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Why are architects interested in graph theory?. . Creating successful buildings
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Nick S Dalton
sdalton@cs.ucl.ac.uk Im an Engineer/Appropriate Technologist turned computer Scientist. I work between the Bartlett School of Architecture and Planning - the only of the Five star rated architectural school.
Im really here to listen as much as I can. The space syntax group has been doing graph theory for a long time but its quite insular and I wanted to make links back out into main stream network theroy. Its quite an exitiing period but I think there is a lot which space syntax has done which might be of intreast and in this case I think there are lots of more mathematical ideas which can be brought kicking and screaming back into space syntax.
Im an Engineer/Appropriate Technologist turned computer Scientist. I work between the Bartlett School of Architecture and Planning - the only of the Five star rated architectural school.
Im really here to listen as much as I can. The space syntax group has been doing graph theory for a long time but its quite insular and I wanted to make links back out into main stream network theroy. Its quite an exitiing period but I think there is a lot which space syntax has done which might be of intreast and in this case I think there are lots of more mathematical ideas which can be brought kicking and screaming back into space syntax.
3. Creating successful buildings & urban spaces Architects are interested both in the internal operation of buildings and the external operation. Most of the matrial function (heat,lighting,structure) has been handed over to the realm of engineering but its the interaction between sociaty,the intervidual and the build form which you might say is at the heart of pure architectural research.
I must also say for architects we are quite unique - we take a more formal approach. Architecture is the overlap between science and art and so you get a bluring between scientific study and art theory.Architects are interested both in the internal operation of buildings and the external operation. Most of the matrial function (heat,lighting,structure) has been handed over to the realm of engineering but its the interaction between sociaty,the intervidual and the build form which you might say is at the heart of pure architectural research.
I must also say for architects we are quite unique - we take a more formal approach. Architecture is the overlap between science and art and so you get a bluring between scientific study and art theory.
4. Building level
Stopping/meeting behavior
How creative environments work (research laboratories, Media)
Interaction and information flow through an organization
Navigation wayfinding (hospitals/airports)
5. Urban level Interested in pedestrian movement
Passing trade important for retail
Relationship between space, design and crime
Avoiding nightmare projects (Oxford Leys, Docklands)
Archeologists interested in historic function
Conversly Conversly
6. Questions Despite the high value of village properties and many attempts. Developers seem incapable of creating a village feel.
Yet historic villages themselves where created by people ignorant of urban design. Today we would say that the vernacular village is the result of a self organising process. Today we would say that the vernacular village is the result of a self organising process.
7. Work began in the late 70s and culinates in thei book - the social Logic of space. Most of what I am talking about is referaned out of this book. Work began in the late 70s and culinates in thei book - the social Logic of space. Most of what I am talking about is referaned out of this book.
8. Process Buildings
Derive maps of discrete space
(space==node)
Where spaces intersect create link
(link == edge)
Build measures of structure of graph
Visualize the results back on the space map
10. We can use this simple technique to show how culture manifests itself in the layout of space. For example we can analyse house plans in terms of the shape of justified graphs from rooms with different functions So now I can begin to start translating - Total depth is now called Cumulative Path length. So now I can begin to start translating - Total depth is now called Cumulative Path length.
11. networks of domestic spaces And colour the results up so we can see see that different functions have different degree of integration into the layout as a whole
12. Are these buildings similar? If we then find that across a sample that the various functions have similar configurational positions, and function have the same order of integration, even when the geometry of the house is difference, we see evidence of culture manifesting itself in the spatial layout, and we can test this statistically. So by defining space in terms of how all other spaces relate to it, and how it relates to all others, we can find a clear and culturally variable spatial meaning to the idea of function.If we then find that across a sample that the various functions have similar configurational positions, and function have the same order of integration, even when the geometry of the house is difference, we see evidence of culture manifesting itself in the spatial layout, and we can test this statistically. So by defining space in terms of how all other spaces relate to it, and how it relates to all others, we can find a clear and culturally variable spatial meaning to the idea of function.
13. If we then find that across a sample that the various functions have similar configurational positions, and function have the same order of integration, even when the geometry of the house is difference, we see evidence of culture manifesting itself in the spatial layout, and we can test this statistically. So by defining space in terms of how all other spaces relate to it, and how it relates to all others, we can find a clear and culturally variable spatial meaning to the idea of function.If we then find that across a sample that the various functions have similar configurational positions, and function have the same order of integration, even when the geometry of the house is difference, we see evidence of culture manifesting itself in the spatial layout, and we can test this statistically. So by defining space in terms of how all other spaces relate to it, and how it relates to all others, we can find a clear and culturally variable spatial meaning to the idea of function.
14. Axial Lines
15. The axial network
16. A Beady Ring Settlement
17.
