A program to analyze movement paths of animal movement paths by Vilis O. Nams.

This is a windows-based program that also plots results and the original movement path, saves results to a file, prints plots, etc (all of the pretty things you expect from windows programs).

  • [482 KB] version 5.26, last revised June 17, 2013

This is meant as a research tool and has been tested thoroughly. However, I cannot guarantee that all bugs have been found if you find any, please email and I will fix them.

Please note: you cannot use Lat-Long coordinates in any movement path analysis because they are not square coordinates (unless you work on the equator).

Fractal does the following

  • Estimates fractal dimension (D) using the basic divider method (as introduced by Mandelbrot).
  • Estimates fractal D, using a resampling version of the divider method, which also estimates fractal D as a function of scale. (Nams 2006: Acta Biotheoretica 54:1-11)
  • Calculates the VFractal estimator, which estimates fractal D as a function of scale but which also provides error estimates (Nams, 1996: Landscape Ecology 11:289-297).
  • Uses the VFractal to calculate other estimators that are useful in analyzing how animals react to spatial scale (Nams 2006: Animal Behaviour. 72: 1197-1203).
  • Estimates Net distance2 travelled as a function of number of steps, and uses this for a statistical test for deviations from a CRW model (Nams and Bourgeois 2004: Can J. Zool, 82:1738-1747).
  • Carries out the scaling test for oriented movement this is used to test whether a movement path is oriented (Nams 2006: Animal Behaviour. 72: 1197-1203).
  • Transforms movement paths by discretizing or rotating them.

Fractal is distributed for free, with the following conditions

  • That if you use it, you mail me postcard with a real stamp (i.e. not a meter stamp) on it. This is for my wife, who collects stamps she needs something for the time I spend on projects like this.
  • That you send me reports of any problems with it (I revise this program often, depending on the current state of my research program, and comments from users).
  • That you send me citations of any papers you publish that use the program.
  • That you do not post it on any web sites instead, add links to this site. This will ensure that only the latest version is posted.

How to install

  • Download the file into the directory you want it to reside in.
  • Decompress it using an unzip program.
  • You don't need any installation program. Just run the Fractal.exe file directly. contains 4 files

  • Fractal.exe the fractal program.
  • Fractal.hlp, Fractal.cnt the help files
  • readme a short file containing this information that you are reading.


5.26 June / 2013

  • bug: when combining paths, estimate of mean path length is really mean # of steps. Changed that, and added mean # of steps

5.25 Nov /2011

  • set default VFractal estimator option "" to On

5.24 July 10/2011

  • bug: FractalMean estimator - had used wrong estimation for gross distance, for adding effect of truncated path length (because divider rarely hits right at end of path), instead of using the last position of  the divider, had been using the closest point on the path of the last position of the divider.  This had a trivial effect on the final estimate.

5.23 April/2011

  • bug: legend for lines not in right place on plots
  • bug: calculation for correlations between turning angles was wrong - had been based on degrees instead of radians.

5.22 March /2011

  • added ability to change some parameters for Oriented Movement estimator: Min step size and N steps

5.21 Sept/2010

  • added legend for lines for orientation test and net distance plots

5.20 Aug 3/2010

  • fixed bug: in Options/Load, when Many Files was unchecked, then program still responded to "Combining" option, and couldn't read in data 

5.19 Feb 25/2009

  • inserted tab after = sign in some of output: (mean FractalD, mean FractalD tranformed, median Fractal D)

5.18 Feb 25/2009

  • added the ability to turn off  the "Path too short" message

5.17 Feb 24/2009

  • how to tell when path ends: now three possibilities:
    1) in first line of data, anywhere after the x,y locations
    2) in a line between the data sets
    3) in last line of data, anywhere after the x,y locations
  • when combining data, add Median Fractal D and transformed (which is Log(D), and then transformed back). This is useful when have many short paths, which may vary greatly in fractal D

5.16 Feb 20/2009

  • fixed bugs: wasn't adding label when had many paths in many files, and combining results
  • in above situation also was not combining the paths after first file

5.15 Sept 25/2008

  • for Oriented analysis: CRWDiff statistic was wrong. In denominator, had used incorrect value for maxR2 (Nams 2006; equation 3).
  • added plot of RWDiff. This is also used in the NetDistance estimator (Nams and Bourgeois 2004). Both RDiff and CRWDiff are zero when path is a CRW, and +ve when oriented. But they differ in precision in various circumstances. Thus if either is not zero, then the path is not a CRW

5.14 Sept 19/2008

  • merged versions 5.13 and 5.13b
    bug: filename for file containing list of files was not saved when clicking an item in Options/Load

5.13b Sept 15/2008

  • bug fix: In some cases wasn't saving to individual files.

