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In order to make sense of a scene, a person must pay attention to several levels of nested order, ranging from the most differentiated details of the display to the integrated whole. In adults, research shows that the processes of integration and differentiation have the signature of self-organization. Does the same hold for children? The current study addresses this question with children between 6 and 9 years of age, using two tasks that require attention to hierarchical displays. A group of adults were tested as well, for control purposes. To get at the question of self-organization, reaction time data were submitted to a detrended fluctuation analysis and a recurrence quantification analysis. Hurst exponents shows a long-range correlations (1/f noise), and recurrence measures (percent determinism, maximum line, entropy, and trend), show a deterministic structure of variability being characteristic of self-organizing systems. Findings are discussed in terms of organism-environment coupling that gives rise to fluid attention to hierarchical displays.