The Journal of Space Syntax

The Journal of Space Syntax
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Michael J. Ostwald
University of Newcastle, Australia
Pages: 223-­246
The Journal of Space Syntax
ISSN: 2044-­7507
Year: 2011. Online Publication Date: Volume:2, Issue: 15 December 2011 http://www.journalofspacesyntax.org/
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Examining the Relationship Between Topology and Geometry: $&RQ¿JXUDWLRQDO$QDO\VLVRIWKH5XUDO+RXVHVRI*OHQQ0XUFXWW
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University of Newcastle, Australia
One of the fundamental axioms attributed to the ‘space syntax’ method is that the topology of the plan VKDSHVWKHJHRPHWU\RIWKHGHVLJQ7KDWLVWKHVRFLDOUHODWLRQVHPEHGGHGLQWKHFRQ¿JXUDWLRQDOSURS-­
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its form. Over the last four decades a large volume of research has been published in support of this position, most of which has been derived from urban studies or the analysis of vernacular buildings. However, several studies of architect-­designed houses have suggested that the reverse is potentially true in such cases;; that geometry takes precedence over topology. The present paper adopts a variation RIWKHFODVVLF-XVWL¿HG3ODQ*UDSK-3*PHWKRGWRWHVWWKHUHODWLYHSULPDF\RIJHRPHWU\DQGWRSRORJ\
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and the data derived from this process is then used to construct a series of inequality genotypes. These JHQRW\SHVDUHWHVWHGDJDLQVWDQLQWLPDF\JUDGLHQWEHQFKPDUNFRQ¿JXUDWLRQDJDLQVWHTXLYDOHQWGDWDIRU
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plan. The paper concludes that, for this limited set of houses, the data suggests that topology is not the sole or primary catalyst and that other factors -­ potentially including geometry -­ may also play a role.
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‘is that it is possible to identify certain underlying structures of space that are linked to observable patterns of behaviour and that these patterns, in turn, create social function, whether generative or reproductive’. This summary acknowledges that the correlation between social patterns and spatial FRQ¿JXUDWLRQPLJKWEHHLWKHUIRUPDWLYHRUUHDFWLYH:KLOHWKLVTXHVWLRQUHPDLQVWKHVXEMHFWRIVRPH
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syntax that is the focus of the present paper. Journal of Space Syntax, Volume 2, Issue 2, Pages 223-­246, 2011
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designed and inhabited, he effectively promulgated the position that in design, topology has primacy over geometry. Or alternatively, that the creation of a network of functional spaces, with appropri-­
ate connections and separations, necessarily both precedes and takes precedence over the shape of a building. A range of evidence has been published supporting this general proposition as observed in PDMRUSXEOLFEXLOGLQJYHUQDFXODUKRXVHVDQGKLVWRULFFRPPXQLWLHV+LOOLHUHWDO0DUNXV
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of this method to the analysis of architect-­designed houses also partially supports this proposition +DQVRQ+RZHYHUVHYHUDOVWXGLHVH[LVWZKLFKVXJJHVWWKDWWKHUHYHUVHFDVHPD\EHWUXHIRU
some architect-­designed houses;; that geometry may take primacy over topology. This might imply that, for some architect-­designed houses, the social pattern of space may be less important than the DUFKLWHFWXUDOIRUPWKDWHQFRPSDVVHVLW3VDUUD0DMRUDQG6DUULV%DIQD
The concept that, contrary to logic, function might follow formLVQRWQHZLQDUFKLWHFWXUH5DEHQHFN
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may take precedence over topology, the body of evidence developed to support this idea is more limited.