5.13 July 23/2008

  • added ability to select only those paths within set limits for min and max length
  • bug fix: when combining results, if not possible to estimate overall FractalD, then a D-value of 1 was still used in the combining
  • bug fix: when combining results and weighting means by N, the variable Npaths was also weighted by N

5.12 June 25/2008

  • bug fix: when combining results of >1 path, and saving results to a file, then Fractal could not read in the results if 0<N<1. Set N=1 in this situation.

5.11 Oct 11/2007

  • with some combinations of settings for analyzing many paths, wasn't saving individual results when there were very small step lengths as compared to the sizes of the coordinates, rounding error caused Fractal to get stuck in an infinite loop couldn't halt program when got stuck in above situation

5.10 July 9/2007

  • fixed bug in CRWDiff statistic. Wording in equation in paper (Nams 2006 Animal Behaviour; equation 4) was wrong.
  • in denominator was n2l2 the l should have been mean step length at the scale of n, not just overall mean step length. thus this also affects the Scaling test. But note that this does not affect the point at which the CRWDiff statistic crosses the axis, which is the key part of the Scaling test

5.09 April 13/2007

  • was not showing discretized expected random for net distance

5.08 March 3/2007

  • only show "Use Time" checkbox if are running Vfractal
    also, only read in time if are running VFractal, and if checked UseTime did this by creating a function UseTime, and changing variable UseTime to UseTimeV
  • also needed to add ShowObjects to TLoadingOptions on show method (had been commented out)

5.07 Feb 22/2007

  • fixed bug was showing plots for each path when combining paths when one path per file

5.06 Dec 19/2006

  • fixed bug sometimes name of path lost when changing Options/Load values
  • fixed bug bad fonts for results screen

5.05 Nov 28/2006

  • better error messages when analysis doesn't work
  • better error handling with too-short paths
  • fixed bug in combined analysis with Oriented and NetDistance, had not set AutoMin, AutMax scales to False
  • fixed bug for NetDist and Directed, in Prob of Same direction, better handling of missing values
  • added ability to change fonts for results page

5.04 Nov 15/2006

  • when time read in, added various speed and time summary stats

5.03 Nov 8/2006

  • added ability for text to separate paths to be at end of data line

5.02 July/2006

  • added discretized stat for directed walk
  • added ability to set whether are starting each V of VFractal on a step bug in Transform Paths had given unequal step lengths for distance transformation
  • fixed display of Display Options Transform Path page wasn't showing

5.00 Feb/2006

  • added scaling test for oriented movement
  • added transform paths

4.11 Dec/2005:

  • when many paths many files, have pausing to stop between files, not paths

4.10 Aug 23/2005

  • bug fix: when batch name file in different directory than previously-accessed data file, then first output file had been placed in wrong directory
  • updated help file

4.09 Nov 4/2004

  • fixed a bug in displaying basic Fractal estimator screen updated too often, slowing down program

4.08 June 30/2004

  • fixed a bug: in NetDistance, when discretizing by changing to a fixed step length, had problems when desired length was smaller than one of the steps

4.07 April 7/2004

  • fixed a bug: when calculating min scale size, when some steps are zero length, sometimes gave error

4.06 Feb 16/2004

  • fixed a bug that had displayed too many messages when analyzing many short paths


  • changed x-axis title for NetDistance estimators       

4.04  Jan 22/2004

  • allow drawing movement paths with many data points. Do this by skipping data points if have more than 10,000.
  • introduce calculation of time vs spatial scale. Either assume same time per step, or time data are in form: x,y,time

4.03  Jan 20/2004

  • fixed a bug introduced in 4.02 that had slowed down the program

4.02  Jan 15/2004

  • removed path length limitations
  • added more run-time messages to allow user to know if Fractal is still running
  • increased Max # of spatial scales from 90 to 200

4.01  Jan 8/2004

  • bug fix: couldn't read in text files when lines separated by line-feed only

4.00  April 28/2003

  • added ability to combine results when analysing several movement paths
  • misc changes to menus
  • changed FractalMean algorithm to only traverse the path twice, once from each end

