The model of the brain as an information processing machine is a profound hypothesis in which neuroscience, psychology and theory of computation are now deeply rooted. Modern neuroscience aims to model the brain as a network of densely interconnected functional nodes. However, to model the dynamic information processing mechanisms of perception and cognition, it is imperative to understand brain networks at an algorithmic level--i.e. as the information flow that network nodes code and communicate. Here, using innovative methods (Directed Feature Information), we reconstructed examples of possible algorithmic brain networks that code and communicate the specific features underlying two distinct perceptions of the same ambiguous picture. In each observer, we identified a network architecture comprising one occipito-temporal hub where the features underlying both perceptual decisions dynamically converge. Our focus on detailed information flow represents an important step towards a new brain algorithmics to model the mechanisms of perception and cognition.