..Introduction
..Laws for generating urban space
..The Spatial Information Field

Introduction

What makes us use (or avoid) urban spaces? Instead of properties of empty space defined by some plan, it is actually the information field originating in the surrounding surfaces, which permeates the space and connects it to the human consciousness. The experience of space is defined by its interaction with people, yet in the late 20th century people tend to conceive of space as an empty volume. In that view, the receptor has no role to play. Defined by the large-scale geometry, empty volumes exist only in an abstract, mathematical sense. They are independent of surrounding structures and of any observers. The point is that abstract space has little to do with experienced space. Being open to the sky, urban space is most easily defined by a plan, and the attention of urban designers has been focussed on the formal design of this plan.
Here, urban space is related in an essential manner to its information field, whose existence is enhanced by the human receptors of this field. Information is generated by surrounding surfaces: building façades, the pavement, and local nodes such as trees and street furniture. The plan has only minor relevance, the focus being on the informational content of surrounding surfaces. Architecture is an extension of the human mind to the environment. We build structures so that we may connect to them; this extends our consciousness to our immediate surroundings. If, on the other hand, we cannot connect to surrounding surfaces, then we find ourselves in an alien environment, and our most basic instincts drive us to leave it.
We define our living space by connecting to solid boundaries, visually and acoustically as well as through physical contact. Indoor space is almost totally enclosed by built structures. Strictly speaking, outdoor space doesn't need buildings at all; only surrounding surfaces, nodes for sitting and standing, and paths. As a large portion of urban space is open to the sky, those small parts that one is able to connect with are crucial since they represent but a fraction of the total subtended solid angle of our perceptual field. Urban space depends on the fine structure of its boundaries, requiring much greater care than the architectural treatment of interior space. It is shown later why the ideal boundary for urban space is fractally generated.
Urban space is far more sophisticated mathematically than we are used to thinking. At the other extreme from a collection of static, non-interacting simple forms and voids, in reality we have a complex system tied together by both static and dynamic interactions (Madanipour, 1996). Most important, this system is linked in a non-linear manner to its users. The presence of observers alters the state of the system by increasing the information content, thus making the urban space more useful (and increasing the frequency of its use). Advances in understanding complex systems during the past few years allow us to tackle problems of great complexity - such as urban space - without being forced to make drastic simplifying assumptions.

Laws for generating urban space

Urban space follows a social logic that influences its growth; this component is analyzed by Bill Hillier and his collaborators (Hillier, 1996; Hillier and Hanson, 1984). We are trying to find laws for urban design: what is clear so far is that paths, spaces, and the design of buildings all depend on some type of connectivity. These essential connections are very difficult to describe. The urban fabric is composed of many different components, whose underlying mechanisms cannot be grasped all at once (Madanipour, 1996). Different aspects have to be understood by means of distinct models, then combined to give an overall picture. Non-linear emergent properties - which create the most memorable features - arise from the interaction of individual components.
Urban space should have certain qualities if it is to be responsive to human feelings and sensibilities. Historical spaces were the result of intuition, traditional rules of thumb, social conditions, and the limitations of available materials (Madanipour, 1996; Moughtin, 1992). They were probably neither the result of conscious thought, nor the application of a set of rules. Nowadays, the complexity of human interaction with space is more confusing; it helps if we can provide a set of rules for urban space. Nature offers us the example of fractal structures, and historical urban spaces do have fractal qualities. Both Lachlan Robertson (Robertson, 1995) and Christopher Alexander (Alexander, 1998) believe that the texture of space is governed by the same rules at all scales; from the scale of the planet, down to the scale of a pebble.
The processes that generate successful urban space (i.e., space that is used, and which feels emotionally nourishing) may be summarized in the following three axioms:

1. Urban space is bounded by surfaces that present unambiguous information.

2. The spatial information field determines the connective web of paths and nodes.

3. The core of urban space is pedestrian space protected from non-pedestrian traffic.

The three urban space axioms influence the layout of public space and buildings. They also provide general rules governing the shape (but not the design) of building façades, structural details, and materials. All of these become interdependent in helping to define urban space. The axioms operate at a more basic level than large-scale design decisions. Plans; patterns; symmetry; axes; while important, are only of secondary importance relative to the fundamental processes that generate urban space. This lends support for the irregularity of successful urban spaces as documented by Camillo Sitte (Collins and Collins, 1986) and by Rob Krier (Krier, 1979). Urban planners in our times, who tend to focus on the formal geometry of the plan, have not created urban spaces that are used.
Surprisingly, the main result has as much to do with architecture as with urban planning. Surface differentiations, color, and texture on pavements and building façades are the essential elements used to define urban spaces. These include structural subdivisions, as well as articulations on the small scale that are traditionally classed as "ornament". The function of ornament on pavements and building façades is to guarantee that every architectural region interacts with the user at any distance. The success of urban space depends on this interaction (Moughtin, Oc et al., 1995), and one of the aims of this paper is to show why this is true.
The relation between cars and pedestrians is a major topic on its own. Pedestrians both need to be protected from, and connected to cars. Although the core of urban space is the web of pedestrian paths, in most cases the space can also contain roads (but not highways), which must be peripheral and not intrude on the core. It is essential to connect car paths to pedestrian paths, even in a narrow street, to guarantee the appropriate density of movement. Very often, however, vehicular traffic encroaches upon and destroys urban space. The best examples come from a time when cars did not yet dominate. Roads limit urban space, yet a road or car park is not a vertical edge that defines a spatial boundary. Urban space is bounded by buildings, trees, and walls; but neither by curbs, nor by cars.
Characteristics of successful urban spaces can be deduced from historical examples (Krier, 1979; Moughtin, 1992; Moughtin, Oc et al., 1995; Paumier, 1988; Wiedenhoeft, 1981). New cities and suburbs have to follow urban templates for the motorized city, whose demands dictate much of the large-scale structure. These tend to destroy urban space. There exists an overwhelming body of literature criticizing suburban forms and modernist planning (Greenberg, 1995; Madanipour, 1996; Paumier, 1988; Wiedenhoeft, 1981). It is not the purpose of this paper to engage in another attack; instead, the author believes that urban space can indeed exist in today's cities and suburbs, and provides a template for creating it.

