Universality in multiscale, turbulent-like self-organization: from algal blooms to heartbeat to stock market dynamics

Many complex systems in natural phenomena organize through the interactions between processes at different scales. In certain cases, when the dynamics has no privileged spacial or temporal scale, the resulting structure becomes scale-invariant. In this context, fractal and multifractal models have often been proposed to describe such scale-invariance. In recent years, there has been a growing interest in the study of multifractal systems, something made possible by the development of new signal processing methods based on singularity analysis. These techniques have the advantage of being robust to common problems of empirical data such as noise, discretization, data gaps and finite-size effects. We present a study of multifractal datasets of very different nature: wind tunnel turbulence, concentration of phytoplankton in the ocean, heartbeat dynamics in different regimes and formation of prices in the stock market. When appropriately characterizing the relevant parameters of their respective multifractal hierarchies, we find evidences of common fractal attractors that have particular and very specific properties. This behaviour can be explained as the result of an effective dynamics that expands from a maximum-singular manifold, which would be the result of multifractal universality classes. Universality classes imply a common macroscopic behaviour independent of the particular microscopic dynamics of each system. Therefore, identifying such universality classes makes possible a better characterization of the studied phenomena, a more accurate and robust fitting of their dynamic parameters and a better modelling. The result is a flexible methodology that can be adapted to the particularities of each system and unveil its effective dynamics. We show applications of these characterizations to the reconstruction of missing data and the forecasting of time series.