Perceptual crossing is the reciprocal interplay of perceiving while being perceived. In this paper we discuss the last iteration of our ongoing research project on designing for perceptive qualities in systems of interactive products. We describe the design of explorative behavior in an artifact to enable the artifact and a person to engage in perceptual crossing. The explorative behavior is compared to the following and active behavior, the results of two earlier iterations. Through the iterations we formulated, applied and evaluated design relevant knowledge in the form of seven design notions. These notions inform design-researchers and design-practitioners on how to design for perceptive qualities in systems of interactive products. Here we specifically focus on how the artifact detects active perceptive behavior of a person, and how the artifact becomes aware of bygone perception and anticipates on future perception. An experiment shows how participants preferred the resulting explorative behavior that is closest to our theoretical framework based on phenomenology.