$fractal time calculator$

In light of this apparent fundamental indeterminacy, Mandelbrot posits that familiar geometrical metrics such as length are inadequate for describing the complexity found in nature. This quality reflects the fact that the outline of the British coastline is an example of a вЂњself-similarвЂќ structure-that is, a structure that exhibits the same statistical qualities, or even the exact details, across a wide range of length scales. Indeed, as the precision of such measurements increases-that is, by decreasing the length of the вЂњrulerвЂќ used to trace the profile-the measured total length appears to increase as well. As Richardson and Mandelbrot note, such a hypothesis is difficult to evaluate, since individual records of the length of BritainвЂ™s west coast varied by up to a factor of three. Richardson, a pacifist and mathematician, sought to investigate the hypothesis that the likelihood that war would erupt between a pair of neighboring nations is related to the length of the nationsвЂ™ shared border. In fact, however, the curious nature of coastline measurements had been discussed by Lewis Fry Richardson 6 years prior in the General Systems Yearbook. Mandelbrot often is credited with introducing the notion of a fractional, or fractal, dimension in his 1967 paper, вЂњHow long is the coast of Britain?вЂќ. Additionally, we investigate the inherent challenges in quantifying fractal characteristics (and indeed of verifying the presence of such fractal characteristics) in time-series traces modeled to resemble physical data sets. We investigate the fidelity of such techniques by applying each technique to sets of computer-generated time-series data sets with well-defined fractal characteristics.

$fractal time calculator$

In this chapter, we introduce and investigate a variety of fractal analysis techniques directed to time-series structures. However, such spatial analyses generally are not well-suited for the analysis of so-called вЂњtime-seriesвЂќ fractals, which may exhibit exact or statistical self-affinity but which inherently lack well-defined spatial characteristics. As a traditional example, a fractal dimension of a spatial fractal structure may be quantified via a box-counting fractal analysis that probes a manner in which the structure fills space. Many methods exist for quantifying the fractal characteristics of a structure via a fractal dimension.

Fractal time calculator