Christopher Alexander: A City is Not a Tree

21/01/14 11:09 pmChristopher Alexander: A City is not a Tree part 1 | RUDI - Resource for Urban Development International

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Christopher Alexander: A City is not a Tree part 1

CHRISTOPHER ALEXANDERThe tree of my title is not a green tree with leaves. It is the name of an abstract structure. I shallcontrast it with another, more complex abstract structure called a semilattice. In order to relate theseabstract structures to the nature of the city, I must first make a simple distinction.

I want to call those cities which have arisen more or less spontaneously over many, many yearsnatural cities. And I shall call those cities and parts of cities which have been deliberately created bydesigners and planners artificial cities. Siena, Liverpool, Kyoto, Manhattan are examples of naturalcities. Levittown, Chandigarh and the British New Towns are examples of artificial cities.

It is more and more widely recognized today that there is some essential ingredient missing fromartificial cities. When compared with ancient cities that have acquired the patina of life, our modernattempts to create cities artificially are, from a human point of view, entirely unsuccessful.

Both the tree and the semilattice are ways of thinking about how a large collection of many smallsystems goes to make up a large and complex system. More generally, they are both names forstructures of sets.

In order to define such structures, let me first define the concept of a set. A set is a collection ofelements which for some reason we think of as belonging together. Since, as designers, we areconcerned with the physical living city and its physical backbone, we must naturally restrict ourselvesto considering sets which are collections of material elements such as people, blades of grass, cars,molecules, houses, gardens, water pipes, the water molecules in them etc.

When the elements of a set belong together because they co-operate or work together somehow, wecall the set of elements a system.

For example, in Berkeley at the corner of Hearst and Euclid, there is a drugstore, and outside thedrugstore a traffic light. In the entrance to the drugstore there is a newsrack where the day's papersare displayed. When the light is red, people who are waiting to cross the street stand idly by the light;and since they have nothing to do, they look at the papers displayed on the newsrack which they cansee from where they stand. Some of them just read the headlines, others actually buy a paper whilethey wait.

This effect makes the newsrack and the traffic light interactive; the newsrack, the newspapers on it,the money going from people's pockets to the dime slot, the people who stop at the light and readpapers, the traffic light, the electric impulses which make the lights change, and the sidewalk which



the people stand on form a system - they all work together.

From the designer's point of view, the physically unchanging part of this system is of special interest.The newsrack, the traffic light and the sidewalk between them, related as they are, form the fixedpart of the system. It is the unchanging receptacle in which the changing parts of the system - people,newspapers, money and electrical impulses - can work together. I define this fixed part as a unit ofthe city. It derives its coherence as a unit both from the forces which hold its own elements togetherand from the dynamic coherence of the larger living system which includes it as a fixed invariantpart.

Of the many, many fixed concrete subsets of the city which are the receptacles for its systems and cantherefore be thought of as significant physical units, we usually single out a few for specialconsideration. In fact, I claim that whatever picture of the city someone has is defined precisely bythe subsets he sees as units.

Now, a collection of subsets which goes to make up such a picture is not merely an amorphouscollection. Automatically, merely because relationships are established among the subsets once thesubsets are chosen, the collection has a definite structure.

To understand this structure, let us think abstractly for a moment, using numbers as symbols.Instead of talking about the real sets of millions of real particles which occur in the city, let usconsider a simpler structure made of just half a dozen elements. Label these elements 1,2,3,4,5,6. Notincluding the full set [1,2,3,4,5,6], the empty set [-], and the one-element sets [1],[2],[3],C4],[5], [6],there are 56 different subsets we can pick from six elements.

Suppose we now pick out certain of these 56 sets (just as we pick out certain sets and call them unitswhen we form our picture of the city). Let us say, for example, that we pick the following subsets:[123], [34], [45], [234], [345], [12345], [3456].

What are the possible relationships among these sets? Some sets will be entirely part of larger sets, as[34] is part of [345] and [3456]. Some of the sets will overlap, like [123] and [234]. Some of the setswill be disjoint - that is, contain no elements in common like [123] and [45].

diagram A diagram B



We can see these relationships displayed in two ways. In diagram A each set chosen to be a unit has a linedrawn round it. In diagram B the chosen sets are arranged in order of ascending magnitude, so that wheneverone set contains another (as [345] contains [34], there is a vertical path leading from one to the other. For thesake of clarity and visual economy, it is usual to draw lines only between sets which have no further sets and linesbetween them; thus the line between [34] and [345] and the line between [345] and [3456] make it unnecessaryto draw a line between [34] and [3456].

Diagrams A & B redrawn by Nikos Salingaros

As we see from these two representations, the choice of subsets alone endows the collection ofsubsets as a whole with an overall structure. This is the structure which we are concerned with here.When the structure meets certain conditions it is called a semilattice. When it meets other morerestrictive conditions, it is called a tree.

The semilattice axiom goes like this: A collection of sets forms a semilattice if and only if, when twooverlapping sets belong to the collection, the set of elements common to both also belongs to thecollection.

The structure illustrated in diagrams A and B is a semilattice. It satisfies the axiom since, forinstance, [234] and [345] both belong to the collection and their common part, [34], also belongs toit. (As far as the city is concerned, this axiom states merely that wherever two units overlap, the areaof overlap is itself a recognizable entity and hence a unit also. In the case of the drugstore example,one unit consists of newsrack, sidewalk and traffic light. Another unit consists of the drugstore itself,with its entry and the newsrack. The two units overlap in the newsrack. Clearly this area of overlap isitself a recognizable unit and so satisfies the axiom above which defines the characteristics of asemilattice.) The tree axiom states: A collection of sets forms a tree if and only if, for any two setsthat belong to the collection either one is wholly contained in the other, or else they are whollydisjoint.

diagram C diagram D

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The structure illustrated in diagrams C and D is a tree. Since this axiom excludes the possibility of overlappingsets, there is no way in which the semilattice axiom can be violated, so that every tree is a trivially simplesemilattice.

Diagrams A & B redrawn by Nikos Salingaros

However, in this chapter we are not so much concerned with the fact that a tree happens to be asemilattice, but with the difference between trees and those more general semilattices which are nottrees because they do contain overlapping units. We are concerned with the difference betweenstructures in which no overlap occurs, and those structures in which overlap does occur.

It is not merely the overlap which makes the distinction between the two important. Still moreimportant is the fact that the semilattice is potentially a much more complex and subtle structurethan a tree. We may see just how much more complex a semilattice can be than a tree in thefollowing fact: a tree based on 20 elements can contain at most 19 further subsets of the 20, while asemilattice based on the same 20 elements can contain more than 1,000,000 different subsets.

