Lattice complexity and fine-graining of symbolic sequence
格子复杂性和符号序列的细粒化

A new measure of complexity for finite symbol sequences, named as lattice complexity, is presented, based on Lempel-Ziv complexity and the symbolic dynamics of one-dimensional iterated maps system. To make lattice complexity distinguished from Lempel-Ziv measure, an approach called fine-graini ng method is also proposed. When fine-graining order is small enough, the two measures are almost equal. When fine-graining order goes to large, th e differentiation between them becomes apparent. Applying these measures to stud ies of logistic map, we find those be regarded as complex sequences by lattice complexity are clearly generated at the edge of the chaotic region. The deriv ed properties of the measures are also discussed.