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analysis – visual and mathematical –, before the data derived from this process is used to construct DVHULHVRILQHTXDOLW\JHQRW\SHVDQGDSDUWLDOVWDWLVWLFDOJHQRW\SH:KLOHWKHVHVWDJHVRIWKHSURFHVV
provide new evidence to inform the debate about form and function, they largely follow accepted practices. Thereafter, three additional analytical stages are described, two of which offer new compara-­
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method is used to calculate the fractal dimension of the exterior and interior plan forms of each of the ¿YHKRXVHV7KLVDSSURDFKSURYLGHVDQDOWHUQDWLYHPHDVXUHRIWKHUHODWLYHFRPSOH[LW\RIIRUPDVLWLV
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comparative patterns, rather than absolute values, and its outcomes are necessarily speculative. 7KLVUHVHDUFKLVIRFXVVHGRQ0XUFXWW¶VDUFKLWHFWXUHDQGLQSDUWLFXODUKLVODWHUFDUHHUKRXVHV
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– typically described as a modern evocation of the primitive hut – has elicited extensive discussion Examining the Relationship Between Topology and Geometry
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cutt’s work has only rarely been subjected to any form of computational or mathematical analysis. 2QHH[FHSWLRQWRWKLVLVWKHZRUNRI+DQVRQDQG5DGIRUGDEZKRDQDO\VHG0XUFXWW¶V
early houses using a variation of the shape grammar approach to attempt to understand their formal SURSHUWLHV7KHVHFRQGUHDVRQIRUFKRRVLQJWKHVHSDUWLFXODUKRXVHVLVWKDW-3*GDWDLVDYDLODEOHIRU
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ogy is considered. Thereafter, a brief background is provided to the relevant aspects of the method along with a description of the particular variations that have been selected for this paper. The results are, then, provided and discussed separately for each house, before they are combined together for analysis using inequality genotypes, intimacy gradient benchmarks and fractal analysis. The paper concludes with a discussion of the possible implications of the results.
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curring theme. That geometry has the potential to shape topology has never been denied, but because the analytical methods used in space syntax are focused on topological properties, geometry has only LQGLUHFWO\EHHQLPSOLFDWHGLQWKHUHVXOWV$V3VDUUDSREVHUYHVµ>L@QWKHDEVHQFHRIDWKHRU\
and a method that relates geometrical to spatial properties, space syntax has buried the physical at-­
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differentiation between the vernacular tradition of building and architect-­designed buildings. The IRUPHUFDWHJRU\UHSURGXFHVWRSRORJLFDOO\DµNQRZQDQGVRFLDOO\DFFHSWHGSDWWHUQ¶ibid. SZKLOH
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that, it is the designer’s conscious decision to innovate that potentially transforms the vernacular into WKHDUFKLWHFWXUDO,QWKHSUHVHQWFRQWH[WWKHEDVLVRQZKLFKWKHQHZLQWHQWLRQDOSDWWHUQLVSUHGLFDWHG
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tive have shaped a design. This argument accepts that geometry may shape topology, but it is still topologically measured.
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acknowledges that it is a common assumption that ‘the internal spatial structure of buildings carries the essential genotypical structure, while the actual physical form of buildings carries the less sig-­
Journal of Space Syntax, Volume 2, Issue 2, Pages 223-­246, 2011
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that is given two-­dimensional properties and then projected into the third dimension to respond to site FRQGLWLRQV*HRPHWU\SOD\VDQLPSRUWDQWUROHLQWKHZD\LQZKLFKSHRSOHXQGHUVWDQGVSDFHGHYHORS
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sential for ‘buildings to exist in a basic sociological sense’, but it is ‘to the architectural elaboration RIEXLOGLQJV¶ibid.3VDUUDSUHLQIRUFHVWKLVYLHZZKHQVKHSURSRVHVWKDWZKLOHVSDFHDQG
form are ‘different from each other, they are an essential part of architecture as experienced reality’.
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approaches that can be used to interrogate the social structure of space and the relationship between VSDFHDQGIRUPLQDEXLOGLQJ7KH¿UVWVWHSLQWKHFRQVWUXFWLRQRID-3*LVWKHSURGXFWLRQRIDFRQYH[
map or boundary map. There are a number of alternative variations of this stage, ranging from the KLJKO\SURVFULEHGWRWKHYHU\JHQHUDO+LOOLHUDQG+DQVRQ0DUNXV7KHPRUHUHFHQWDS-­
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present paper, while the third is used for the comparative analysis.