This enormously greater variety is an index of the great structural complexity a semilattice can havewhen compared with the structural simplicity of a tree. It is this lack of structural complexity,characteristic of trees, which is crippling our conceptions of the city.

To demonstrate, let us look at some modern conceptions of the city, each of which I shall show to beessentially a tree.

Figure 1. Columbia, Maryland, Community Research and Development, Inc.:Neighbourhoods,in clusters of five, form 'villages'. Transportation joins thevillages into a new town. The organization is a tree.





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Figure 2. Greenbelt, Maryland, Clarence Stein: This 'garden city' hasbeen broken down into superblocks. Each superblock contains schools,parks and a number of subsidiary groups of houses built around parkinglots. The organization is a tree.

Figure 3. Greater London plan (1943), Abercrombie and Forshaw: Thedrawing depicts the structure conceived by Abercrombie for London. It ismade of a large number of communities, each sharply separated from alladjacent communities. Abercrombie writes, 'The proposal is to emphasizethe identity of the existing communities, to increase their degree ofsegregation, and where necessary to recognize them as separate and definiteentities.' And again, 'The communities themselves consist of a series of sub-units, generally with their own shops and schools, corresponding to theneighbourhood units.' The city is conceived as a tree with two principallevels. The communities are the larger units of the structure; the smallersub-units are neighbourhoods. There are no overlapping units. Thestructure is a tree.

Figure 4. Mesa City, Paolo Soleri: The organic shapes of Mesa City lead us, ata careless glance, to believe that it is a richer structure than our more obviouslyrigid examples. But when we look at it in detail we find precisely the sameprinciple of organization. Take, particularly, the university centre. Here we findthe centre of the city divided into a university and a residential quarter, whichis itself divided into a number of villages (actually apartment towers) for 4000inhabitants, each again subdivided further and surrounded by groups of stillsmaller dwelling units.

Figure 6. Chandigarh (1951), Le Corbusier: The whole city is served by acommercial centre in the middle, linked to the administrative centre at thehead. Two subsidiary elongated commercial cores are strung out along themaior arterial roads, running north-south. Subsidiary to these are furtheradministrative, community and commercial centres, one for each of thecity's 20 sectors.

Figure 7. Brasilia, Lucio Costa: The entire form pivots about the centralaxis, and each of the two halves is served by a single main artery. This mainartery is in turn fed by subsidiary arteries parallel to it. Finally, these arefed by the roads which surround the superbiocks themselves. The structure












is a tree.

Figure 8. Communitas, Percival and Paul Goodman:Communitas is explicitly organized as a tree: it is first divided intofour concentric major zones, the innermost being a commercialcentre, the next a university, the third residential and medical,and the fourth open country. Each of these is further subdivided:the commercial centre is represented as a great cylindricalskyscraper, containing five layers: airport, administration, lightmanufacture, shopping and amusement; and, at the bottom,railroads, buses and mechanical services. The university isdivided into eight sectors comprising natural history, zoos andaquariums, planetarium, science laboratories, plastic arts, musicand drama. The third concentric ring is divided intoneighbourhoods of 4000 people each, not consisting of individualhouses, but of apartment blocks, each of these containingindividual dwelling units. Finally, the open country is divided intothree segments: forest preserves, agriculture and vacation lands.The overall organization is a tree

Figure 9.The most beautiful example of all I have kept until last,because it symbolizes the problem perfectly. It appears inHilberseimer's book The Nature of Cities. He describes the factthat certain Roman towns had their origin as military camps, andthen shows a picture of a modern military encampment as a kindof archetypal form for the city. It is not possible to have astructure which is a clearer tree. The symbol is apt, for, of course,the organization of the army was designed precisely in order tocreate discipline and rigidity. The photograph on the [left] isHilberseimer's own scheme for the commercial area of a citybased on the army camp archetype.

Each of these structures, then, is a tree. Each unit in each tree that I have described, moreover, is thefixed, unchanging residue of some system in the living city (just as a house is the residue of theinteractions between the members of a family, their emotions and their belongings; and a freeway isthe residue of movement and commercial exchange).

However, in every city there are thousands, even millions, of times as many more systems at workwhose physical residue does not appear as a unit in these tree structures. In the worst cases, the unitswhich do appear fail to correspond to any living reality; and the real systems, whose existenceactually makes the city live, have been provided with no physical receptacle.







Neither the Columbia plan nor the Stein plan for example, corresponds to social realities. The physicallayout of the plans, and the way they function suggests a hierarchy of stronger and stronger closedsocial groups, ranging from the whole city down to the family, each formed by associational ties ofdifferent strength.

In a traditional society, if we ask a man to name his best friends and then ask each of these in turn toname their best friends, they will all name each other so that they form a closed group. A village is madeup of a number of separate closed groups of this kind.

But today's social structure is utterly different. If we ask a man to name his friends and then ask them inturn to name their friends, they will all name different people, very likely unknown to the first person;these people would again name others, and so on outwards. There are virtually no closed groups ofpeople in modern society. The reality of today's social structure is thick with overlap - the systems offriends and acquaintances form a semilattice, not a tree (Figure 10).

Christopher ALEXANDER: A city is not a tree© Christopher AlexanderRUDI Classics or Files on...'A City is not a Tree'by Christopher Alexander

Part II

The units of which an artificial city is made up are always organized to form a tree. So that we get areally clear understanding of what this means, and shall better see its implications, let us define atree once again. Whenever we have a tree structure, it means that within this structure no piece ofany unit is ever connected to other units, except through the medium of that unit as a whole.

The enormity of this restriction is difficult to grasp. It is a little as though the members of a familywere not free to make friends outside the family, except when the family as a whole made afriendship.

In simplicity of structure the tree is comparable to the compulsive desire for neatness and order thatinsists the candlesticks on a mantelpiece be perfectly straight and perfectly symmetrical about thecentre. The semilattice, by comparison, is the structure of a complex fabric; it is the structure ofliving things, of great paintings and symphonies.

It must be emphasized, lest the orderly mind shrink in horror from anything that is not clearlyarticulated and categorized in tree form, that the idea of overlap, ambiguity, multiplicity of aspectand the semilattice are not less orderly than the rigid tree, but more so. They represent a thicker,tougher, more subtle and more complex view of structure.

Let us now look at the ways in which the natural, when unconstrained by artificial conceptions,shows itself to be a semilattice.



