Living geometry, AI tools, and Alexander's 15 fundamental properties. Remodel the architecture studios!

A universal set of mathematical qualities combine complexity with geometry to define “living geometry”. Those properties apply equally to organisms as to inanimate matter. A special type of geometry that merges approximate fractal structure with nested symmetries on all scales describes most biological and natural forms. Christopher Alexander discovered 15 geometrical properties in the context of architecture adapted to human feelings, and those provide a practical toolkit for creating living geometry in artifacts, buildings, and urban spaces. AI can be used to both validate the importance of living geometry for human health, and to evaluate architectural designs before and after they are built. Human beings evolved their neurological system to interpret living geometry defined by the ancestral natural environment, and the same interpretative reference is used to navigate today's built environment. This knowledge helps to understand how geometry affects cognition, emotions, and health. Asking large-language models about the best learning environments for creative thought produces a list of suggestions for renovating lecture and studio spaces in architecture schools. A severe disconnect between the contemporary urban experience and living geometry has negative effects on human health, intelligence, and the learning process. AI helps to completely rethink design aesthetics and design-making strategies.