Emergence of bi-fractal time series from noise via allometric filters

¹  Department of Physics, Duke University - Durham, NC 27708, USA
²  Mathematical & Information Science Directorate Army Research Office - Research Triangle Park, NC 27709, USA

Received: 10 April 2007
Accepted: 13 June 2007

Abstract

We show how fractal time series can naturally emerge from an input signal, which might be also random noise, when processed by some allometric mechanisms. In particular, we introduce and study the properties of allometric low and high-pass filters. We also argue that in nature pure monofractal signals could be unphysical, while bi-scaling signals might be extremely common, a fact that might be due to allometric geometrical constraint. Finally, we suggest how allometric physical mechanisms could give an approximative interpretation of the fractional calculus.