The classical approach of complicated structures relies on system decomposition into constituent 'simpler' parts. This approach proves its limitations in many cases, when important properties emerge from the relations between the parts at different scales, between systems at different hierarchic levels.

Fractal theory is specifically meant to approach structural relations, long range correlations in space and time, relations between hierarchic levels, in an effective way. 

In the case of irregular shapes, as found in a huge number of practical applications, simplicity acquired by assimilation with figures of Euclidean geometry would not do. 

Fractal theory is able to help capture the fingerprint of highly complex, irregular structures, paving the way to new horizons both in scientific research and in practical applications.

An ideal way to make this methodology work for practical needs is represented by virtual instrumentation technique, by providing a flexible, fast and low-cost direct link with the real world.

General Description
The toolbox consists of a comprehensive set of functions that make up a powerful environment for fractal time series analysis. 
It blends the effectiveness of nonlinear signal analysis with the advantages of virtual instrumentation:

•  the methods dedicated to the computing of fractal exponents imply iterative data processing, which particularly fits a digital approach (the purely analogical alternative is not practical, an implementation of equivalent functions in a box instrument being prohibitive);

• relying on specific hardware devices (DAQ cards and SCXI signal conditioning modules), fractal analysis methods are applicable upon real physical systems;

• the toolbox is a set of instruments that may be used to generate, in a modular and flexible way, an unlimited number of specific applications;

• the user benefits from all the advantages of graphical programming in LabView, and sophisticated theoretical concepts are handled in a practical and friendly way.

The toolbox comprises two sets of instruments: fractal analysis and gauge generation, for time series analysis. 
Fractal exponents reflect properties of the system structure, the implemented methods being able to highlight distinct aspects. A rigorous and effective evaluation must rely on the possibility to calibrate the instruments, this being performed with specific fractal signal generators.

Toolbox components

1. Fractal analysis instruments
Exponents for time series using:
      - pre-existing fractal methodology (Hurst exponent by R/S, 
         Eta-variations, Height-height correlation);
      - original fractal methodology: smoothing dimensions Di', Dnt', Dnf' 
         (Munteanu et al.,1995a, 1995b; Ioana et al., 1997) (see Appendix);

2. Fractal gauge generators 
Based on: 
 Brownian Motions, Weierstrass-Mandelbrot, 
 Successive Random Addition,  Spectral Synthesis;

While the various fractal analysis methods may reflect different properties of the system, it is always desirable to obtain a) a low relative error and b) a low scattering of results. The set of fractal analysis methods we developed (Munteanu et al., 1995a, 1995b), which lead to smoothing dimensions, prove to surpass the previously existing methods from both points of view (Ioana et al., 1997).
The smoothing dimensions evaluation relies on the computing of the way in which signal parameters (like the Euclidean norm in L2 space) scale with the threshold of a lowpass filter used to successively smoothen the signal graph (see Appendix).

Applications currently developed by AsTech Solutions using the present toolbox:

• integrated circuit discrimination by fractal noise analysis;
• diagnostics of mechanical wear of machine tools by fractal analysis of vibrations;
• delocalyzed survey system of patients subject to intensive therapy (diagnostic support by fractal on-line analysis of fluctuations in significant physiologic parameters, using Remote Device Accessing);
• surface quality characterization with technological applications.

Lacking such an instrumentation, many possible applications remained isolated ideas in books or in several laboratories of the world.
A vicious circle was experienced: 

• the absence of a large number of fractal applications was caused, until this day, by the lack of proper instrumentation able to help their practical implementation; 
• and the lack of instruments was motivated by the fact that there were not enough palpable concrete applications yet.