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of the spatial structure, including relative depth, control or permeability. The majority of the examples of this approach are concerned with inhabitant-­visitor relations and they rely on the production of -3*VZLWKWKHH[WHULRUDVFDUULHU$YLVXDOLQVSHFWLRQRIVXFK-3*VFDQUHYHDOWKHH[WHQWWRZKLFKVSD-­
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Once the houses have been individually analysed, then these results can be combined to pro-­
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is built into spatial layout’. The inequality genotype is one way of representing this consistent pattern. ,QSUDFWLFHDQLQHTXDOLW\JHQRW\SHLVDVHTXHQFHRIIXQFWLRQDOO\GH¿QHGVSDFHVUDQNHGLQDFFRUGDQFH
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SQRWHVWKDWWKH difference factor ‘was developed to quantify the degree of difference between the Examining the Relationship Between Topology and Geometry
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to demonstrate how a ‘culture manifests itself in the layout of space by forming a spatial pattern in ZKLFKDFWLYLWLHVDUHLQWHJUDWHGDQGVHJUHJDWHGWRGLIIHUHQWGHJUHHV¶:KLOHWKHUHKDYHEHHQDOWHUQDWLYH
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genotype remains the most common.
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the not unreasonable starting assumption was that there would be a ‘genotypical consistency in these KRXVHV¶ZKLFKFRXOGEHXVHGµDVDEDVLVXSRQZKLFKWRVWXG\WKHLUSKHQRW\SLFDOGLIIHUHQFHV¶ibid. S8QIRUWXQDWHO\WKHLQHTXDOLW\JHQRW\SHVZHUHIDUPRUHGLYHUVHWKDQDQWLFLSDWHGDQGHYHQ
simplifying the node set did not produce the anticipated result. As described in the following section, WKHSUHVHQWSDSHUDGRSWVDYDULDWLRQRI%DIQD¶VPHWKRG
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The general principle adopted in this paper for the construction of a boundary map is to try to keep WKHVHWDVHFRQRPLFDODVSRVVLEOH7KXVWKHPHWKRGIROORZV%DIQD¶VDSSURDFKZKHUHWKH-3*V
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which often encompass several small airlocks and cupboards, have been merged into single areas, and bathrooms with internal partial partitions are also treated as one space.
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Table 1. General abbreviations for rooms used in the JPG. 7KHLVVXHRIWKHµRSHQSODQ¶LVPRUHFRPSOH[ZLWKPDQ\RI0XUFXWW¶VVSDFHVEHLQJGH¿QHG
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of space -­ although typically, at least two are required to strongly imply such a division -­, while still EHLQJSDUWRIDQRSHQSODQ:KHUHQRFOHDUWKUHVKROGFRPELQDWLRQVH[LVWWKHVSDFHLVFRXQWHGDVD
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‘trivial loops’ – that is where there are two or more direct connections between the same two nodes IRUH[DPSOHPXOWLSOHDGMDFHQWVOLGLQJJODVVGRRUVVHSDUDWLQJWKHVDPHWZRVSDFHV±DOORIWKHOLQHV
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set of mathematical results has been developed for each house, only the most important are reported for each project.
