An essential question of morphogenesis is how patterns arise without preexisting positional information, as inspired by Turing. In the past few years, cytoskeletal flows in the cell cortex have been identified as a key mechanism of molecular patterning at the subcellular level. Theoretical and in vitro studies have suggested that biological polymers such as actomyosin gels have the property to self-organize, but the applicability of this concept in an in vivo setting remains unclear. Here, we report that the regular spacing pattern of supracellular actin rings in the Drosophila tracheal tubule is governed by a self-organizing principle. We propose a simple biophysical model where pattern formation arises from the interplay of myosin contractility and actin turnover. We validate the hypotheses of the model using photobleaching experiments and report that the formation of actin rings is contractility dependent. Moreover, genetic and pharmacological perturbations of the physical properties of the actomyosin gel modify the spacing of the pattern, as the model predicted. In addition, our model posited a role of cortical friction in stabilizing the spacing pattern of actin rings. Consistently, genetic depletion of apical extracellular matrix caused strikingly dynamic movements of actin rings, mirroring our model prediction of a transition from steady to chaotic actin patterns at low cortical friction. Our results therefore demonstrate quantitatively that a hydrodynamical instability of the actin cortex can trigger regular pattern formation and drive morphogenesis in an in vivo setting.