Calculating climate attractor dimension from δ18O records by the Grassberger-Procaccia algorithm

The Grassberger-Procaccia method of calculating dimension from a time series is applied to 14 late Pleistocene ¹⁸O records. The difficulties encountered when using this algorithm on limited data sets are reviewed and the step-by-step procedure actually used to calculate the dimension of each record is explicitly listed. Although the results must be viewed with caution, they do indicate that the dimension cannot be measured accurately enough to determine whether or not it is fractal. However, in spite of inaccuracies in the time scale, the underlying dynamics do not appear to be random and there is a suggestion that a lower bound to the Grassberger-Procaccia dimension is somewhere between 4 and 6.