Automatic identification of fractal scaling region in GP algorithm

The identification of the linear segment in the double logarithmic curve, also known as scaling region or non-scale range, is important in Grassberger-Procaccia (GP) algorithm. The second-order derivative of log-log curves within the scaling region should be zero or near to zero because the line is nearly straight in that region. Based on this idea, a new method to automatically determine the fractal scaling region is presented. The time series data of the Lorenz strange attractor is applied to validate the method. The numerical results show that the scaling region can be determined accurately and automatically by this method which is both simple and with clear physical meaning.