Alan Turing decoded nature in drawings and algorithmic programming. His botanical decryptions helped situate synthetic AI/ALife processes in digital realms now encompassing algorithmic simulation. These little-known drawings prompted the author's analysis via Maturana and Varela's theory of autopoiesis because of its emphasis on self-organization and minimal requirements for life. Autopoiesis, if hybridized with Andy Clark's extended cognition, then supports an underpinning hypothesis for generative architecture. Together, the theory and drawings propel design research, leading to the question: Can buildings think?—reprocessing Turing's original question: “Can machines think?” This paper thus situates Turing's 1950s' nature-to-computation images as unacknowledged design patrimony appropriated for generative architecture derived from nature and implemented via autopoietic-extended design.