Asthma is a common disease affecting an increasing number of children throughout the world. In asthma, pulmonary airways narrow in response to contraction of surrounding smooth muscle. The precise nature of functional changes during an acute asthma attack is unclear. The tree structure of the pulmonary airways has been linked to complex behaviour in sudden airway narrowing and avalanche-like reopening. Here we present experimental evidence that bronchoconstriction leads to patchiness in lung ventilation, as well as a computational model that provides interpretation of the experimental data. Using positron emission tomography, we observe that bronchoconstricted asthmatics develop regions of poorly ventilated lung. Using the computational model we show that, even for uniform smooth muscle activation of a symmetric bronchial tree, the presence of minimal heterogeneity breaks the symmetry and leads to large clusters of poorly ventilated lung units. These clusters are generated by interaction of short- and long-range feedback mechanisms, which lead to catastrophic shifts similar to those linked to self-organized patchiness in nature. This work might have implications for the treatment of asthma, and might provide a model for studying diseases of other distributed organs.