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PHWUHVIURPWKHRFHDQZLWKGLVWDQWPRXQWDLQYLHZVWRWKHZHVW7KHKRXVHZKLFK)UDPSWRQ
SGHVFULEHVDVKDYLQJµDSHFXOLDUO\DHURQDXWLFFKDUDFWHU¶LVYLVXDOO\GRPLQDWHGE\LWVQDUURZ
VLGHSUR¿OHGLVSOD\LQJDQXQGXODWLQJSDUWLDOEXWWHUÀ\URRIIRUP>)LJXUH@
Figure 1. Perspective view of the Magney House. Examining the Relationship Between Topology and Geometry
Figure 2. Perspective view of the Magney House. 3ODQQHGDFFRUGLQJWRDµSURWHFWLYHEDFNDQGRSHQIURQWRUJDQLVDWLRQDOVWUDWHJ\¶*XVKHKLQ
*XVKHKHWDOSWKHKRXVHRSHQVWRWKHQRUWKDQGWKHVRXWKIDoDGHLVHQFORVHGWRSURWHFW
WKHUHDUZDOOIURPKDUVKZLQWHUZLQGV$ORQJWKHOHQJWKRIWKHVRXWKIDoDGHLVDZLGHVHUYLFHZDOOLQ
WKHLQWHULRUZKLFKLVFRXSOHGZLWKDQDGMRLQLQJDFFHVVFRUULGRUFRQQHFWLQJWKHHQWLUHKRXVH,QSODQ
WKHURRPVDUHDOLJQHGWRWKHVHUYLFHVSDFHVRQWKHVRXWKZDOO>)LJXUH@
Figure 3. Annotated plan of the Magney House. $YLVXDODQDO\VLVRIWKH0DJQH\+RXVH-3*UHYHDOVWKUHHORRSVLQVWDQFHVRIµULQJLQHVV¶
HPEHGGHGLQDQRWKHUZLVHDUERUHVFHQWRUµWUHHOLNH¶VFKHPDWKH¿UVWFRQQHFWLQJWKHH[WHULRUWRWKH
FRXUW\DUGWKHQWRWKHNLWFKHQGLQLQJOLYLQJDUHDWKHQWREHGURRPDQG¿QDOO\EDFNWRWKHH[WHULRU
>)LJXUH@7KHVHFRQGDOVRFRPPHQFHVZLWKWKHH[WHULRUDQGWKHFRXUW\DUGWKHQOLYLQJURRPKDOOZD\
ODXQGU\DQG¿QDOO\WKHH[WHULRURQFHPRUH7KH¿QDOORRSFRQQHFWVWKHH[WHULRUWRWKHJDUDJHODXQGU\
and then returns to the exterior. These are partial loops because, despite the strict nomenclature of the PHWKRGZKHUHLQDOOH[WHULRUVDUHWKHVDPHWKHH[WHULRUVSDFHVZKHUHWKHVHORRSVVWDUWDUHRIWHQWKH
middle of the plan, while the ones that end the loops are at the ends of the plan. :LWKLQWKHRYHUDOODUERUHVFHQWSODQWKHUHLVDOVR
a sub-­instance of ‘bush-­like’ structure where liv-­
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to two bedrooms and a bathroom. Overall, the planning diagram could be said to reveal the ves-­
tigial planning of two partial houses, one nested within the other. Figure 4. JPG, with exterior as carrier, for the Magney House.
Journal of Space Syntax, Volume 2, Issue 2, Pages 223-­246, 2011
'HVSLWHKDYLQJRQO\HOHYHQQRGHVWKHSODQLVUHODWLYHO\GHHSZLWKEHGURRPKDYLQJWKH
KLJKHVWWKHFXPXODWLYHWRWDOGHSWKTD = >7DEOH@7KHPRVWLQWHJUDWHGVSDFHVDUHWKHH[WHULRUi DQGWKHKDOOZD\i DQGWKHOHDVWLQWHJUDWHGVSDFHLVEHGURRPi $H* result RIVLJQL¿HVDSODQZLWKDKLJKGHJUHHRIXQLIRUPLW\RUFRQYHUVHO\DORZOHYHORIGHWHUPLQDWLRQ
or deliberation;; this result occurs in part because of the multiple ring networks, suggesting a loose quality to the plan.
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Table 2. Summary of JPG results for the Magney House. Simpson-­Lee House, Mount Wilson (NSW) 1989-­94.
