Eye contact, even momentarily between strangers, plays a pivotal role in fostering human connection, promoting happiness, and enhancing belonging. Yet, the physical rigidity of public spaces, such as airport terminals, often limits opportunities for meaningful interactions between strangers who often remain absorbed in their personal activities. This paper introduces Mirrorbot, a robotic mirror system that transforms static environments into dynamic, socio-spatial interfaces. Through autonomous navigation and adaptive mirror control, Mirrorbot facilitates serendipitous, non-verbal interactions by dynamically transitioning reflections from self-focused to mutual recognition, sparking eye contact, shared awareness, and playful engagement. By integrating mirrors—a familiar and accessible architectural element—Mirrorbot disrupts conventional isolation in public spaces, enabling embodied, accessible interactions that go beyond screen-based solutions. This work demonstrates the potential of interactive mirrors to enrich public spaces, fostering spontaneous connections in shared environments.