Nested strange attractors in spatiotemporal chaotic systems

A self-similar fractal structure for phase-space attractors is observed for time series produced by spatiotemporal chaotic systems. Two data sets produced by (1) coupled logistic maps and (2) the complex Ginzburg-Landau equation are studied numerically. The attractor reconstructed in a time-delay embedding space has a coarse-grained dimension growing exponentially with increasing resolution. A coarse-grained ${\mathit{K}}_2$ entropy in the region of scaling grows linearly with the embedding dimension. This type of scaling behavior is expected for developed spatiotemporal chaos in spatially homogeneous extended systems when the correlation length is much smaller than the system size. The growth rate of the dimension (differential dimension) is proportional to a density of dimensions and a correlation length of the system. The growth rate of ${\mathit{K}}_2$ entropy is proportional to the entropy density and the correlation length.