The paper by Edward N. Lorenz explores the behavior of finite systems of deterministic nonlinear differential equations, particularly focusing on forced dissipative hydrodynamic flow. Solutions of these equations are identified with trajectories in phase space. For systems with bounded solutions, it is found that nonperiodic solutions are typically unstable, meaning that slightly different initial states can lead to significantly different outcomes. Systems with bounded solutions are shown to have bounded numerical solutions. Lorenz examines a simple system representing cellular convection, solving it numerically and finding that all solutions are unstable and mostly nonperiodic. This analysis has implications for the feasibility of long-range weather prediction, as even small errors in initial conditions can lead to significant differences in future states. The paper also discusses the concept of phase space, where each point represents a possible state of the system, and trajectories in this space describe how the system evolves over time. The instability of nonperiodic flow is established, showing that stable central trajectories are quasi-periodic, while noncentral trajectories are unstable if they are nonperiodic. Numerical integration methods are described, including forward-difference, centered-difference, and double-approximation procedures, which are used to solve the equations numerically. The convection equations of Saltzman are introduced as a simplified example of deterministic nonperiodic flow, and their solutions are analyzed using these numerical methods. Finally, the paper presents numerical solutions of the convection equations, showing that the system exhibits chaotic behavior with nonperiodic oscillations. The behavior is visualized through phase space projections and plots of the maximum values of certain variables, revealing a complex, nonrepeating pattern. This chaotic behavior suggests that long-term predictions of the system's state are inherently difficult due to the sensitivity to initial conditions.The paper by Edward N. Lorenz explores the behavior of finite systems of deterministic nonlinear differential equations, particularly focusing on forced dissipative hydrodynamic flow. Solutions of these equations are identified with trajectories in phase space. For systems with bounded solutions, it is found that nonperiodic solutions are typically unstable, meaning that slightly different initial states can lead to significantly different outcomes. Systems with bounded solutions are shown to have bounded numerical solutions. Lorenz examines a simple system representing cellular convection, solving it numerically and finding that all solutions are unstable and mostly nonperiodic. This analysis has implications for the feasibility of long-range weather prediction, as even small errors in initial conditions can lead to significant differences in future states. The paper also discusses the concept of phase space, where each point represents a possible state of the system, and trajectories in this space describe how the system evolves over time. The instability of nonperiodic flow is established, showing that stable central trajectories are quasi-periodic, while noncentral trajectories are unstable if they are nonperiodic. Numerical integration methods are described, including forward-difference, centered-difference, and double-approximation procedures, which are used to solve the equations numerically. The convection equations of Saltzman are introduced as a simplified example of deterministic nonperiodic flow, and their solutions are analyzed using these numerical methods. Finally, the paper presents numerical solutions of the convection equations, showing that the system exhibits chaotic behavior with nonperiodic oscillations. The behavior is visualized through phase space projections and plots of the maximum values of certain variables, revealing a complex, nonrepeating pattern. This chaotic behavior suggests that long-term predictions of the system's state are inherently difficult due to the sensitivity to initial conditions.