3.24 Feb 14/2003

  • fixed two bugs in the fractal routines. Tested effects of these two bugs by running several analyses on paths, using new vs old version: fixed version gave D's slightly larger (~0.01-0.02 more), in a haphazard fashion. Thus, bug had not created significant problems.
  • for Net Distance, added the ability change the step size of the movement path before analysis
  • change format of fractal.ini file to Windos format
  • FINALLY found the source of the occassional Allocation Error when closing plot windows

3.23 Jan 7/2003

  • bug in batch run run-no labeling: had used name of file out, rather than file in

3.22 Nov 22/2002

  • in batch mode can add label for data for each run

3.21 Oct 10/2002

  • data values can now be separated by commas also

3.20 March 25/2002

  • changed message when movement path file is empty instead of previous cryptic error message

3.19 Feb 9/2001

  • fixed bug in NetDistance, incorrect N for each size
  • in output, added: Min,Max Scale, and N Scales that was set up, and added Random Seed
  • fixed bug where Fractal stopped sometimes when a plot was removed # of steps was one too many. Had been counting # of data points

3.18 Oct 4/2000

  • added ability to set random number seed
  • added expected random walk
  • added pause after each batch
  • added plot n for netdistance
  • added ci and randomwalk to NetDist2 plots
  • fixed bug: removed min and max check for MinScale and MaxScale in Options/Setup. previously had not allowed MinScale to be <1. Don't know why
  • fixed bug: couldn't switch off NetDist2 plotting 

3.17 July 20/2000

  • fixed bug: error check for ranges of min/max for scaling shouldn't have been run for auto

3.16 18-May-2000: bug fixes

  • didn't read in last data line if no blank line afterwards
    for NetDistance estimator, had calculated auto min&max scales based on net distance, rather than # of steps. Now, min is 1 and max is # steps
    in auto scaling, when removed duplicate step sizes, had dropped all the ones of that size. This would only have been seen in NetDistance, since other step sizes are not integer in SegmentedCorr, had previously removed CVD estimates from output. Now removed from plotting and help file also

3.15 27-Jan-2000

  • bug fix in FractalMean. Window ranges had been saved and displayed incorrectly, but were used in calculations correctly. Help file was also incorrect (will be changed soon). Correct ranges are SizeMin = size/(1-window), and SizeMax = size*(1+window).

3.14 20-July-99

  • bug fixed which had been created in the previous version. Reading in of some results files had caused an error

3.13 11-May-99

  • bugs fixes: first x,y coordinate had been dropped if was 0,0
    when measuring path length, first step had been dropped
    output for saving and displaying results was mixed for last line when many digits

3.12 12-Feb-99

  • ability to handle no travel between coordinates
  • fixed bug: when reading results from FractalMean, gross distance and not been converted from log scaling.
  • added ability to have tabs between x,y values read in }


  • more digits for output results for sizes and N

3.10 27-Nov-98

  • add ability to exit from options screens by using Esc key
  • fixed bug which caused crashes with x,y coordinates that contained many (10-11) digits

3.09 24-Jul-98

  • for batch mode, added ability to put all movement paths in one file
    b/c of this, split Options/File into Options/Save and Options/Load.

3.08 24-Jul-98

  • moved manual from separate, Word file, into help system


  • removed bug in batch mode, where incorrect directory was sometimes searched

3.06 24-Sep-97

  • added batch mode capability

3.05 Aug 25/97

  • changed VFractal estimator now each V starts on a movement path step. Without this, corr cos was slightly positively biased at small scales.
  • changed segmented corr cos (in VFractal) had a slight +ve bias at small # Max segment lengths. Used a different estimate for mean in that calculation.
  • Derivation for this will be given in Nams 1998.
  • added a few more summary statistics to main results
  • only do 32-bit compilation of this version
  • moved Scaling options to a separate screen Options screen was getting too crowded

3.04 May 5/97

  • added ability to place movement plot in main screen
  • added probability of same turns
  • changed titles of some of the plot headings ("VFractal NetCos" ->"VFractal Fractal Dimension"

3.03Feb 25/97

  • bug fix: Fractal had displayed Log(grossdist) instead of Distance in plots

3.02Feb 11/97

  • fixed bug that caused math error when reading in past results file

3.01Jan 24/97

  • added segmented correlation
  • changed name: Segmented Fractal had been called FractalBootstrap. Was not intuitive name.
  • name of data file to open had not saved. Fixed it.

3.0 Windows version

  • Oct 5/96 version 3.0 first released
  • 2.0 DOS user interface added for external use.
  • 1.0 Original DOS version, for internal use.