A major aspect of the city's social structure which a tree can never mirror properly is illustrated byRuth Glass's redevelopment plan for Middlesbrough, England, a city of 200,000 which sherecommends be broken down into 29 separate neighbourhoods. After picking her 29neighbourhoods by determining where the sharpest discontinuities of building type, income and jobtype occur, she asks herself the question: 'If we examine some of the social systems which actuallyexist for the people in such a neighbourhood, do the physical units defined by these various socialsystems all define the same spatial neighbourhood?' Her own answer to this question is no. Each ofthe social systems she examines is a nodal system. It is made of some sort of central node, plus thepeople who use this centre. Specifically she takes elementary schools, secondary schools, youth clubs,adult clubs, post offices, greengrocers and grocers selling sugar. Each of these centres draws its usersfrom a certain spatial area or spatial unit. This spatial unit is the physical residue of the social systemas a whole, and is therefore a unit in the terms of this discussion. The units corresponding todifferent kinds of centres for the single neighbourhood of Waterloo Road are shown in Figure 11.

The hard outline is the boundary of the so-called neighbourhooditself. The white circle stands for the youth club, and the small solidrings stand for areas where its members live. The ringed spot is theadult club, and the homes of its members form the unit marked bydashed boundaries. The white square is the post office, and thedotted line marks the unit which contains its users. The secondaryschool is marked by the spot with a white triangle in it. Togetherwith its pupils, it forms the system marked by the dot-dashed line.

As you can see at once, the different units do not coincide. Yetneither are they disjoint. They overlap.

We cannot get an adequate picture of what Middlesbrough is, or of what it ought to be, in terms of 29large and conveniently integral Chunks called neighbourhoods. When we describe the city in terms ofneighbourhoods, we implicitly assume that the smaller elements within any one of theseneighbourhoods belong together so tightly that they only interact with elements in otherneighbourhoods through the medium of the neighbourhoods to which they themselves belong. RuthGlass herself shows clearly that this is not the case.

Next to Figure 11 are two representations of the Waterlooneighbourhood. For the sake of argument I have broken it into anumber of small areas. Figure 12 shows how these pieces sticktogether in fact, and Figure 13 shows how the redevelopmentplan pretends they stick together.

There is nothing in the nature of the various centres which says that their catchment areas should bethe same. Their natures are different. Therefore the units they define are different. The natural city ofMiddlesbrough was faithful to the semilattice structure of the units. Only in the artificial-treeconception of the city are their natural, proper and necessary overlaps destroyed.








Consider the separation of pedestrians from moving vehicles, a tree concept proposed by LeCorbusier, Louis Kahn and many others. At a very crude level of thought this is obviously a goodidea. Yet the urban taxi can function only because pedestrians and vehicles are not strictly separated.The cruising taxi needs a fast stream of traffic so that it can cover a large area to be sure of finding apassenger. The pedestrian needs to be able to hail the taxi from any point in the pedestrian world,and to be able to get out to any part of the pedestrian world to which he wants to go. The systemwhich contains the taxicabs needs to overlap both the fast vehicular traffic system and the system ofpedestrian circulation. In Manhattan pedestrians and vehicles do share certain parts of the city, andthe necessary overlap is guaranteed (Figure 14).

Another·favourite concept of the CIAM theorists and others is the separation of recreation fromeverything else. This has crystallized in our real cities in the form of playgrounds. The playground,asphalted and fenced in, is nothing but a pictorial acknowledgment of the fact that 'play' exists as anisolated concept in our minds. It has nothing to do with the life of play itself. Few self-respectingchildren will even play in a playground.

Play itself, the play that children practise, goes on somewhere different every day. One day it may beindoors, another day in a friendly gas station, another day down by the river, another day in aderelict building, another day on a construction site which has been abandoned for the weekend.Each of these play activities, and the objects it requires, forms a system. It is not true that thesesystems exist in isolation, cut off from the other systems of the city. The different systems overlapone another, and they overlap many other systems besides. The units, the physical places recognizedas play places, must do the same.

In a natural city this is what happens. Play takes place in a thousand places it fills the interstices ofadult life. As they play, children become full of their surroundings. How can children become filledwith their surroundings in a fenced enclosure! They cannot.

A similar kind of mistake occurs in trees like that of Goodman's Communitas or Soleri's Mesa City,which separate the university from the rest of the city. Again, this has actually been realized in thecommon American form of the isolated campus.

What is the reason for drawing a line in the city so that everything within the boundary is university,and everything outside is nonuniversity? It is conceptually clear. But does it correspond to therealities of university life? Certainly it is not the structure which occurs in nonartificial universitycities.

There are always many systems of activity where university life and city life overlap: pub-crawling,coffee-drinking, the movies, walking from place to place. In some cases whole departments may beactively involved in the life of the city's inhabitants (the hospital-cum-medical school is an example).In Cambridge, a natural city where university and city have grown together gradually, the physicalunits overlap because they are the physical residues of city systems and university systems whichoverlap (Figure 15).





Let us look next at the hierarchy of urban cores realized in Brasilia, Chandigarh, the MARS plan forLondon and, most recently, in the Manhattan Lincoln Center, where various performing arts servingthe population of greater New York have been gathered together to form just one core.

Does a concert hall ask to be next to an opera house? Can the two feed on one another? Will anybodyever visit them both, gluttonously, in a single evening, or even buy tickets from one after going to aperformance in the other? In Vienna, London, Paris, each of the performing arts has found its ownplace, because all are not mixed randomly. Each has created its own familiar section of the city. InManhattan itself, Carnegie Hall and the Metropolitan Opera House were not built side by side. Eachfound its own place, and now creates its own atmosphere. The influence of each overlaps the parts ofthe city which have been made unique to it.

The only reason that these functions have all been brought together in Lincoln Center is that theconcept of performing art links them to one another.

But this tree, and the idea of a single hierarchy of urban cores which is its parent, do not illuminatethe relations between art and city life. They are merely born of the mania every simple-mindedperson has for putting things with the same name into the same basket.

The total separation of work from housing, started by Tony Garnier in his industrial city, thenincorporated in the 1929 Athens Charter, is now found in every artificial city and acceptedeverywhere where zoning is enforced. Is this a sound principle? It is easy to see how bad conditionsat the beginning of the century prompted planners to try to get the dirty factories out of residentialareas. But the separation misses a variety of systems which require, for their sustenance, little partsof both.

Finally, let us examine the subdivision of the city into isolated communities. As we have seen in theAbercrombie plan for London, this is itself a tree structure. The individual community in a greatercity has no reality as a functioning unit. In London, as in any great city, almost no one manages tofind work which suits him near his home. People in one community work in a factory which is verylikely to be in another community.

There are therefore many hundreds of thousands of worker-workplace systems, each consisting ofindividuals plus the factory they work in, which cut across the boundaries defined by Abercrombie'stree. The existence of these units, and their overlapping nature, indicates that the living systems ofLondon form a semilattice. Only in the planner's mind has it become a tree.