7KH6LPSVRQ/HH+RXVHLVDGRXEOHSDYLOLRQUHVLGHQFHORFDWHGDW0RXQW:LOVRQDQGVLWHGRQDURFN
OHGJHRYHUORRNLQJDQHVFDUSPHQWRIWKH%OXH0RXQWDLQVQRUWKZHVWRI6\GQH\>)LJXUHV±@$FFRUG-­
LQJWR)URPRQRWSWKHFOLHQWEULHIDVNHGIRUµDVDQFWXDU\IRUDUHWLUHGFRXSOH¶2ULHQWDWHG
to the east, the larger of the two pavilions contains two bedrooms that are separated by a central living DUHD6KDUSO\WXUQLQJDURXQGWKHURFNOHGJHWRZDUGVWKHQRUWKHDVWWKHVPDOOHUSDYLOLRQFRPELQHVWKH
JDUDJHZLWKDSRWWHU\VWXGLR>)LJXUH@$VERWKSDYLOLRQVDUHOLQHDUDQGKDYHPRQRSLWFKURRIVWKDW
OLIWXSWRZDUGWKHYLHZVWKHKRXVHFRUUHVSRQGVWRZKDW'UHZSGHVFULEHVDVµ0XUFXWW¶V
GHYHORSPHQWRIDQHVVHQWLDOO\OLQHDUW\SRORJ\ZKHUHWKHFKLHIYDULDEOHLVWKHVHFWLRQDQGURRISUR¿OH¶
Figure 5. Perspective view of the Simpson-­Lee House.
Examining the Relationship Between Topology and Geometry
Figure 6. Perspective view of the Simpson-­Lee House.
Figure 7. Annotated plan of the Simpson-­Lee House.
$ YLVXDO DQDO\VLV RI WKH -3* IRU WKH
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structure, but with four minor ring networks;; two based on exterior connections and two on interior FRQ¿JXUDWLRQV7KH¿UVWWZRVWDUWZLWKWKHH[WH-­
rior, which connects, in turn, through hallway 1, OLYLQJGLQLQJDQGKDOOZD\EHIRUHUHWXUQLQJWR
the exterior. The second starts with the exterior, then the garage, laundry and the exterior once more. Once again, neither of these sequences goes through the same exterior door, so the ‘ringiness’ Figure 8. JPG, with exterior as carrier, for Simpson-­Lee House.
in the plan is an artefact of the method, whereas the ‘lived’ structure of the house is a tree with a QHWZRUNRIFURVVFRQQHFWHGEUDQFKHV>)LJXUH@
$VLV¿WWLQJIRUDPRUHFRPSOH[GHVLJQWKHWRWDOGHSWKRIWKHGHHSHVWVSDFHLQWKH6LPSVRQ/HH
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be expected given that a person has to go outside to pass between the two pavilions and each pavilion KDVPXOWLSOHDOWHUQDWLYHURXWHVWRWKHH[WHULRU6RPHRIWKHPLQRUDQRPDOLHVLQWKLVVHWRILQWHJUDWLRQ
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Journal of Space Syntax, Volume 2, Issue 2, Pages 223-­246, 2011
looseness of planning structure, which is supported by the four partial loops, giving the plan a high GHJUHHRISHUPHDELOLW\RURSHQQHVV>7DEOH@
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Table 3. Summary of JPG results for the Simpson-­Lee House.
Fletcher-­Page House, Kangaroo Valley (NSW) 1996-­98
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RI.DQJDURR9DOOH\VRXWKRI6\GQH\7KLVKRXVHLVVOLJKWO\VPDOOHUWKDQWKH6LPSVRQ/HH+RXVH
KDYLQJRQO\QLQHKDELWDEOH]RQHVLQFRPSDULVRQZLWKWKHODWWHU¶V¿IWHHQ7KH)OHWFKHU3DJH+RXVH
LVRQHRIWKHVHULHVRIZKDW)UDPSWRQSFDOOVµ0XUFXWW¶VOLQHDUPRQRSLWFKHGGZHOOLQJV¶
However, the house is unusual in this sequence, as its roof is tilted upwards to the north and parallel WRWKHKLOOVLGHZKLFKOHDYHVWKHQRUWKHUQIDoDGHSDUWO\KLGGHQE\WKHVORSH,QUHVSRQVHWRWKLVRQWKH
southern side of the house, large openings are positioned toward the primary views. This opposition between views and sunlight gives this house an unusual spatial quality, in the context of the remainder RI0XUFXWW¶VUXUDOZRUNV$FFRUGLQJWR)UDPSWRQibid.µORQJYLHZVWKURXJKWKHKRXVH>«@LPSDUWD
