Fractal Analyses: Statistical And Methodological Innovations And Best Practices

Abstract

Fractal statistics now routinely appear in the scientific literature. Examples originate from many disciplines, including aquatic sciences, biology, computer science, ecology, economics, geology, mathematics, medicine, neuroscience, physics, physiology, and psychology. This eBook provides a broad range of resources to support the application of fractal methods and theory in physiology and related disciplines. It is comprised of a set of research topic articles that appeared in the Frontiers in Physiology specialty section: Fractal Physiology. Our eBook chapters are organized along a loose continuum defined by the characteristics of the empirical measurements a given statistical technique is intended to confront.At one end of the continuum are techniques designed for application to stochastic systems. van Rooij et al. (2013) describe histograms, probability distributions, and scaling distributions in fractal terms. The next step on the continuum concerns self-affine random fractals and methods intended for outcome measures that entail scale-invariant 1/f patterns or related patterns of temporal fluctuation. Stadnitski (2012) The deterministic end of the statistical continuum emphasizes techniques used to investigate systems that express differentiable trajectories. Webber (2012) illustrates recurrence analysis on time-series derived from several multi-dimensional dynamic systems. Gao et al. (2012) introduces a very general analysis that is suitable for use on both stochastic and continuous measurements. Finally, Richardson et al. (2012) describe techniques that assess relative dynamic synchrony among multiple coupled oscillatory time-series. Taken together, the chapters offer a gamut of analytic strategies alongside contemporary expertise on how to best conduct and interpret the outcomes of fractal analyses.