PART A. The Spatial Information Field

The geometry influences the information field

A rough surface will in general scatter light and sound in all directions, with a peak in the orthogonal direction (90° to the surface). One always holds a page orthogonal to the sight line when reading. Optimizing the presentation of information contained in surfaces will influence the geometry to a considerable extent. By orienting structural pieces surrounding an open space so that they present maximal information, a piecewise concave boundary is generated. In this way, optics and acoustics determine in part the local (i.e., small scale) geometry of urban spatial boundaries. This process leads to what Alexander calls "positive space", which he proposes as a fundamental property shared by all coherent structures (Alexander, 1998).
Maximizing the information field through geometry and surface texture opens the possibility of information overload. That could lead to chaos, but is avoided by harmonizing the ensemble through mathematical symmetries and connections. The harmonization process lies outside the scope of the present paper. Alexander describes in detail how "wholeness" results from a painstaking balance and cooperation among different design segments (Alexander, 1998). This state is extremely difficult to achieve. Note that the harmonization process is the opposite from removing information from the environment so that the lack of harmony is no longer evident, even though the latter approach does reduce visual disorder (Salingaros, 1997).

Information use and the success of urban space

We need to distinguish two general information measures: (i) content, and (ii) accessibility. The content of information is what is described (i.e., the message of text on a page), whereas its accessibility is the inverse effort needed to receive that information (i.e., how easy it is to read). The frequency or intensity of use of information is, to first order, the product of content with accessibility. This simple relation attempts to balance these two independent factors. For a particular task or situation, information can be ranked according to its direct relevance in content. Readily available information that has little relevant content is going to be used less, or not at all. On the other hand, pertinent information that is less readily accessible will also not be used as much.
Human beings are information-processing machines whose existence depends on the ability to interpret the information present in their surroundings. We must be able to instantly judge and respond to environmental information, and our evolution has equipped us with the sensory and perceptive tools to do so: it is precisely this ability that makes us human. Moreover, since spatial information plays such a fundamental role in our functionality as complex living systems, we require it just as much as we require air and nutrients in order to sustain us. The complexity and organization of architectural information is crucial to our state of mind (Salingaros, 1997). An equivalence is proposed here between the physical use of space and the use of the information field it generates.
In communications engineering, it is assumed that information is available, and that its access depends on the ability to retrieve and transmit it without losses. Human perception is instantaneous, however, so access to architectural information involves presentation rather than transmission. The perception of architectural forms can be divided into two aspects, as above: (i) The information content depends on the design, geometry of forms, and their subdivisions, insofar as design organizes elements in particular ways. (ii) Information access is governed by the orientation of surfaces, their differentiations on the smallest scale, and the microstructure in the materials. These independent factors generate the information field, which in turn determines the use of urban space.
The information content of surfaces surrounding urban space is low for empty or plain surfaces, and high for interesting patterns; it becomes too high in distressingly chaotic environments. One may use here the L-measure of complexity defined in (Salingaros, 1997), which distinguishes between empty forms, on the other hand, and two opposites: organized or disorganized complexity, on the other. The accessibility factor is a separate issue, depending both on the physical surfaces, and on the pedestrian receiver. There exists a non-linear interaction between built surfaces and the density of protected paths that they enclose. This contribution is harder to assess, yet one can easily form a qualitative idea of the factors that either increase or decrease the accessibility of information.
Reading the older literature on urban design, late nineteenth century authors understood the need for an information field to guarantee the use of urban space, although nothing like the present formulation was ever presented (Madanipour, 1996; Moughtin, 1992; Moughtin, Oc et al., 1995). Sitte brings this issue forward in observing that every great façade has a corresponding urban space from which it can be experienced (Collins and Collins, 1986). Conversely, every successful urban space tends to have a interesting building façade as one bounding surface, to add life to the space, as well as to provide a reason for a person to be there (Collins and Collins, 1986).

The automobile replaces urban space

The author sees the automobile as the protector of human feelings in an age of urban hostility. The automobile supplanted urban space after the second world war. Car interiors have always been marvels of design; they epitomize a comfortable, tactile bubble. Such an environment outside was rarely available to people in the past. With mass production, everyone could surround themselves with a concave shell during travel. One has a mobile, protected spot in which to receive spatial information. This puts the car into direct competition with the pedestrian experience of urban space. The only advantage of the latter is the possibility of face-to-face interaction with other human beings (now partially erased with the advent of car telephones), and contact with nature.
Deciding between the concavity inside one's own car, and pedestrian urban space, the former usually wins out. Part of the reason for this is the systematic elimination of urban space in post-war cities (as detailed in a later section). The need to introduce efficient automobile transport necessarily subordinated pedestrian streets containing urban space (Krier, 1979; Paumier, 1988; Wiedenhoeft, 1981). The solutions applied, however, are crude and effectively destroy the pedestrian environment. Successful planning requires a balanced attention to car connections while not eliminating pedestrian connections. If we are not careful, then we create a hostile pedestrian environment that forces one's retreat to the safety - physical as well as psychological - of the car interior.

