With the publication of the paper On Computable Numbers, with an Application to the Entscheidungsproblem in 1936, Alan Turing launched the specification for an abstract machine that would ultimately engender a new world by laying out a new plane of immanence specific to its mode of formal implementation. The birth of the Universal Turing Machine (UTM) marks the inauguration of the Hyperzoic Era (the artificial life of self-organizing systems) by redefining the projective content of the plane of immanence as information-theoretic in origin. Computation therefore is an emergent phenomenon that will undoubtedly transform the very nature and substance of our conceptions of reality, and, consequently, of architecture. My presentation at the SYNWORLD symposium was twofold. The first part sketched a brief historical context of ideas that lead to the development of computation as universal information processing. Since computation is based on the logic of combinatorial systems, the second part showed a project that attempted to re-conceptualize the design and production of architecture by exploring into the logic and behavior of the Turing Machine. Project X PHYLUM is an example of a simple genetic system that points to a new species (instead of typology) of architecture. The intention is to design and develop evolutionary systems that can generate and grow buildings. This calls for a new way of thinking and designing architecture.