Building on the growing literature in algorithmic accountability, this paper investigates the use of a process visualisation technique known as the Petri net to achieve the aims of Privacy by Design. The strength of the approach is that it can help to bridge the knowledge gap that often exists between those in the legal and technical domains. Intuitive visual representations of the status of a system and the flow of information within and between legal and system models mean developers can embody the aims of the legislation from the very beginning of the software design process, while lawyers can gain an understanding of the inner workings of the software without needing to understand code. The approach can also facilitate automated formal verification of the models’ interactions, paving the way for machine-assisted privacy by design and, potentially, more general ‘compliance by design’. Opening up the ‘black box’ in this way could be a step towards achieving better algorithmic accountability.