The fact that we have so far failed to give this any physical expression has a vital consequence. Asthings are, whenever the worker and his workplace belong to separately administered municipalities,the community which contains the workplace collects huge taxes and has relatively little on which to



spend the tax revenue. The community where the worker lives, if it is mainly residential, collects onlylittle in the way of taxes and yet has great additional burdens on its purse in the form of schools,hospitals, etc. Clearly, to resolve this inequity, the worker-workplace systems must be anchored inphysically recognizable units of the city which can then be taxed.

It might be argued that, even though the individual communities of a great city have no functionalsignificance in the lives of their inhabitants, they are still the most convenient administrative units,and should therefore be left in their present tree organization. However, in the political complexity ofa modern city, even this is suspect.

Edward Banfield, in his book Political Influence, gives a detailed account of the patterns of influenceand control that have actually led to decisions in Chicago. He shows that, although the lines ofadministrative and executive control have a formal structure which is a tree, these formal chains ofinfluence and authority are entirely overshadowed by the ad hoc lines of control which arise naturallyas each new city problem presents itself. These ad hoc lines depend on who is interested in thematter, who has what at stake, who has what favours to trade with whom.

This second structure, which is informal, working within the framework of the first, is what reallycontrols public action. It varies from week to week, even from hour to hour, as one problem replacesanother. Nobody's sphere of influence is entirely under the control of any one superior; each personis under different influences as the problems change. Although the organization chart in the Mayor'soffice is a tree, the actual control and exercise of authority is semilattice-like.

Now, why is it that so many designers have conceived cities as trees when the natural structure is inevery case a semilattice? Have they done so deliberately, in the belief that a tree structure will servethe people of the city better? Or have they done it because they cannot help it, because they aretrapped by a mental habit, perhaps even trapped by the way the mind works - because they cannotencompass the complexity of a semilattice in any convenient mental form, because the mind has anoverwhelming predisposition to see trees wherever it looks and cannot escape the tree conception?

I shall try to convince you that it is for this second reason that trees are being proposed and built ascities - that is, because designers, limited as they must be by the capacity of the mind to formintuitively accessible structures, cannot achieve the complexity of the semilattice in a single mentalact.

Let me begin with an example. Suppose I ask you to remember the following four objects: an orange,a watermelon, a football and a tennis ball. How will you keep them in your mind, in your mind's eye?However you do it, you will do it by grouping them. Some of you will take the two fruits together, theorange and the watermelon, and the two sports balls together, the football and the tennis ball. Thoseof you who tend to think in terms of physical shape may group them differently, taking the two small



spheres together - the orange and the tennis ball and the two large and more egg-shaped objects - thewatermelon and the football. Some of you will be aware of both.

Let us make a diagram of these groupings (Figure 16). Eithergrouping taken by itself is a tree structure. The two together are asemilattice. Now let us try and visualize these groupings in themind's eye. I think you will find that you cannot visualize all foursets simultaneously - because they overlap. You can visualize onepair of sets and then the other, and you can alternate between thetwo pairs extremely fast, so that you may deceive yourself intothinking you can visualize them all together. But in truth, youcannot conceive all four sets at once in a single mental act. Youcannot bring the semilattice structure into a visualizable form fora single mental act. In a single mental act you can only visualize atree.

This is the problem we face as designers. While we are not, perhaps, necessarily occupied with theproblem of total visualization in a single mental act, the principle is still the same. The tree isaccessible mentally and easy to deal with. The semilattice is hard to keep before the mind's eye andtherefore hard to deal with.

It is known today that grouping and categorization are among the most primitive psychologicalprocesses. Modern psychology treats thought as a process of fitting new situations into existing slotsand pigeonholes in the mind. Just as you cannot put a physical thing into more than one physicalpigeonhole at once, so, by analogy, the processes of thought prevent you from putting a mentalconstruct into more than one mental category at once. Study of the origin of these processes suggeststhat they stem essentially from the organism's need to reduce the complexity of its environment byestablishing barriers between the different events that it encounters.

It is for this reason - because the mind's first function is to reduce the ambiguity and overlap in aconfusing situation and because, to this end, it is endowed with a basic intolerance for ambiguity -that structures like the city, which do require overlapping sets within them, are neverthelesspersistently conceived as trees.

The same rigidity dogs even perception of physical patterns. In experiments by Huggins and myselfat Harvard, we showed people patterns whose internal units overlapped, and found that they almostalways invent a way of seeing the patterns as a tree - even when the semilattice view of the patternswould have helped them perform the task of experimentation which was before them.

The most startling proof that people tend to conceive even physical patterns as trees is found in someexperiments of Sir Frederick Bartlett. He showed people a pattern for about a quarter of a secondand then asked them to draw what they had seen. Many people, unable to grasp the full complexityof the pattern they had seen, simplified the patterns by cutting out the overlap. In Figure 17, theoriginal is shown on the left, with two fairly typical redrawn versions to the right of it. In the redrawnversions the circles are separated from the rest; the overlap between triangles and circles disappears.






These experiments suggest strongly that people have an underlying tendency, when faced by acomplex organization, to reorganize it mentally in terms of non-overlapping units. The complexity ofthe semilattice is replaced by the simpler and more easily grasped tree form.

You are no doubt wondering by now what a city looks like which is a semilattice, but not a tree. Imust confess that I cannot yet show you plans or sketches. It is not enough merely to make ademonstration of overlap - the overlap must be the right overlap. This is doubly important because itis so tempting to make plans in which overlap occurs for its own sake. This is essentially what thehigh- density 'life-filled' city plans of recent years do. But overlap alone does not give structure. It canalso give chaos. A garbage can is full of overlap. To have structure, you must have the right overlap,and this is for us almost certainly different from the old overlap which we observe in historic cities.As the relationships between functions change, so the systems which need to overlap in order toreceive these relationships must also change. The recreation of old kinds of overlap will beinappropriate, and chaotic instead of structured.

One can perhaps make the physical consequences of overlap more comprehensible by means of animage. The painting illustrated is a work by Simon Nicholson (Figure 18). The fascination of thispainting lies in the fact that, although constructed of rather few simple triangular elements, theseelements unite in many different ways to form the large units of the painting - in such a way indeedthat, if we make a complete inventory of the perceived units in the painting, we find that eachtriangle enters into four or five completely different kinds of unit, none contained in the others, yetall overlapping in that triangle.

Thus, if we number the triangles and pick out the sets of triangles whichappear as strong visual units, we get the semilattice shown in Figure 19.

