Haptic exploration usually involves stereotypical systematic movements that are adapted to the task. Here we tested whether exploration movements are also driven by physical stimulus features. We designed haptic stimuli, whose surface relief varied locally in spatial frequency, height, orientation, and anisotropy. In Experiment 1, participants subsequently explored two stimuli in order to decide whether they were same or different. We trained a variational autoencoder to predict the spatial distribution of touch duration from the surface relief of the haptic stimuli. The model successfully predicted where participants touched the stimuli. It could also predict participants' touch distribution from the stimulus' surface relief when tested with two new groups of participants, who performed a different task (Exp. 2) or explored different stimuli (Exp. 3). We further generated a large number of virtual surface reliefs (uniformly expressing a certain combination of features) and correlated the model's responses with stimulus properties to understand the model's preferences in order to infer which stimulus features were preferentially touched by participants. Our results indicate that haptic exploratory behavior is to some extent driven by the physical features of the stimuli, with e.g. edge-like structures, vertical and horizontal patterns, and rough regions being explored in more detail.