Detecting Patterns in Irregular Time Series with Fractal Dimension

Fractal geometry is a tool to quantitatively describe objects that are considered as extremely complex and disorder. Fractals are objects which have a similar appearance when viewed at different scales. They are assigned a dimension which is non integer. In particular, time series data has been represented as a curve with dimension between one and two. Effective algorithm for fractal dimension is developed based on fractal interpolation functions so that it can be applied to time series interpreting the chaotic behaviour. The fractal dimension is computed for these times series of irregular types and discriminate the patterns depending on similarity. We have applied these fractal analysis techniques to electroencephalogram (EEG) time series data from a number of electrodes fixed in the brain cortex. Detection of the fractal patterns in each electrode positions is useful for analyzing the brain activity.