlogN), where N is the size of the input file.) It will turnaround in seconds or less if you are inputting hundreds of numbers or a few thousand. But don't expect instantaneous results if your input file contains tens of thousands of numbers. FD3 will tell you what it's doing while it's doing it. It will let you know as it finishes each main phase of the job. You may not be interested in knowing this stuff most of the time, but it can be nicely reassuring when you are waiting for a long-running analysis to complete. FD3 outputs a report of length about two pages. If you want, you can ignore everything but the last few lines. Assuming that there were enough distinct points to satisfy FD3, you will see overall estimates of the capacity, information, and correlation dimensions of the input set. If you understand how box-counting works, you can probably decode the columns of output above the overall estimates, and use them to learn some more about your input set. A discussion of that black art is beyond the scope of this document. There is however, a document called REPORT.INF included in this package that should serve to help with the basic interpretation of FD3 reports. This program should be considered a "beta-version", or pre-release. We cannot warrantee the program in any way. No claim is made concerning the quality of the program, or the accuracy that you will get using it. We hope that you WILL use it to experiment, and to learn what you can. We certainly will not be surprised if we learn that there are a few bugs in it. If you can identify any problems, we would be grateful to have your input. /* BEGIN NOTICE Copyright (c) 1992 by John Sarraille and Peter DiFalco (john@ishi.csustan.edu) 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, (1***9). This program is not warranteed: use at your own risk. END NOTICE */

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