Built examples, looking parallel to the ground

The next few sections discuss the creation of the urban information field. Examples listed below illustrate structures that maximize surface information. Architectural features shared by building exteriors throughout the world arise from the human need for spatial information. These effects work only on the full-scale structure; a miniature construction often fails to indicate their impact. A right-handed Cartesian coordinate system is used for the figures, with x-y as the horizontal plan, and z as the vertical axis. The pedestrian observer is placed along the x-axis looking in towards the origin. A figure represents either a plan (x-y), or side view (x-z), according to the coordinate axes. Dotted lines show no visual or acoustical contact; solid lines show information transmitted towards the viewer.

1. Vertical facets and flutes close to the ground. To obtain visual and acoustic information looking horizontally, a surface must reflect in a variety of horizontal angles. A structure is subdivided into vertical facets - thin vertical strips, or flutes - that offer many different angles of reflection (Figure 1). Non-reflective surfaces give a maximal signal when they are orthogonal to the viewer. Flat walls and protruding elements of rectangular cross-section provide only one normal contact point. Note that this mechanism is effective at or near ground level; extending the vertical facets or flutes above eye level does nothing to enhance the desired signal.

Figure 1. Decomposition of building surface at ground level into vertical facets and flutes.

2. Amphitheaters. The ancient Greek theatre is the archetypal open-air concave structure, where the curvature gives a very precise acoustic and visual focus. Medieval plazas use concavity to great effect. Contemporary plazas are invariably rectangular, either too enclosed or too open (Whyte, 1980); they fail to focus information.

3. Courtyards. Vernacular domestic architecture throughout the Mediterranean employs the open courtyard as the largest living space. Its boundaries carefully direct information inwards. The same pattern applies to Medieval Islamic Madrassas, Caravanserais, Christian Cloisters, and provides the prototype for the university building surrounding a green or paved yard.

4. Colonnades. Colonnades gave definition to urban space in the ancient world, and continue to do so today in the few remaining street arcades. Regularly spaced columns create a partial enclosure (Figure 2). Note that a colonnade has many more normal contact points than a continuous flat wall, and is thus a far more effective boundary for urban space.

Figure 2. Each column provides one point of contact.

5. Columns and pilasters. The reflectivity of a plane or convex exterior wall is increased by a line of columns in front of it. These could be either whole columns in front, or half-columns in relief on the wall (Figure 3). The former solution is used in ancient Greek façades; the latter in European Medieval and Renaissance architectures.

Figure 3. Embedded columns provide contact points along a flat wall where there would otherwise be none.

6. Fluting on columns. An isolated unfluted column drum presents a convex surface having a single normal line of reflection. Fluting the column turns an originally convex surface into a piecewise concave surface, thus multiplying the contact points (Figure 4). On a larger scale, faceted or flanged minarets utilize the same effect.

Figure 4. Fluting a column multiplies the points of contact.

7. Column clusters. In the engaged pillars of Medieval European cathedrals, a principal column is surrounded with four smaller half-columns. The concavity is improved, which increases the reflectance properties (Figure 5). This solution appears also on the scale of a cylindrical building to break the convexity of an outside wall.

Figure 5. Complex column clusters increase points of contact.

Built examples, looking up from the horizontal
The preceding examples facilitate information access on a horizontal plane parallel to the ground. We also have to consider all the vertical angles subtended between eye level and the total height of a building. In addition to the horizontal solutions, cases are listed now of visual and acoustical contact while a viewer is looking up. (The crucial question of the optimal building height surrounding urban space will not be addressed here). It is remarkable that contemporary architectural styles offer little surface information from any angle higher than the horizontal, yet this feature is hardly ever discussed. This drastic loss of information significantly reduces the urban space in front of such a structure.

1. Horizontal facets and flutes above eye level. In order to scatter light and sound downwards towards an observer, a surface has to reflect in a narrow range of angles in the vertical plane. Horizontal strips or flutes should be defined, oriented at a variety of downward angles (Figure 6). The general pattern leads to architectural features that present vertical lines around eye level, and horizontal lines above eye level. The historical architecture of India, especially the Hindu temple tradition, employs this solution very effectively. Horizontal articulations with strictly orthogonal corners do not achieve the desired signal.

Figure 6. Decomposition of vertical wall into horizontal facets and flutes.

2. Roof edges. With the exception of those in desert climates, buildings historically had protruding roof edges or cornices. Without this edge, the connection of a pedestrian to the building's height is lost. This happened to Louis Sullivan's Carson Pirie Scott building when the roof cornice was removed in the 1950's in an attempt to "modernize" it (Elia, 1996).

3. Roof corners. The roofs on Chinese, Japanese, and Korean temples all curl up at the corners. Overhanging eaves protruding towards the viewer are visually ambiguous, and possibly threatening, whereas corners that point up present surface information from the underside to an approaching pedestrian. This extends the effective signal to a region outside the building.

