Fractals and multifractals in human brain dynamics

Fractal and multifractal properties can be observed in different types of time series data (stock prices, earthquakes, gait). Informally, fractal and multifractal properties indicate that the time series is similar to itself in certain properties on a different time scale (e.g. seconds, minutes, hours). Such behaviour is usually generated by processes with long memories, and also processes displaying self-organised criticality.

In my talk, I will focus on human brain activity recorded from the electroencephalogram (EEG), and show our most recent results on applying fractal and multifractal measures to such signals. Importantly, we investigated the crucial question of how such measures relate to more intuitive signal properties. We also systematically compared different methods of fractal and multifractal estimation, and different estimation parameters. Finally, I will discuss the implications of our findings on how (multi-)fractal analyses of time series data can be interpreted, and perhaps understood by using generative models of the underlying process.