The paper evaluates techniques for determining changing system complexity from data, focusing on the convergence of correlation dimension algorithms and their implications for chaotic and stochastic processes. It introduces approximate entropy (ApEn) as a measure that can classify complex systems with a relatively small amount of data (at least 1000 values). The author argues that ApEn can distinguish between deterministic chaotic and stochastic processes, unlike correlation dimension, which can yield finite values for stochastic processes with correlated increments. The paper provides theoretical foundations and examples to illustrate the effectiveness of ApEn in various contexts, including low-dimensional chaotic systems, periodic and multiply periodic systems, and stochastic processes. It also discusses the limitations of other measures like K-S entropy and the Lyapunov spectrum, emphasizing the need for more robust and versatile tools to assess system complexity.The paper evaluates techniques for determining changing system complexity from data, focusing on the convergence of correlation dimension algorithms and their implications for chaotic and stochastic processes. It introduces approximate entropy (ApEn) as a measure that can classify complex systems with a relatively small amount of data (at least 1000 values). The author argues that ApEn can distinguish between deterministic chaotic and stochastic processes, unlike correlation dimension, which can yield finite values for stochastic processes with correlated increments. The paper provides theoretical foundations and examples to illustrate the effectiveness of ApEn in various contexts, including low-dimensional chaotic systems, periodic and multiply periodic systems, and stochastic processes. It also discusses the limitations of other measures like K-S entropy and the Lyapunov spectrum, emphasizing the need for more robust and versatile tools to assess system complexity.