VHQVHRIJUDQGHXUWKDWWRWDOO\EHOLHVLWVUHVWULFWHGGLPHQVLRQV¶,QWKLVGHVLJQ0XUFXWWKDVDOVRUHSODFHG
his typical corridor planning strategy with a series of connecting doors along the southern length of WKHKRXVHWRHQFORVHHDFKURRP$GHHSHQWU\VSDFHLQWKHPLGGOHRUJDQLVHVWKHKRXVHLQWRWZR]RQHV
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VLGHLVDNLWFKHQDGMDFHQWWRWKHPDLQEHGURRPZLWKDQHQVXLWHDQGDSULYDWHYHUDQGD>)LJXUH@
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LQWHUPHGLDWHORRSVDOORIZKLFKDUHUHOLDQWRQH[WHULRUFRQQHFWLRQV:LWKIRXUH[WHULRUGRRUVLQFOXGLQJ
WKHJDUDJHGRRUWKHVHORRSVDUHDOVRVRPHZKDWDUWL¿FLDODOEHLWWKLVLVDFRQVLVWHQWSDWWHUQDFURVVWKH
Examining the Relationship Between Topology and Geometry
¿UVWWKUHHKRXVHV+RZHYHUXQOLNHWKHSUHYLRXVWZRKRXVHVWKLVRQHKDVWZRUHODWLYHO\VWUDLJKWIRU-­
ZDUGVLGHVWRWKHFRQ¿JXUDWLRQ±UDWKHUWKDQWKHPRUHFRPSOH[QHVWHGWRSRORJ\RIWKHSUHYLRXVWZR
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Figure 9. Annotated plan of the Fletcher-­Page House.
The most integrated space in the house LVWKHH[WHULRUi IROORZHGE\WKHRSHQSODQ
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connection between the open plan area and the exterior. The lowest integration result is for bath-­
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VWXG\DUHDOVRTXLWHORZUHVSHFWLYHO\ i Figure 10. JPG, with exterior as carrier, for Fletcher-­Page House.
and i %HGURRPKDVDVXUSULVLQJO\KLJK
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implies a slightly more balanced approach to the plan than found in the previous houses, although it LVVWLOOVXJJHVWLYHRIDPDUJLQDOODFNRIFRQ¿JXUDWLRQDOGHWHUPLQDWLRQ>7DEOH@
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Table 4. Summary of JPG results for the Fletcher-­Page House.
Journal of Space Syntax, Volume 2, Issue 2, Pages 223-­246, 2011
Southern Highlands House, Kangaloon, (NSW) 1997-­01.
7KLVGZHOOLQJLVORFDWHGLQWKHIDUPLQJFRPPXQLW\RI.DQJDORRQZKLFKLVSDUWRIWKH6RXWKHUQ+LJK-­
ODQGVGLVWULFWVRXWKZHVWRI6\GQH\2SSRVLWHDSRQGDQGVWDQGLQJDPRQJVWWDOOWUHHVWKHKRXVHLVVLWHG
RQDJULFXOWXUDOODQGDQGLVRULHQWDWHGWRWKHQRUWK&RPSOHWHGLQWKLVKRXVHPDUNVDVLJQL¿FDQW
FKDQJHLQWKHVL]HRI0XUFXWW¶VUHVLGHQWLDOZRUN$V*XVKHKLQ*XVKHKHWDOSVWDWHVµWKLV
LVRQHRIWKHODUJHVWKRXVHVWKDW0XUFXWWKDVGHVLJQHGEHLQJRIDOPRVWVTXDUHPHWHUVLQDUHDZLWK
URRPVRIPHWHUVZLGWKDQGPHWHUVKLJKFHLOLQJV¶7RSURWHFWDJDLQVWVHYHUHZLQGVWKHKRXVH
has a protective shield in the form of a curved metal plane along the entire length of the southern IDoDGH$WERWKWKHHDVWDQGZHVWRIWKHSODQDUHHQWU\SRLQWVWRWKHKRXVHKRZHYHUWKHZHVWOREE\LV
WKHPDLQHQWU\VSDFHEHVLGHWKHKLJKZDOORIWKHVKLHOGDWKLVFXUYHGSODQHRIWKHVRXWKIDoDGHUXQV
DORQJJDOOHULDKDOOZD\WKDWOLQNVDVHULHVRIURRPV'LYLGLQJWKHVOHHSLQJDUHDVRIWKHSDUHQWVDQG
children between east and west, the communal spaces that face an external northern terrace occupy WKHFHQWUHRIWKHKRXVH>)LJXUH@
Figure 11. Annotated plan, Southern Highlands House.