4. Window lintels. Throughout history, windows used to have a lintel or deep exterior frame that connected visually and acoustically to a viewer outside. Making the windows flush with the exterior wall - as if they were from a "single skin" - removes this essential information, leaving no other point of contact (Figure 7).

Figure 7. Vertical undifferentiated building surface offers no points of contact above eye level.

5. Arches. The magnificent stone carved Romanesque doorways and Seljuk entrances to mosques and caravanserais, and Timurid tiled iwans, are concave elements based on the arch. All of them focus surface information. In our times, the Sidney opera house is an example of an open arched entrance. Arcades on the street level serve the same purpose for an approaching pedestrian.

6. Domes and vaults. From the Pantheon, to the Hagia Sophia, to the tomb of Oljeytu Khan, to Sinan's numerous mosques, great buildings have recreated indoors the amplitude of enclosed outdoor space. Those interior spaces offer us lessons for generating urban space. On a much smaller scale, covered structures offering protection from the weather - either attached, or free-standing - generate a vertical information canopy.

7. Pediments and friezes. Sculptural friezes in Classical Greek and Hindu architectures, and calligraphic relief friezes in Islamic architecture, represent a diffractive area that scatters light in all directions; principally downwards. Quite separate from their artistic and religious value, therefore, they function as visual and acoustical information sources.

Curvature, fractals, and the multiplicity of observers

The above examples describe the signal received by a single observer. It is necessary to consider an entirely distinct matter, which is the total subtended angle for which each solution works. This is equivalent to asking: how many different observers, standing in different locations, will receive information from a particular structure? Clearly, the focus cannot be just onto a single point, because it is likely that other observers will not receive any signal. For this reason, flutes are better than straight facets. Curved surfaces permit a multiplicity of reflection angles, directing a signal towards many different observers. This simple rule explains why traditional exteriors employ curved elements at one or more scales.
Each individual piece need not be concave - indeed, some solutions call for convex elements - yet the overall, piecewise concavity requires a wide variety of spatial differentiations on the smaller and intermediate scales. With enough segmentation, any magnification will show different substructures. This is one definition of a fractal (Batty and Longley, 1994; West and Deering, 1995). Random fractals are indeed generated by the stochastic process of building richly complex, detailed structures to surround urban space. In historical examples, ornament and decoration subdivide building façades on many different scales: the most effective of these create a fractal geometry (Moughtin, Oc et al., 1995). The connection between fractals and hierarchical scaling in architecture is independent of design or style.
Michael Batty and his group (Batty and Longley, 1994; Batty and Xie, 1996), and Pierre Frankhauser (Frankhauser, 1994) prove that successful urban forms are intrinsically fractal. Those results refer primarily to the plan, which shows the large-scale design and path distribution. Nevertheless, the fractal structure extends to architectural elements such as building exteriors surrounding urban space. A far-reaching consequence of enhancing the information field through geometric subdivisions is to endow building façades with fractal scaling, from the size of the buildings all the way down to the microscopic scale in the materials. Successful urban spaces have fractal boundaries (Eilenberger, 1985; Robertson, 1995); just as obvious is that unsuccessful ones have non-fractal boundaries.

Concavity and enclosure

The idea of enclosure is not new. For example, Charles, the Prince of Wales identifies "Enclosure" as one of his "Ten Principles" (Charles Prince of Wales, 1989). He has derived this rule from observing traditional architecture in England, Europe, and the East. Part of his outspoken criticism of contemporary buildings hinges on the fact that they provide no sense of outdoor enclosure, and that open spaces, in particular, are no longer enclosed but are just left over after the buildings are put into place (Moughtin, 1992; Moughtin, Oc et al., 1995). Concavity is more general than enclosure: enclosure is simply concavity at the largest scale. Concavity throughout the scaling hierarchy is essential for defining the spatial information field.
With Pattern No. 106 "Positive Outdoor Space", Christopher Alexander and his colleagues identify the need for concavity and enclosure in open spaces (Alexander, Ishikawa et al., 1977). The result is precisely the one derived here from informational arguments. "A New Theory of Urban Design" (Alexander, Neis et al., 1987) states this in the strongest terms: space for pedestrians, streets, gardens, even parking lots, should be formed by surrounding buildings, not vice-versa. It is the space that is important, and the buildings are the means to define it. Whenever buildings are the focus of attention, space is left undefined. With "The Nature of Order" (Alexander, 1998), Alexander goes further to anchor the urban fabric on a continuous ribbon of public space.
That concave surfaces should bound public space was put forward earlier by Sitte (Collins and Collins, 1986) and by Herman Sörgel (Sörgel, 1918). They argued that all successful spaces have certain geometrical characteristics, which need to be followed in creating new urban spaces (Moughtin, 1992; Moughtin, Oc et al., 1995). Gordon Cullen's book "The Concise Townscape" is widely referred to as having been influential to urban planning since its initial publication in 1961 (Cullen, 1961). The evidence does not support those claims. Much of the built environment of the past forty years could have been humanized by applying Cullen's explicit observation: The typical town is not a pattern of streets but a sequence of spaces created by buildings. It is regrettable that this statement was (and is) ignored by the planning profession.

