A new measure of complexity for finite symbol sequences, named as lattice comple xity, is presented, based on LempelZiv complexity and the symbolic dynamics of onedimensional iterated maps system. To make lattice complexity distinguished from LempelZiv measure, an approach called finegraining method is also prop osed. When finegraining order is small enough, the two measures are almost equ al. When finegraining order goes to large, the differentiation between them be comes apparent. Applying these measures to studies of logistic map, we find thos e be regarded as complex sequences by lattice complexity are clearly generated a t the edge of the chaotic region. The derived properties of the measures are als o discussed.
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