Three and 5 form a unit because they work together as a rectangle; 2 and4 because they form a parallelogram; 5 and 6 because they are both darkand pointing the same way; 6 and 7 because one is the ghost of the othershifted sideways; 4 and 7 because they are symmetrical with one another;4 and 6 because they form another rectangle; 4 and 5 because they form asort of Z; 2 and 3 because they form a rather thinner kind of Z; 1 and 7because they are at opposite corners; 1 and 2 because they are a rectangle;3 and 4 because they point the same way as 5 and 6, and form a sort ofoff-centre reflection; 3 and 6 because they enclose 4 and 5; 1 and Sbecause they enclose 2, 3 and 4. I have only listed the units of twotriangles. The larger units are even more complex. The white is morecomplex still and is not even included in the diagram because it is harderto be sure of its elementary pieces.

The painting is significant, not so much because it has overlap in it (many paintings have overlap inthem), but rather because this painting has nothing else in it except overlap. It is only the fact of theoverlap, and the resulting multiplicity of aspects which the forms present, that makes the paintingfascinating. It seems almost as though the painter had made an explicit attempt, as I have done, tosingle out overlap as a vital generator of structure.

All the artificial cities I have described have the structure of a tree rather than the semilattice






structure of the Nicholson painting. Yet it is the painting, and other images like it, which must be ourvehicles for thought. And when we wish to be precise, the semilattice, being part of a large branch ofmodern mathematics, is a powerfu1 way of exploring the structure of these images. It is thesemilattice we must look for, not the tree.

When we think in terms of trees we are trading the humanity and richness of the living city for aconceptual simplicity which benefits only designers, planners, administrators and developers. Everytime a piece of a city is torn out, and a tree made to replace the semilattice that was there before, thecity takes a further step toward dissociation.

In any organized object, extreme compartmentalization and the dissociation of internal elements arethe first signs of coming destruction. In a society, dissociation is anarchy. In a Person, dissociation isthe mark of schizophrenia and impending suicide. An ominous example of city-wide dissociation isthe separation of retired people from the rest of urban life, caused by the growth of desert cities forthe old like Sun City, Arizona. This separation isonly possible under the influence of treelike thought.

It not only takes from the young the company of those who have lived long, but worse, it causes thesame rift inside each individual life. As you pass into Sun City, and into old age, your ties with yourown past will be unacknowledged, lost and therefore broken. Your youth will no longer be alive inyour old age - the two will be dissociated; your own life will be cut in two.

For the human mind, the tree is the easiest vehicle for complex thoughts. But the city is not, cannotand must not be a tree. The city is a receptacle for life. If the receptacle severs the overlap of thestrands of life within it, because it is a tree, it will be like a bowl full of razor blades on edge, ready tocut up whatever is entrusted to it. In such a receptacle life will be cut to pieces. If we make citieswhich are trees, they will cut our life within to pieces.

Originally published in:Architectural Forum, Vol 122, No 1, April 1965, pp 58-62 (Part I),Vol 122, No 2, May 1965, pp 58-62 (Part II)

Also published in :Design, No 206, February 1966, pp46-55Ekistics, Vol 23, pp 344 - 348, June 1967Bell, G & Tyrwhitt, J(eds) Human Identity in the Urban Environment, Harmondsworth, UK,Penguin Books, 1972

This version taken from:Thackara, J. (ed.) (1988), Design After Modernism: Beyond the Object, Thames and Hudson,



London, pp. 67-84.

Christopher ALEXANDER: A city is not a tree© Christopher Alexander

A critique of design theory and method as presently applied to city design

[This article was originally published under the title 'If the City is not a Tree, nor is it a System' in Planning Outlook New Series, Volume Sixteen, Spring 1975, pp 4 -18]

Most people seem to agree that modern cities are pretty awful. We can be persuaded to enjoy aspectsof them, such as thrilling new structures which win design awards, or the feeling of movement onnew communication systems, but most of the time they are just plain boring, dull, and tawdry; tingedwith a sense of 'welfare' that it's all we can afford. Wherever one goes one sees the same standardanswers; stereotyped housing blocks, neat soulless shopping centres, or schools, fire stations orchurches (which might be interchangeable), and standard amounts of 'public open space' (ugh!). Atthe centre of the city there is more standard kit - television mast, faceless tower and slab blocks, andregulation neon signs (when there's electricity) to whoop it up a bit.

Critics, casting around for people to blame latch on to the planner as the villain. He's unimaginative.His thinking is stuck in a rut of neighbourhoods, zoning, densities, and plot ratios. His view of thecity is far too simplistic for such a complex machine. We must match the complexity of the city withmore complex multi-purpose and intricate development, so we try complex schemes - and whathappens? Despite a plethora of ideas and conferences, despite a great deal of endeavour andarchitectural ingenuity, the plans and sketches which seem to show such high promise turn out to beyet another collection of pedestrian bridges, car park ramps, and plastic paving surroundinganonymous building blocks. We still seem unable to match the life and liveliness of 'real cities'.

Consequently critics have turned their attention to querying the planner's method of operation whichrequires him to make such assumptions. The problem, they suggest, is not that city planners areinherently simplistic but that the design process they operate forces them to make simplisticassumptions. For example Christopher Alexander (1966) argues that much of people's dissatisfactionwith the modern city stems from their artificial organisation into hierarchical groupings of facilitieswhich, he suggests, are based not on the way people use the city, but on the way designers conceivethe process of design and apply it to the design of a city. Similarly, Maurice Ash (1969) condemnstown planners for what he regards as their attempt to organise people and facilities into idealisedpatterns based on what he asserts is an unproven theory of settlement hierarchy. Like Ash, MelvinWebber (1968/69) argues that the philosophy of town planning is not founded on social realities.Instead, he suggests, city planners have defined their problems and solutions in idealised terms



because they adopted the design style of the parent professions of engineering and architecture, andtherefore adopted their design assumptions.

What is design? What are its assumptions?

Herbert Simon (1969) has called design the 'science of the artificial' because it is an artificial creationto catalyse the requirements of man with those of his environment. It can be defined as the orderingof relations between components in order to satisfy predetermined objectives. As a process it canonly start when the problem has been defined in terms of objectives to be satisfied; that is when thevarious aspects or component parts of the problem which together need satisfying have beenidentified. The solution represents a synthesis which should satisfy the requirements of eachcomponent and the problem as a whole. It is this process of synthesis that I would define as Design: aprocess in which the designer is an innovator, an inventor of solutions.