18. Line Representation of Spatial Configuration
19. Axial Lines
20. Justified Graphs
21. Axial Integration Map
22. Oxford Axial map (out of date)
23. Central Oxford (out of date)
25. Central Oxford (out of date)
26. images of London
27. Observing of patterns of movement
28. The results show that nearly 60% of the differences in pedestrian movement rates, and over 70% of those in vehicular movement rates are related to the pattern of the urban grid. This is very surprising, since no one previously thought the grid itself might affect movement. But because movement is so vital in cities, we can again use this as a design aid, by modelling the context of a site, checking against real movement, and re-analysing with designs inserted, also drawing design ideas from strong potential lines shown by the analysis of the area.
The results show that nearly 60% of the differences in pedestrian movement rates, and over 70% of those in vehicular movement rates are related to the pattern of the urban grid. This is very surprising, since no one previously thought the grid itself might affect movement. But because movement is so vital in cities, we can again use this as a design aid, by modelling the context of a site, checking against real movement, and re-analysing with designs inserted, also drawing design ideas from strong potential lines shown by the analysis of the area.
29. Just a reminder Just a pure graph
No attractors (shops)
No sources (housing,stations)
No resistances (congestion,traffic)
No distances (pure topology)
Ideal model for early design stage - master planning.
31. Relativisation
32. Justified Graphs Radius 3
33. Radius subgraphs Each sub graph (up to a radius) has access to different numbers of nodes.
Need a method to permit comparison of structure of different sized graphs.
Subgraphs from a node
Different houses buildings or urban systems
Does anyone else look at cumulative path length sub-graphs (Social networks?)
34. Relativisation
35. Normalization
36. Relativisation
40. Spatial Layout Drives Communication & Innovation at Work
41. The End Further information
www.spacesyntax.org
http://bat.vr.ucl.ac.uk/webmap/
The Social Logic of Space [Hillier & Hanson]
Space is the Machine[Hillier]
The Social Logic of Housing[Hanson]
42. Extra Time Small world or not small world ?
Intelligibility (measure)
nameing places
More localization methods
Highly non planar mapping
43. Is it a Small world? Mean path length is typically low
Degree distribution more Poisson than power law
Axial maps are highly clique free (Watts and Strogatz) definition of small world
Also lack of cliques means not scale free.
Cities Have structural hubs (high street) but tend to be more robust to blockage. Depends on distribution.Depends on distribution.
44. Is a city a small world? Path length distribution is also wrong for a small- world ( but consistent across all axial maps)
45. Extra Time Intelligibility
Correlation between
Connectivity( Degree)
Global integration (normalized cumulative path length )
The relation between what I can see and how I can go in the system
Appears to be strong for historic neighborhoods and weak for dysfunctional housing estates
47. For the maiden lane estate we see weak correlations between connectivity and integration ( global).For the maiden lane estate we see weak correlations between connectivity and integration ( global).
49. Intelligibility Mapping
50. Remember theses are not maps of movement but similarity. - Remember theses are not maps of movement but similarity. -
53. Extra time Local cumulative path length
Radius ( count of onion rings)
Relativisation only works with rational steps
Needs strong scaling structure
Vicinity (new)
Decay (new) Hoon Pack Hoon Pack
54. Vicinity vs Radius Ordered J-graph sequence 1,2,2,2,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6
V9 = [1,2,2,2,3,3,4,4,4]
R3= [1,2,2,2,3,3]
1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,
R3=[1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3]
V9=[1,2,2,2,2,2,2,2,2]
55. Extra time K eccentricity appears to be the reverse of Vicinity
Is there a proper mathematical term for vicinity?
56. Empirical Evidence
58. Random grand final thought Possible to layout non planar graphs in a planar way ?
60. Convex Spaces
61. Convex Spaces
62. Convex Spaces
63. Mean Shortest Paths & Mean Out-of-group Utility: Numbers for Nine Organizations
64. UCL Departments
65. Density of Internal Phone Traffic
66. Sample Building
67. Cognizing Urban Spatial Configurations To decide how to navigate the urban grid, we must have some picture of its geometric and topological properties.
This is why we say that before cities are social products, they are human products. They reflect how our minds read their ambient space and use it to guide both their actions and their bodies in space.
Moreover, insofar as cities are human products, they tend to be universal, and insofar as they are products of culture, they tend to be differentiated. The individuality of cities arises because both of these are partial orderings against a random background, so a large number of idiosyncratic facts also shape cities.
68. Towards a Theory of Urban Configuration & Cognition Our theory of how we cognize urban configurations requires that human beings interact with spatial complexity in their ambient space by building a picture of its geometry and topology. Is this possible?
We have recently had some very strong evidence that this is the case, but showing quite unambiguously that people use the geometry and topology of their spatial environment as the main guides to navigation, rather than, say, simple distance minimisation or landmarks.
69. Conclusion This has a consequence of huge importance for urbanism. It means that people are reading the architecture of the grid in order to move and animate the city. They are not responding like automatons to the simplicities of location and distance.
The architecture of the large scale urban network is then the prime determinant of how the city functions, and how they become the diverse and wonderful things they are.
The implication is that we have to reclaim the large scale architecture of the city for careful and knowledgeable design.