Materials, texture, and pigments

The materials used in building façades play a crucial role in creating the spatial information field; the surface quality being an independent factor from the geometry. High-tech materials are a necessary component of any new architecture. Of all new materials encompassing a wide range of qualities, however, those favored so far have one feature in common: they minimize surface information. Therefore, one of their principal effects is to diminish information access (as argued in a later section, this is deliberate). If we wish to help the formation of urban space, then we have to start using materials, both old and new, with the aim of enhancing surface information.
Historical buildings employ traditional materials in a way that maximizes optical and acoustical information at all angles: an incident signal is dispersed in all directions so that it can be received by many observers. Surfaces that act in this way have special characteristics. They are: 1. Textured, with articulated relief that reflects signals in different directions; and 2. Painted in bright colors with a high color value close to white. Relief, surface texture, and sculpted decoration reflect sound and light all around (non-specular reflection), whereas pigments absorb an incident ray, then re-radiate the energy in all directions (scattering). The net effect is the same.
Relief patterns throughout traditional architecture distribute sound and light, making a wall partially reflective at an oblique angle. By contrast, smooth polished walls reflect back only at a single normal (orthogonal) angle to their surface. There is no optical contact above eye level (Figure 7). Even worse, a reflective mirror finish prevents all contact because the eye cannot focus on a mirror. (Small mirrors are useful, however, when juxtaposed with matte regions). At the other extreme, very dark colors of any hue, and especially matte black, dark grey and dark brown, absorb all the visual spectrum and don't retransmit anything at any angle. Building exteriors in such colors minimize information access, independently of any surface relief. Bare concrete is usually a matte medium grey, with poor reflective and light scattering properties.
Large panes of plate glass create informational ambiguity: the visual signal indicates a surface, but there is no information. Depending on the angle, dark tinted windows are either too transparent, too reflective, or too absorptive to define a spatial boundary. The only way to reinforce the visual signal is to use a structural frame between window panes; enough of it to provide unambiguous information. This solution worked for centuries, as long as glass could only be produced in relatively small panes. The need for small window panes is noted by Alexander as Pattern No. 239 "Small Panes" in terms of indoors transmitted light (Alexander, Ishikawa et al., 1977), whereas we are concerned here with outdoors reflected light.

PART B. How Information Determines Nodes and Paths

The information field influences the space

The first part of this paper established methods for generating a spatial information field, and argued that it is responsible for defining successful urban space. That relates the information field to the surrounding surfaces. The second part of this paper goes further, and relates the information field to the structure of the open space it permeates. What exists in space in terms of paths and local nodes is in fact determined by the information field. To most readers, this result is surprising, because it implies that one does not need to design open space at all. The "design" is already fixed by the surrounding surfaces; one simply has to discover it. This fundamental result is unfortunately ignored throughout history. In many instances, an open space is "designed", and the result has nothing to do with the information field generated by the surrounding structures.
Each of the two components of urban space (i.e., the built boundary, or the open space) could be good, yet they often don't belong together. That diminishes the ensemble, precisely because each component does not reinforce the other; there is no unity. The best urban spaces rely on this mutual reinforcement, which occurs via the information field. Even some historical urban spaces are weakened by the lack of cohesion between the space and its surrounding structures. At the basis of this problem is a dichotomy between design (which usually implies an imposed order) versus discovery (which represents latent qualities waiting to be brought out). There are at present no guidelines on when to apply each method. We are going to offer some solutions that remedy the situation.

Complementarity of paths and spaces

Inhabitable space defines a three-dimensional volume, which encloses and directs paths of human movement and interaction (Bacon, 1974). At the same time, paths and activity nodes need urban space to surround and protect them. Paths, activity nodes, and spaces reinforce each other in every successful urban region. A graph-theoretic model for connections in the urban web is introduced in (Salingaros, 1998). The path-connective role of urban spaces is a crucial determinant to their success. More than that, however, which paths are actually used is determined by the geometry and information content of urban boundaries. How observers interact with the spatial information field will guarantee their presence in sufficient numbers. That determines, and is in turn determined by, the path structure.
In mathematics, there exist different qualities that are always linked. For example (omitting pathological cases), every object has both mass and volume; every surface has another side; every open line has two endpoints. In the same way, every functioning urban space is anchored on a network of connective paths. This fact has serious implications that are not well known. The paths and nodes forming the urban web - and its complement, urban space - cannot be decided on the basis of a regular plan, because paths follow their own rules (Salingaros, 1998). An overall symmetry helps only if it organizes all the connective elements in a region; it cannot by itself establish paths, but it can damage them. If imposing a rational ordering severs paths, then it destroys urban space.
Treating spaces and paths as an indivisible whole helps to establish the appropriate continuity. Paths do not end suddenly; they crisscross open spaces, and cut through built areas (Salingaros, 1998). Urban space obeys the same topology (connectivity), so it cannot be isolated. Ideally, all the urban spaces in a city should be connected in a giant chain. It is not only the larger, open spaces that comprise urban space; every pedestrian path and node defines a local region of urban space, which can therefore have widely different sizes and widths (Bacon, 1974; Paumier, 1988). Conversely, two regions of urban space are not really connected if they are linked by a space but no paths.