Investigations into the way designers design show that they go through a series of definite stages.The first is concerned with clarifying the problem by breaking it down into its component parts orfunctions and identifying their requirements. The second is to gather 'like' components together into'sets' (i.e. collections of elements which are thought to have something in common). The third stageis to link those components which work together into a system (i.e. a set of components which arelinked together in order to perform a function). The aim is to create what Alexander calls 'good fit'

between problem and solution.1

For example, imagine designing a house. You break it down into the kind of rooms, or better stillactivities, which are required, such as sleeping, cooking, sitting etc. [fig. 1]. You analyse thoseactivities which have common or related features (for instance requiring service) and group them assets [fig. 2]. Then you link those components which require inter-connection (e.g. cooking to eating)into a system [fig. 3]. Structuring the solutions you try to satisfy the known wants and functionsinvolved, by making enough space for the different activities to be accommodated; trying to ensurethat those activities which are most linked are put in the closest relationship. But no matter howobjective you attempt to be your image or idea of how each part, and the whole, might function, lookand feel will also greatly influence any solution you propose. Consequently, although the designprocess must attempt to be objective, in most cases it will also reflect the designer's own philosophy

and values. You can only put forward solutions which you think are satisfactory.2

Examining the design process, the fundamental point emerges that designers create systems. Of allthe stages in the design process this is the one where he uses his expertise - this is what the clientpays for. Whereas the client should be concerned with helping to define the various parts of theproblem, and possibly their grouping into sets, the designer is responsible for ordering therelationships in the system, or between systems and sub-systems, to satisfy functional and aesthetic

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requirements. The links which make the system are designed to maintain equilibrium between thecomponents, future change being controlled by the links. Consequently, the designer is in a verypowerful position. He is creating frameworks relative to the way he thinks they should be. When hecreates a system he is not only providing opportunities, but also constraints. His design will stabilisea set of relationships allowing only changes acceptable to the structure. Consequently he must besure that the relationships he sees are valid, and the links he creates are needed. Identification of aset does not automatically make it a system; it is the links that create the system.

Summarising, the design process would seem to rest on four assumptions:

1. That the problem can be defined, in terms of agreeable objectives.2. That the components can be isolated and their requirements analysed.3. That there is a 'best-fit' relationship.4. That the end product can be achieved in reality, because design takes account

of the variables in the control of the designer and client.

Thus in engineering and architecture the aim is to produce an artifact which satisfies a client's knownrequirements. The operational style assumes that a client's requirements can be identified andarranged into a rational ordered solution to satisfy agreed objectives. Although the design can havebuilt-in 'flexibility' there is an overriding assumption of stability, such that there are ascertainableand agreeable goals based on common values (held by client and designer); that any change will like-wise conform to existing values; that a 'best-fit' arrangement can be found to meet these goals andthat controls can be agreed which will allow the plan to be implemented.

The application of design principles in town planning

Although the assumptions underlying design would seem questionable if applied to city planning,their application by city planners is clearly seen in many recent planning reports particularly for NewTowns and new Cities. For example, consider the report for the new city in Central Lancashire (for

which a Development Corporation was appointed early in 1971).3

In that study an attempt is made to identify all the facilities that the population will require in a'large' city, and economic levels of provision are ascribed to each facility based on populationthresholds [fig. 4]. Facilities are then grouped into sets, which create a hierarchy of 'communities'[fig. 4].

play areadoctors surgerypublic house



corner shopnursery schoolcrecheprimary schoolmeeting roomplaygroundcafepost officeclinicprotestantchurchbranch libraryhealth centrecatholic churchpublic parkindustrial estatebankarts centresecondary schoolassembly hallrestaurantmarkethotelsports centregpocentral librarytown hallswimming poolgolf course

dance hallcinemavariety storesnight clubmuseumbowling alleytechnical collegecoll, of arts & craftsregional parkzooart gallerylaw courtstheatrebotanical gardensspecialised shopsconcert hallreference librarycounty admin. officessports stadiumindust. retrainingcentrepolytechnic

Fig. 4 Facilities relative to population thresholds (Central Lancashire: Study for a City)Each grouping is assumed to work as a system and becomes a sub-system in a city wide system,which is itself organised for ease of traffic movement [fig.6]. The assumption is that a city can berationalised on the basis of the provision of economic facilities and movement patterns to thosefacilities [fig.7], that people move to their nearest centre providing the particular facilities theyrequire, and that facilities having similar economic thresholds are best located in areas havingcongruent boundaries. Functions and movement are brought into a 'best-fit' relationship based onassumed likely behaviour patterns, as in any other engineering or architectural product. The city hasbeen treated as if it were a system and designed as such. The plan is presented as an aesthetically andmathematically coherent solution to the problem of designing a city and all its major functions.

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3 Township

2 District

1 Neighbourhood

Like the architect and engineer, the city planner has designed his plans around the assumed needs ofhis client, in this case the people (sic. 'Planning is for People'), ordering and arranging the variousfacilities in locations and groups thought to be best suited to the clients' demands. The city has beentreated as an artifact, so that, even though it is ostensibly designed for growth and change, growth isassumed to take place in roughly equi-size units up to some finite level, each phase being regarded asa rationally planned unit and taking its place within the ordering framework of the whole city system.As Alexander has shown, this approach, whereby the city is designed as 'a tree' [fig. 8] in which allfacilities are treated as subsystems having an hierarchically ordered relationship within a single

system, is a common to the design of new cities throughout the world.4

Dispersal Movement Pattern

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Fig. 7 Assumed transport modes to facilities (Central Lancashire: Study fora City)The planner, like the architect and the engineer, has assumed that similar functions serving similarneeds can be grouped, and that these groupings and arrangements reflect generally agreed forms ofsocial organisation and social objectives. But can there be generally agreed forms of socialorganisation or social objectives except at the most abstract level? It is really possible to list thepeople's requirements except at the most minimum or basic level? Is it valid to assume that theagencies who provide for the multiplicity of people's requirements can be expected to conform tosome overall pattern based on assumed optimum standards of provision, which once achieved willhold good for the foreseeable future?

Criticism of Planners' design approach

Here then is the nub of the criticism. Because the city planner adopted the operational style of theengineer and architect, he was forced to work on similar assumptions; that he was producing anartifact representing the known requirements of 'the people', that these could be identified and onceidentified would remain relatively stable, and that there was some rational arrangement of the citywhich would be satisfactory not only for the present but also for the future. As Webber suggests, thecity planner adopted the assumptions of the engineer designing public works including:

1. That social organisation and social objectives will remain stable during thetime period under review;

2. that there is a society wide consensus on city development goals;3. that these goals are stable, future goals will be like present goals and that they

are knowable by professionals."5

Furthermore the adoption of the architectural / engineering design style assumed the need for asimilar approach to implementation, whereby "the sorts of deliberate outcomes accomplished in the



centralised decision setting of engineer client relationship, or centrally controlled government

enterprise" could be extended to the market place.6 In place of the 'real world' of multipleownerships and multiple power, an 'ideal world' was required where the planner could play the roleof designer for the people, represented by a statutory authority, knowing that his plan could beimplemented. As Webber points out, the planners produced a remarkably inventive set of controls -the technical standard (providing minimum levels of quality), the master plan (setting forth overallsystem design) and the land use regulation (which constrained the locational decisions of individualestablishments). But these methods only allow the 'negative' controls of stopping 'unsatisfactory'development.

