Chaotic dynamics is a significant systematic feature of infrared electromagnetic wavefields that requires further study. Understanding the chaotic dynamics of infrared radiation wavefields can lead to advancements in high-performance detection, imaging, and recognition of weak, moving, time-varying signals. To extract the time series of the dynamic system, we have established a 4D time-space observing system. We then use the FFT transform on a random time series of frequency-band infrared data to obtain the fractional Brownian motion dimension, indicating a fractal structure in the atmospheric infrared radiation wavefield. By using time-delay analysis, we construct a dimensional phase space and compute the fractal dimension. We also observe that the first Lyapunov exponent remains positive in different phase spaces, leading to the initial conclusion that the atmospheric infrared wavefield is chaotic. To measure the chaotic strength of real cases in the time-space domain, we use the permutation entropy. These results serve as a foundation for further research, such as understanding the dynamic evolution mechanism of moving objects and their background wavefields, capturing time-varying signals, and making long-term nonlinear predictions of infrared wave behaviors in different domains.