Volume 285, Number 5431 Issue of 20 Aug 1999, p 1228
SOFTWARE: Order From Chaos William Seffens
BENOIT is a fractal analysis software product for Windows 95, Windows 98, or Windows NT used to find order and patterns in seemingly chaotic data, particularly where traditional statistical approaches to data analysis fail. It is widely used in disciplines as diverse as biology, chemistry, physics, economics, medicine, and geology. The U.S. Geological Survey, for example, employs fractal analysis to accurately predict the volume of undiscovered deposits of oil and natural gas, on the basis of data from known deposits.
BENOIT measures user-supplied data by standard fractal methods. For a fractal, measures change in value as the scale decreases in size because ever-smaller pieces become included in the analysis. Measures are plotted as a function of ruler size on a log-log plot, and a fractal dimension is calculated from the slope of the resulting line. Users select one of 10 analytical measures with the software. Five of the available measures in the program act upon bitmap images in Windows BMP format. These are described as the "self-similar" or two-dimensional (2D) methods, while the remaining group of routines act upon time-series or 1D data. The latter group requires data to be in a simple but specific data format, such as is available in Excel. The program also features a data generator that produces files with a given fractal dimension. Users may find this useful for testing and control purposes.
The self-similar or image methods available in BENOIT measure different characteristics of bitmap objects in ways that should be scale-invariant. A real dataset normally has some fractal limit, and outside the limit, the fractal dimension will return a trivial value (1 for time-series or 2 for image data). Upper and lower fractal limits are controlled by the size of the dataset. Self-similar methods available in BENOIT are well known in fractal analysis: box dimension, perimeter-area dimension, information dimension, and ruler dimension. All methods are explained in standard Help files that contain several pages of information for each topic.
The 1D analysis routines use "self-affine" methods of analysis. Self-affine fractals differ from self-similiar fractals in that their parts need to be rescaled by different factors in different coordinates to resemble the original. In the roughness-length method, the root-mean-square variation or roughness of the data is calculated for a variety of horizontal scales. The operation provides an estimate of the Hurst exponent, H, in a log-log plot, which is related to the fractal dimension. Standard self-affine methods available include R/S (Rescaled Range) analysis, power spectrum, roughness-length, variogram, and wavelets.
Printing of log-log figures is provided, but without many features that would be found in a spreadsheet. Documentation for the program is available online. BENOIT has a highly visual interface, complete with an animated grid or ruler for self-similar fractal methods, and it gives users control of all calculations that the program performs, unlike other fractal software.
Benoit is not without flaws. Some operations, such as name registration with the Windows NT 4.0 taskbar and the Open File requester, do not conform to standard Windows conventions. It would be of help to have an outline or flowchart of the operation of the different routines available in BENOIT for newcomers to fractal analysis.
In summary, the variety of fractal analysis methods available in BENOIT, together with generally detailed help files and significant user control of operations, make BENOIT a good resource for learning about and using fractal analysis methods.