In Britain the Government went further by providing powers which allowed 'creative' planning - theComprehensive Development Area (1944) and the New Town (1946), and subsidised local authorityhousing (1919). In each case the relevant authority could draw up plans and, through its powers ofland ownership and finance, could implement its proposals. The trouble is that almost all 'creative'planning has been used for the poorer sections of the community, particularly through the use ofsubsidised housing for estate development and comprehensive redevelopment of slum areas, and foroverspill to New Towns and Town Expansion schemes. The better off, including those who were onceworse off but have joined the 'private sector', can afford to move out of the clutches of the 'creative'planner with his concepts of rationally ordered communities. The car-borne mother doesn't have tomove where the Gravity Model suggests she should go - the bus-borne mother has no choice!

Thus critics are suggesting that the stereotyped planned environment is not so much a product ofpoor imagination on the part of city planners, as a product of the idea of designing cities as if theywere a public works artifact. As a consequence of centralised design, instead of catering for thevariety of people's aspirations, there has been a tendency to reduce people's needs to formalisticmodels where the quality of life and environment which comes from individual innovation issqueezed out in order to safeguard 'the public interest'. The city planners' admirable desire to ensurethat people have a satisfactory minimum of facilities far too often seems to produce stereotypedresults where minima become maxima. All too often it is for one class of society: what Maurice Ash

calls 'an alliance with poverty'.7 The idea that the city can be designed as a coherent system made upof a rational arrangement of subsystems is a static concept. The pursuit of city wide equilibrium forwhatever high ideals, will result in its stagnation, decline and eventual death.

The design of cities

How then should city planners approach the design of cities? Should they drop thearchitect/engineering design style, as implied by Webber, and concentrate on social and economicpolicy? Should they seek to design more complex city structures like the semi-lattic advocated byAlexander?



Whatever the objectives of city planning should be, I do not think we can find another design style(like Bruce Archer, I believe that "the logical act of designing is largely independent of the thing

designed"8). Nor do I believe it is possible to 'design in' complexity or deliberately create semi-lattices; for as Alexander has shown (1966) design is inherently concerned with rationalisation andsimplification of the parts of the problem into a hierarchical arrangement. So if we can only design inone way, and we cannot design complexity, how can we create complex satisfying cities?

I believe the answer lies in a paradox set by Peter Levin in his paper 'Decision making in UrbanDesign' (1966). He suggested "perhaps it is a valid aim to try deliberately to achieve a situation inwhich the functioning of the system is as independent as possible of the design. The design, in other

words, should have the minimum effect on human organisation and activities."9 But, as we have seendesigners derive their designs from the functioning of the system. Furthermore I don't think you candesign a system unrelated to its function. Thus the paradox: but only a paradox so long as the city isregarded as a system.

The city is not a system

Looked at from the viewpoint of its development and operation, the city is not a single system.Rather it is a multiplicity of systems under the control of a multiplicity of agencies. These agencies,both public and private, provide and operate facilities [fig. 9] and both the agencies' attitude toprovision and the people's demand for provision is subject to change. Some facilities will grow andothers will die without the city planner having much say. Consequently, although he may attempt todesign his city plans on the basis of linkages between activity systems, and the use the people makeof them, he cannot implement and maintain his plan unless he has autocratic powers to stabilise theworld he has attempted to create. Without autocratic powers, which I am sure few people will beprepared to accord, the city planner is wasting his time designing the city as a system. As MargaretWillis has suggested "the narrow and restricted approach of what is primarily a physical plan, andthat is devised for the most part independently of the agencies that actually build and administer a

town shows the limitation of this type of planning in trying to meet social realities".10 She quotesProfessor Peter Wilmot, ". . . If city planning is to respect social criteria, it must increasingly enable

the design to work",11 that is work through the agencies which develop and operate the city. As theseagencies cannot be welded and subsumed within a single comprehensive system, the city is betterregarded as a set of semi-independent systems with each agency responsible for the design andpositive direction of its own system [fig. 10].

Examples ofAgencies :

1. Education



Committee2. WelfareCommittee3. Ind Coope4. Express Dairy5. Water Board6. Bus Company

Fig. 9. Examples ofAgencieswhich 'develop' a city

Fig.10 The city a number of separate system basedon agencies

Although this might appear as an advocation of 'non-plan', it is not. Rather it is a plea for designbeing applied only where it is valid. The areas each agency controls are only semi-independent [fig.11]. To the extent they do not affect other activity areas they should be free to plan and developthemselves. To the extent they are linked to others they should be subject to supra-planning. Almostall activity systems are linked to others, albeit in a transient fashion, through policies for land and theinfrastructure which serves it. These links provide the framework of constraints and opportunitieswithin which the multifarious agencies work. The design of plans and policies for these links (the

'public' area as opposed to the 'private' area of an agency's own sphere) is the city planner's field'12

[fig. 12].

Fig.11 Interrelationship ofsystems: 'Public' and 'Private'space

Fig.12 Planners design and control theoverlap between systems -The 'Publicspace'.

It is a more limited area than he attempts to design at present, but it is none the less positive. Thecity planner can continue to manage and control the spatial organisation distribution, arrangementand visual quality of land use through his development control powers over links between activitysystems. He should be concerned with the positive design of public areas and resources as aframework for semi-independent agencies.



Given that each agency will create a rational design solution to its own problem but would no longerbe subject to some supra-rationality of how the various activities should best fit together, complexitywould be created in the way it occurs in normal cities. Instead of the city being cut up in discreetneighbourhoods around centres with congruent catchment areas for each activity system, eachactivity system would arrange itself to suit its own demands. Alexander's 'semi-lattice' would resultfrom activity systems solving their problems in their way. Levin suggests that making the function ofthe city independent of overall design should provide freedom and choice: "A choice of nearbyschools for a child, a choice of convenient shops for a housewife, a choice of nearby friends to call on

in an emergency, and a choice of routes to work."13 As he suggests this might involve some over-provision of facilities (an anathema to the city planner?), but surely that would be no bad thing forthe consumer. We might actually get away from the stereotyped standardised world that seems theonly end product available from present city design.

