Structural principles developed in biology, computer science and economics are applied here to urban design. The coherence of urban form can be understood from the theory of complex interacting systems. Complex large-scale wholes are assembled from tightly interacting subunits at many different levels of scale, in a hierarchy going down to the natural structure of materials. A variety of elements and functions at the small scale is necessary for large-scale coherence. Dead urban and suburban regions may be resurrected in part by reconnecting their geometry. If these suggestions are put into practice, new projects could even approach the coherence that characterizes the best-loved urban regions built in the past. The proposed design rules differ radically from ones in use today. In a major revision of contemporary urban practice, it is shown that grid alignment does not connect a city, giving only the misleading impression of doing so. Although these ideas are consistent with the New Urbanism, they come from science and are independent of traditional urbanist arguments.

Pattern languages help us tackle the complexity of a variety of systems ranging from computer software, to buildings and cities. Each ‘pattern’ represents a rule governing one working piece of a complex system, and the application of pattern languages can be done systematically. Design that wishes to connect to human beings needs the information contained in a pattern language. This paper describes how to validate existing pattern languages, how to develop them, and how they evolve. The connective geometry of urban interfaces is derived from the architectural patterns of Christopher Alexander.

An associative algebra of differential forms with division has been constructed. The algebra of forms in each different space provides a practical realization of the universal Clifford algebra of that space. A classification of all such algebras is given in terms of two distinct types of algebras N_k and S_k. The former include the dihedral, quaternion, and Majorana algebras; the latter include the complex, spinor, and Dirac algebras. The associative product expresses Hodge duality as multiplication by a basis element. This makes possible the realization of higher order algebras in a calculationally useful algebraic setting. The fact that the associative algebras, as well as the enveloped Lie algebras, are precisely those arising in physics suggests that this formalism may be a convenient setting for the formulation of basic physical laws.

This article reviews current research in visual urban perception. The temporal sequence of the first few milliseconds of visual stimulus processing sheds light on the historically ambiguous topic of aesthetic experience. Automatic fractal processing triggers initial attraction/avoidance evaluations of an environment’s salubriousness, and its potentially positive or negative impacts upon an individual. As repeated cycles of visual perception occur, the attractiveness of urban form affects the user experience much more than had been previously suspected. These perceptual mechanisms promote walkability and intuitive navigation, and so they support the urban and civic interactions for which we establish communities and cities in the first place. Therefore, the use of multiple fractals needs to reintegrate with biophilic and traditional architecture in urban design for their proven positive effects on health and well-being. Such benefits include striking reductions in observers’ stress and mental fatigue. Due to their costs to individual well-being, urban performance, environmental quality, and climatic adaptation, this paper recommends that nontraditional styles should be hereafter applied judiciously to the built environment.