The core of urban space is pedestrian

This is not a paper on pedestrian zones and historical plazas; it describes the total environment between buildings. The core of all urban space is pedestrian, and any structure has to enhance and not disturb this core. Buildings, walls, arcades, and pavements define urban space by generating an information field. Roads, highways, vehicular bridges, and parking lots do not; they should be carefully designed around the pedestrian core, otherwise they will damage it. Those elements enhance urban space by providing the visual excitement of city traffic, as well as the transportation network that feeds into the pedestrian paths. We are not advocating the physical separation of pedestrian from vehicular traffic, but rather their interconnection while carefully protecting the former.
The urban information field generates transient pedestrian nodes by interacting with the observer. One is compelled to stop at certain points where information is either focussed, or is concentrated by the intersection and resonance of different signals (this is impossible while in a car). Such information-induced nodes - representing a momentary, standing stop for a pedestrian - may be fleeting in time, yet their frequency can be enormous. Their importance for urban space is numerically far greater than for fixed nodes such as a bench. The presence of other pedestrians increases the number of temporary nodes by clustering groups of people, and generally forming complex interactions between human beings. Pedestrian flow turns out on closer examination to consist of many rather short paths between temporary pedestrian nodes (Whyte, 1980).
Apart from the interest in the details of the environment that motivate a person to be there, urban space requires the absence of anxiety that comes from two different sources: 1. Ambiguity of the bounding surfaces; and 2. Threat from cars or other vehicles. Either of these creates a negative psychological reaction in the pedestrian, thus invalidating any information which that region might offer. The urban space axioms given at the beginning of this paper lie at the core of environmental psychology. Conceptualization and unencumbered use of space has the prerequisites of firm boundaries, and free movement within those boundaries. This is the concept of "Spielraum" or the space of a favorable environment in child psychology.
It is well known that, under stress from the environment, the human brain "downshifts" into its more primitive part, which does not include higher thinking. In so doing, our perceptual field narrows, and we lose much of our capacity for rational and creative thought. When one is feeling threatened, there is a decrease in the ability to learn. An environment that creates anxiety decreases our intelligence. This is characteristic of poor urban spaces. The human brain is constantly trying to turn sensory data into meaning; looking to organize information into patterns. When it is frustrated by surfaces that have material size, but which do not provide information, the reaction is one of stress.
In only a few places where pedestrians and cars coexist is the pedestrian protected enough for that region to anchor urban space. In most cities and suburbs urban space has shrunk around an unprotected, one meter wide sidewalk, which is chopped up by driveways every few meters (Greenberg, 1995). New stores with old-fashioned façades surrounding a parking lot could have defined urban space, but usually there is none there other than a disconnected sidewalk along the storefronts. This dramatic loss of urban space is partly attributable to the careless mixing of pedestrian paths with vehicular paths. If not handled with great care, car paths (which are stronger elements) will replace pedestrian paths altogether (Salingaros, 1998).

a- The need for physical contact

Any function requiring a pedestrian to stop, even momentarily, defines a node (Salingaros, 1998), which is fixed by some physical structure one can touch. Pedestrian nodes for standing and sitting should provide unambiguous tactile information. Local structures such as arches, niches, columns, bollards, or accessible trees, which offer spots of physical contact, are necessary components of urban space (Gehl, 1987). A combination of touchable wall surfaces and local nodes contributes to the success of a street by establishing contact with a pedestrian (Gehl, 1987; Moughtin, 1992; Moughtin, Oc et al., 1995; Whyte, 1980). The same is true for sitting. The most frequently used plazas also have the most spaces to sit, but ledges and fixed benches are often placed in all the wrong spots (Gehl, 1987; Paumier, 1988; Whyte, 1980) (for an explanation, see below).
Urban space depends just as much on the tactile information provided by local pedestrian nodes - which establish a strong connection to the pedestrian - as it does on the global surroundings. Nowadays, however, even when pedestrian nodes are included in the right places, they are still designed so as to minimize visual and especially tactile information. This defeats their purpose. Contemporary columns, bollards, benches, and seats are built from dull or reflective metal with sharp edges, and stone or concrete in abrupt, simplistic shapes. Huge, smooth concrete planter tubs offer nothing to touch. If the smallest built structures do not generate a rich and complex information field, they are ineffective as local nodes and only clutter urban space.

b- Positioning of pedestrian nodes

Rational ordering often diminishes the functionality of urban space. Boundaries, nodes, and paths combine according to their own rules: this organization cannot be formally imposed. External nodes whose position is determined by extending some building's interior plan outwards will in most cases interfere with the path structure. Buildings only define the spatial boundaries of urban space, and their façades and corners provide points of entry for roads and pedestrian paths. Plazas conceived on the drawing board in abstract geometric terms are often unsuccessful, because they ignore the complexity of all the interacting elements they have to contain. Historical urban spaces - in some cases even monumental ones - have asymmetries that accommodate paths.
There is a correct sequence for determining urban nodes, and it is crucial to their success. Once the buildings are put up, usually within an existing road and path system, one has to judge whether their exteriors provide enough information to support urban space. If at all possible, the pedestrian paths must be re-defined (in most cases, shifted altogether) so as to interact maximally with the information field. One then determines which points are intense enough to benefit from reinforcement, and what is the best way of taking advantage of their position (e.g., by a fixed bench, ledge, canopy, kiosk, or tree; or conversely, by clearing nearby obstructions). These decisions can be taken only on the site itself. The result, viewed on a plan, will bear no relation to decisions that might be taken on the basis of abstract symmetry, which is why the latter (now standard) procedure fails to create urban space.
Ideally, one should start with the space, and put buildings around it. Vegetation and natural features complement and help to define urban space, which can in turn protect them from encroachment by all the other built elements. In his Pattern No. 104 "Site Repair", Alexander proposes saving the most beautiful parts of the land, and placing buildings on those areas that need repair (Alexander, Ishikawa et al., 1977). This approach puts priority on the space, urban or rural, and uses buildings to reinforce the space rather than the opposite. A tree is the largest immobile living object; it has a wonderfully fractal structure, and provides an intense information field at any distance. You have a choice where to put the buildings and roads, but you need a century or more to grow a magnificent tree in a spot that you choose.