I believe that 'Planning is for People' is in fact a static and paternalistic concept which serves toreduce the quality of life and the environment in which it is lived. City Planning must provide theopportunity for people to enhance their own lives. Andrew Kopkind quoted Catherine Bauer assaying "the worst kind of dictatorship is the kind that gives people what they want, the kind in whichyou can't tell you're being controlled." As he comments, "if that is one of the possible futures it is too

important to be left only to the planners."14

REFERENCES1 See Christopher Alexander 'Notes on the Synthesis of Form'.

2 In the introduction to Design Methods in Architecture. Anthony Ward queries the 'objective'approach to design which suggests that the nature of design is independent of the thing designed andsuggests that perhaps the way a designer goes about designing something does affect the thing that isdesigned (p. 12). He suggests that "if we are to contribute significantly to the development of designmethod, we have no alternative but to make explicit the philosophical premises upon which we baseour conclusions. Otherwise the logical nature of our task will remain impenetrable." This suggeststhe beginning of an acceptance by the architectural design theorists that the designer cannot bewholly objective; that there is a place for the subjective as preached by one of the foremostArchitectural theorists, Goodhart-Rendall, in the 1930's: "Many modern theorists of architecture, byrefusing to let the (design) process disappear from sight, have observed with dismay or neglected toobserve that there is then no architecture at the end of it." Goodhart-Rendell (1934). This all echoesthe plea of the German philosopher Karl Mannheim (1966) for designers and decision makers to bemore self aware and thus gain greater freedom.



3 Robert Matthew, Johnson-Marshall and Partners: Central Lancashire, Study for a City. 1964.

4 Christopher Alexander: A City is not a Tree. 1966.

5 Melvin Webber: Planning in an Environment of Change Part I, Town Planning Review October1968, p. 192.

6 ibid. Part II January 1969, p. 284.

7 Maurice Ash: Regions of Tomorrow 1964.

8 Bruce Archer: The Structure of the Design Process in 'Design Methods in Architecture' (ed. A.Ward and G. Broadbent, AA Paper No. 4 1969).

9 Peter Levin: Decision Making in Urban Design B.R.S. 1966, p.11.

10 Margaret Willis: Sociological Aspects of Urban Structure Town Planning Review, January 1969,p. 305.

11 Peter Wilmot: Social Research & New Communities Journal of the American Institute of PlannersNov. 1967.

12 See Fumihiko Maki: Linkage in Collective Form in 'Investigations in Collective Form' 1964. AlsoJane Jacobs: Death and Life of Great American Cities (1961).

13 Peter Levin: op. cit. p. 11.

14 Andrew Kopkind: 'The Future Planners' in 'America the Mixed Curse' 1969.

Figures 4, 5, 6 and 7 are based on diagrams from 'Central Lancashire, Study for a City' (1967) and arepublished by kind permission of RMJM (formerly Robert Matthew, Johnson-Marshall andPartners).

Selected BibliographyALEXANDER, CHRISTOPHER A City is not a Tree in Human Identity in the Urban Environment (ed. Bell & Tyrwhitt). Penguin,1973

Notes on the Synthesis of Form; Harvard University Press, 1964

ASH, MAURICERegions of Tomorrow. Evelyn Adams & Mackay, 1969.

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GOODHART-RENDELL, L Fine Art. Clarendon Press, 1934

JACOBS, JANEDeath & Life of Great American Cities. Penguin, 1973.

LEVIN, PETERDecision Making in Urban Design. Building Research Station Design Series No.49, 1966.

MAKI, FUMIHIKOInvestigations in Collective Form. Washington State University. 1964.

MANNHEIM, KARLIdeology & Utopia. Routledge, 1966

MINISTRY OF HOUSING AND LOCAL GOVERNMENTCentral Lancashire: Study for a City. HMSO, 1967.

SIMON, HERBERTThe Sciences of the Artificial. M.I.T., 1969.

WARD, A. and BROADBENT, G.Design Methods in Architecture. Architectural Association Paper No.4, Lund Humphries, 1969.

WEBBER, MELVINPlanning in an Environment of Change. Town Planning Review, October 1968 and January 1969.

WILLIS, MARGARETSociological Aspects of' Urban Structure. Town Planning Review, January 1969.

John Minett presently practices urban design in Phoenix, Arizona, USA. Here he spends much of histime promoting the concept of 'Sociable Cities': places where multi-modal streets supportcommunity, traffic is calm, parking is civilized, and places are friendly for pedestrians and bicyclists.It is the antithesis of Auto City which is still the dominant paradigm of the USA. To read more see hisnew web site www.sociablecity.net (under construction). This article in RUDI was written in the1970's when he was a lecturer at the School of Planning in Oxford, England. The concept thatunderlies it continues to underpin his attitude to city planning, and has influenced much of his workand writings since.

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John Minett. As the city is not a tree...it should not be designed as a system © John Minett .

Nikos A. Salingaros,Division of MathematicsUniversity of Texas at San AntonioSan Antonio, Texas 78249

Abstract. Scientific principles applied to city form help to understand the role of various types ofurban connectivity. The degree of "life" in a city or region of a city is tied to the complexity of visual,geometrical, and path connections. There is an optimal distribution of connection lengths in a livingcity, and violating this distribution removes life from the urban environment. Alternativeparcellations of a living city reveal the complex structure that is required to generate human contact,which is the basis for city life. These results are compared to the work of Christopher Alexander.

Dr. Nikos A. Salingaros is Professor of Mathematics at the University of Texas at San Antonio, has aPh. D. in theoretical physics from the State University of New York at Stony Brook, and has madecontributions to mathematical physics, field theory, and thermonuclear fusion. He is the author ofmore than seventy scientific publications, and has served as associate editor for two journals, andreferees for fourteen others.

Since 1983, he has been learning from and working with architectural theorist ChristopherAlexander. This interaction has inspired an entirely new direction of research, which usesmathematics to describe aspects of nature that are traditionally regarded as being in the domain ofart. These phenomena have so far eluded a scientific explanation. Dr. Salingaros is applying insightsgained from complex physical systems to architecture and urbanism. His latest publications combineideas from complexity theory, fractals, and thermodynamics to develop a mathematical theory ofstructural form. The same ideas apply to architecture as well as to other complex systems, be theyurban regions or biological organisms. From this work, a new picture of urban and architectural formemerges; one that is more consistent with natural structures. As a result, it is now possible to connectmathematically the built environment with the natural environment.

More information is available from Dr. Salingaros' homepage.

© Nikos Saligaros

All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem or transmitted in any form or by any means, electronic, mechanical, photocopying,

mailto:[email protected]

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recording or otherwise, without the prior written permission of the publishers.

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Christopher Alexander: A City is Not a Tree

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