Increases in the low attenuation areas (LAA) of chest x-ray computed tomography images in patients with chronic obstructive pulmonary disease (COPD) have been reported to reflect the development of pathological emphysema. We examined the statistical properties of LAA clusters in COPD patients and in healthy subjects. In COPD patients, the percentage of the lung field occupied by LAAs (LAA%) ranged from 2.6 to 67.6. In contrast, LAA% was always <30% in healthy subjects. The cumulative size distribution of the LAA clusters followed a power law characterized by an exponent D. We show that D is a measure of the complexity of the terminal airspace geometry. The COPD patients with normal LAA% had significantly smaller D values than the healthy subjects, and the D values did not correlate with pulmonary function tests except for the diffusing capacity of the lung. We interpret these results by using a large elastic spring network model and find that the neighboring smaller LAA clusters tend to coalesce and form larger clusters as the weak elastic fibers separating them break under tension. This process leaves LAA% unchanged whereas it decreases the number of small clusters and increases the number of large clusters, which results in a reduction in D similar to that observed in early emphysema patients. These findings suggest that D is a sensitive and powerful parameter for the detection of the terminal airspace enlargement that occurs in early emphysema.