c- The indoor shopping mall as urban space

The principles outlined in this paper create a successful urban space indoors. Following the tradition of the great domed buildings of the past, and the enclosed Bazaar - the covered street of stores in the Islamic world - and Milan's 19th century Galleria, an indoor space replaces an outdoor urban space. Mall planners define a piecewise concave surface enclosing a protected pedestrian area full of contrasting detail - both visual and tactile - and potted plants. Part of the information field is generated by the merchandise displayed in shop windows. The rest of the information field is provided by fellow shoppers: one does not usually frequent a mall where there are only a few people.
Despite the phenomenal commercial success of malls, their lessons have still not been grasped well enough to apply elsewhere. In many of today's cities, an indoor mall may be the only urban space in which high-density human interaction is possible in the absence of cars. This proves our points about (a) the need for information and interaction; and (b) the psychological safety of a pedestrian realm. The indoor mall separates urban space from parking, which is free and conveniently near. The only flaw is that the parking lot surrounding the indoor mall isolates it from the web of pedestrian paths outside. This characteristically American pattern is not followed elsewhere in the world, however, where parking may be on top of a mall.

d- Sidewalks, city streets, and street corners

An incredible opportunity to connect the pedestrian to the pavement has been missed all around the world, by using plain, featureless surfaces (even with expensive materials). The standard concrete sidewalk contains no visual information, and anyway, it is far too narrow. Even when brick is used for paving, perceivable patterns are usually avoided. Yet, patterns on the surface of pedestrian paths can make a great difference. Recall, for instance, all the wonderful mosaic and tiled pavements of the Roman world. Among notable historical examples are the pavement of the Piazza San Marco, and the Portuguese architectural tradition of lively sidewalk designs. Some of the most famous modern patterned sidewalks are in Brazil, a former Portuguese colony.
In a very narrow street, which exists only in older cities, the opposite face of buildings can work as a boundary in spite of the car path dividing the space. Trees help to define the outer (curbside) boundary of a sidewalk; planted along a road median, they present a somewhat less effective solution. A sidewalk's inner boundary consists of an architectural edge of building façades and entries. It is essential that no gaps exist in the spatial information field, except for cross-paths that are themselves branching urban spaces. Discontinuities such as vacant lots, open parking, or excessively deep building setbacks violate the first urban space axiom and dissolve urban space (Paumier, 1988). Just as disruptive is a loss of the information field due to a sheer blank wall or mirror façade.
Different types of street corners are matched to their success according to physical form (Moughtin, Oc et al., 1995). The worst is the re-entrant or negative corner, which leaves a gap; of average success is the usual angular or curved corner; while the towered or projecting corner is the best of all types (Moughtin, Oc et al., 1995). This ranking can be explained by the amount of visual information afforded a pedestrian. As one approaches along the street, a plain angular corner gives a minimal definition of the edge, whereas a re-entrant corner gives none. On the other hand, a projecting corner is visible from any point along the street. An example is the projecting rounded-corner bay of Louis Sullivan's Carson, Pirie, Scott department store (Elia, 1996).
The same effect explains the greater success of streets having partial closure at either end. In historical cases, streets rarely broaden out into squares directly; the transition is usually marked by some narrowing structure. This serves as a join between street and square, or between different sections of street, offering visual information to anyone walking along the axis. An arch over a street (now unfortunately forbidden by silly rules) is a useful and powerful boundary for urban space. Ending the street with a façade, as the closing wall of a T junction, provides axial information (Moughtin, 1992; Moughtin, Oc et al., 1995). The same principle helps to break up a long street through the use of bends and monuments placed in round-abouts.

e- Parking lots and strip malls

Many commercial buildings throughout the world allow only car access. Urban space is replaced by a parking lot, yet people still need to get from their car to the building's door. Unless one can park right at the building entrance, this involves finding a temporary, unprotected pedestrian path among parked and moving vehicles. In many parking lots the car paths are also undefined, creating a chaotic, disorganized, and dangerous system. Ironically, some recent strip malls do provide spatial information in old-fashioned building façades (thus satisfying Axiom 1), but violate Axioms 2 and 3. The architectural information is therefore wasted because it is focussed onto a parking lot instead of a region of urban space.
We have to totally re-design parking lots to be urban spaces. One idea is to have covered pedestrian walks protected by a curb from the cars. Now, perversely, we cover the cars and leave the pedestrians out in the open. The less asphalt and concrete, the fewer the problems with water runoff when it rains. The ideal is a garden in which there are paving stones for streets and parking places. Between these, a pedestrian should be able to walk safely, protected both from the cars and from the elements while being visible from almost every point. This last problem - affecting personal safety - is what keeps high-rise or subterranean parking structures from being successful. Intermediate nodes like kiosks inside the parking lot can solidify the network of paths. The author envisions something like an airport corridor open on the sides, possibly with newsstands and snack bars.

