The effective information dimension: a metric for system complexity

摘要

The fractal inforamtion dimension, derived from Shannon's information theory, many provide a useful measurement of the complexity of a system trajectory in state space. A weakness to this argument appears when trajectories of identical geometric patterns appear at differing locations in state space. Such patterns have the same fractal information dimension. A new measurement, termed the effective inforamtion dimension, is proposed which numerically aggregates sequential inforamtion dimension measurements. The resulting measurement reflects changes both in a pattern's geometry and location.