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The central task in the study of self-organization is to explore the generalmechanism of emergences. However, this is inhibited by the missing of a fullknowledge of the microscopic dynamics of emergence. Here, in this study, themicroscopic dynamics of self-organization for patterns is investigated andquantified in a periodically propelled Quincke system. The periodical couplingbetween propulsion and repulsion at the particle level leads to local directedoscillating particle flows and promises a loop of positive feedback to densityfluctuations. Nevertheless, the global evolution of the resulting cluster phaseis dominated by a global dual transformation. As stable attractors of the dualtransformation, self-dual patterns including stripe patterns and squarelattices can be achieved by tuning the strength and the frequency ofpropelling. However, stripes are possible only at strong propelling whereboundary particle flows can form. The findings in this study show that thedynamics of emergence on different length scales are controlled by differentmechanisms. The competition and the interplay between different microscopicdynamic processes play the central role in determining the product ofemergence. Moreover, the periodically oscillating self-dual patternsdemonstrate a classical approach to time crystals.

Emergence of Self-dual Patterns in Active Colloids with Periodical Feedback to Local Density