The nasal cycle is a chaotic ultradian rhythm with a period ranging from about 75 to 200 minutes. It has been shown to correlate highly with EEG amplitude in the contralateral hemisphere at virtually all frequencies, suggesting a connection between this rhythm and laterality of brain function. During a three-week period, five participants estimated airflow from both nostrils every 30 minutes during waking hours. Estimates were recorded on Likert scales and analyzed in three distinct phases: (1) reconstructing two-dimensional attractors by lagging and embedding; (2) computing Fourier frequency analyses; and (3) estimating fractal dimensions. Attractor reconstructions demonstrate noticeable order when compared to Monte Carlo reconstructions of the same data sets, and dimension estimates are in the fractal range. The attractor reconstructions, in combination with the frequency analyses, show distinct individual differences in the structure of the nasal cycle. The advantages of chaotic systems analyses over traditional behavioral statistics are discussed.