PART C. Practices That Weaken Urban Space

Open spaces that are not urban spaces

Plazas develop from the amalgamation of a multitude of overlapping pedestrian paths; the urban space merely shelters and accommodates those existing paths, by providing a protective edge (Salingaros, 1998). This logic has been turned around in recent years, so that now we expect (incorrectly) that an open space, sited in any region we choose, will somehow spontaneously generate the paths that will make it a functioning urban space. Since we have eliminated the pedestrian paths connecting residential with commercial nodes, open space will not function as urban space. Some new plazas are entirely in the open, with no buildings or walls nearby. If they receive no information from the sides, they cannot be urban spaces. A floor design legible only from the air is totally ineffective.
Copying a working urban space from Europe into a contemporary American downtown doesn't work. Not only are there no paths or functional pedestrian nodes, but usually, the surrounding high-rise buildings do not provide the surface information of the old-fashioned façades in the original. They may look the same on a plan, but all the essential elements are different. A separate problem is that even if we mimic pieces of traditional façades, but use materials that minimize the information field, we fail to reproduce the original effect. Contemporary architectural surfaces are sheer and reflecting, and corners are sharp and abrupt; by using contemporary building styles, we can mimic the superficial qualities of an urban space but miss its essence.

Proper and improper uses of lawn

Successful green areas are themselves urban spaces: parks and gardens that are partially surrounded by buildings, walls, hedges, trees, a river, etc. (Alexander, Ishikawa et al., 1977). According to the second urban space axiom, they must be crossed by footpaths to be used (Salingaros, 1998). Planted green areas are revitalizing to people if they can actually touch them, sit in them, and walk through them (Whyte, 1980). Today green areas often serve to fill up left-over pieces on a plan. Buildings and parking lots leave loose odd-shaped areas that are made into lawn, which, however, is off limits to pedestrians. This attitude also shapes our most common contemporary green area - the suburban lawn - which is designed more to be seen than to be experienced.
Vast ornamental lawns with paths that are too long to be functional tend to become desolate wastelands (Salingaros, 1998). On the other hand, a private lawn fronting a house is neither connected to, nor sufficiently isolated from the road. Originally used for sheep and cow pasture in wet climates, the present version is copied from eighteenth century palatial estates. Legally - though not visually, or spatially - it belongs to the house, so neighbors will not step on it. Private front lawns define an ambiguous region without connections or concave boundaries, requiring regular mowing and maintenance for a purely decorative symbol of social status.
From the air, a lawn might appear both as a good boundary, and as urban space, but it is neither. Human beings need vertical boundaries to connect to, yet elements that define urban space don't show on a plan. A wire fence is the opposite of a solid wall with gaps for paths, which is an appropriate boundary element for urban space. Trees, hedges, sections of low wall or a picket fence help to create a private open space by partially closing off the front lawn from the street. The opposite solution - to include the street into a public open space - also works. Children often play in the street and across several open front lawns. It is impossible, however, to define this area as urban space bounded by surrounding houses and trees, when distances between opposite houses are enormous (Gehl, 1987). Also, traffic flow must be reduced; either by paving the enclosed road with stones and gravel, or by using other slowing-down devices (Alexander, Ishikawa et al., 1977; Gehl, 1987).
Pedestrian paths require a building edge to run along (Salingaros, 1998); instead, they are now pushed as far away from a building as possible, right to the edge of the road. By distancing the sidewalk from the house front, a lawn prevents the formation of urban space. A second edge such as a low wall or wooden fence is a poor substitute, but even that is now outlawed by zoning laws in many residential areas. Suburban commercial areas frequently contain pieces of two disconnected, parallel paths: one along some of the store fronts, and another next to the road. This practice splits an already weak path system by interposing strips of lawn and parking lot. Pieces of decorative lawn that define spaces without paths violate Axiom 2.

Non-euclidean geometry and ideal forms

Urban space is not bounded by buildings having a pure, rectilinear form. If buildings stand out as isolated cubic or convex abstract volumes, they cannot act as concave surfaces to define spatial boundaries. The idea of large-scale Platonic solids is fundamentally flawed, since buildings with a regular shape are not actually perceived that way. Architects concentrate on creating exact orthogonal corners and straight lines, yet block buildings do not look straight. Our visual geometry is highly non-Euclidean. The picture we see of our surroundings is comparable to that through a fish-eye lens of short focal length, in which there are no straight lines. Photos of rectangular structures have to be taken from afar, using a perspective-altering lens to straighten edges and make angles appear orthogonal.
Imposing straight edges and pure, flat surfaces on our environment has assumed an unshakable authority in our times, at the expense of human needs and activities. Today, when one proposes breaking the geometry of a grid or rectangle, many people feel something close to terror. There is no logic behind this: it is an emotional reaction resulting from psychological conditioning. We have been taught that modern civilization depends on straight lines. Yet, this is a recent idea reinforced by our schooling and media; an obsession absent from traditional urbanism. It represents an arbitrary style and not a fundamental pattern. By accepting a value system in which rectangular forms and plans have priority over both natural and artificial non-rectilinear structures, our civilization cannot create urban space.

Information provided by:
 http://sphere.math.utsa.edu/sphere/salingar/urbanstructure.html