相关论文: Geography as a Science of the Earth's Surface Foun…

As Christopher Alexander discovered, all space or matter - either organic or inorganic - has some degree of order in it according to its structure and arrangement. The order refers to a kind of structural character, called living structure,…

Inspired by Christopher Alexanders conception of the world - space is not lifeless or neutral but a living structure involving far more small things than large ones a topological representation has been previously developed to characterize…

Discovered by Christopher Alexander, living structure is a physical phenomenon, through which the quality of the built environment or artifacts can be judged objectively. It bears two distinguished properties just like a tree: "far more…

This chapter investigates the concept of living structure - which is defined as a structural hierarchy that has a recurring pattern of an abundance of small substructures compared to larger ones - and the application of such structures in…

As Christopher Alexander conceived and defined through his life's work - The Nature of Order - wholeness is a recursive structure that recurs in space and matter and is reflected in human minds and cognition. Based on the definition of…

Sustainable urban design or planning is not a LEGO-like assembly of prefabricated elements, but an embryo-like growth with persistent differentiation and adaptation towards a coherent whole. The coherent whole has a striking character -…

Conceived and developed by Christopher Alexander through his life's work: The Nature of Order, wholeness is defined as a mathematical structure of physical space in our surroundings. Yet, there was no mathematics, as Alexander admitted…

The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where…

As urban critic Jane Jacobs conceived, a city is essentially the problem of organized complexity. What underlies the complexity refers to a structural factor, called living structure, which is defined as a mathematical structure composed of…

Geographic space demonstrates scaling or hierarchy, implying that there are far more small things than large ones. The scaling pattern of geographic space, if visualized properly (i.e., based on head/tail breaks), can evoke a sense of…

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in…

Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of…

In this work, we introduce a new geometry based on the difference angle, an angle defined as the difference of slopes of two lines, together with an axiomatic system for angles. This framework provides a constructive approach to the…

One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…

A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…

The molecular biology revolution of the last seventy five years has transformed our view of living systems. Scientific explanations of biological phenomena are now synonymous with the identification of the genes, proteins, and signaling…

Any image is perceived subconsciously as a coherent structure (or whole) with two contrast substructures: figure and ground. The figure consists of numerous auto-generated substructures with an inherent hierarchy of far more smalls than…

A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life-giving order or simply a living structure. To characterize the wholeness…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19th-century founders of modern geometry contemplated the possibility that a piece of empty…