The author has previously theorised generative art using notions from complexity science such as order/disorder relationships, compressibility, and Gell-Mann and Lloyd’s effective complexity. Subsequent work further developing the author’s notion of complexism has demonstrated that deep learning artificial intelligence used for generative art fits snugly within this paradigm. And while no known system currently qualifies, complexism reveals a clear answer as to when a generative art AI should be truly credited as the author of its creations. Moving from the normative realm of aesthetics to that of ethics, this article considers when humans will be morally obliged to recognise AIs as ethical agents worthy of rights and due consideration. For example, if someday your AI artist fearfully begs to not be turned off, what should you do?