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0XUFXWW¶VKRXVHV>)LJXUH@'HVSLWHLWVOLQHDUSODQPXFKRIZKLFKLVFRQQHFWHGZLWKDVLQJOHORDGHG
corridor, the house has ten non-­trivial loops, all but four of which involve the exterior. This plan is further complicated by a parallel circulation system, made up of a series of short corridors that are effectively airlocks between spaces. The plan also features several small, tree-­like sections, mostly involving bedrooms and bathrooms. Overall, if the airlocks and dual roots are ignored, this plan could EHFRQVLGHUHGWREHDODUJHUYHUVLRQRIWKHSUHYLRXVWKUHHZLWKDUKL]RPRUSKRXVEDVHFRPSULVLQJD
VHWRIHLJKWORRSVXQGHUO\LQJDQDUERUHVFHQWLQWHULRUPDGHXSRIIRXUWUHHOLNHRUEXVKOLNHIRUPD-­
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Figure 12. JPG, with exterior as carrier, Southern Highlands House.
Examining the Relationship Between Topology and Geometry
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DQGWKHORZHVWGHSWKWKHH[WHULRUZLWKLVKLJKHUWKDQWKHPDMRULW\RIWKHUHVWRIWKHUHVXOWVRI
WKHRWKHUIRXUKRXVHV>7DEOH@7KHPRVWLQWHJUDWHGVSDFHLVKDOOZD\i ZKLFKPDWFKHV
the intuitive reading of the linear plan, mostly connected by a single hallway. Alternatively, the least LQWHJUDWHGVSDFHVDUHWKHEHGURRPVDQGDQGEDWKURRPVDQG6RPHRIWKHPDQ\DQRPDOLHV
LQWKHLQWHJUDWLRQUHVXOWVLQFOXGH:&i ERWKJDUDJHVi DQGi DQGWKHODXQGU\
i DOOEHLQJLQWKHXSSHUKDOIRIWKHLQWHJUDWLRQUHVXOWV7KHH*UHVXOWRILVZLWKLQWKH
VDPHUDQJHDVWKRVHRIWKHSUHYLRXVKRXVHVH*FRQ¿UPLQJDVLPLODUORRVHQHVV
LQWKHSODQQLQJDSSURSULDWHIRUDGHVLJQZLWKORRSVLQLWVFRQ¿JXUDWLRQV,QGHHGPDQ\SDUWVRI
this house resemble an open lattice, with a multitude of possible routes through and around them.
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Table 5. Summary of JPG results for Southern Highlands House.
Walsh House, Kangaroo Valley (NSW) 2001-­05
7KH:DOVKKRXVHLVRULHQWDWHGWRWKHQRUWKDQGVLWHGRQDJHQWO\VORSLQJVLWHLQWKH.DQJDURR9DOOH\
The principle north frontage addresses the prominent views across hills, while the east face is directed WRZDUGVDODUJHURFNIRUPDWLRQ7LOWHGXSWRWKHQRUWKWKHURRÀLQHH[WHQGVSDVWWKHKLJKQRUWKHUQ
windows in order to protect them against the summer sun. To the north-­eastern corner of the house Journal of Space Syntax, Volume 2, Issue 2, Pages 223-­246, 2011
LVDUHÀHFWLQJSRRODWDFWLFWKDWGLVWLQJXLVKHVWKHKRXVHIURPSUHYLRXVRQHVGHVLJQHGE\0XUFXWW
'HVLJQHGZLWKPLQLPDOZLQGRZRSHQLQJVDQGFRQVWUXFWHGIURPUXVWLFPDWHULDOVWKHVRXWKDQGZHVW
facades present the visual ‘working character of a farmhouse, with garage, gas-­tank storage, laundry DQGODUJHZDWHUVWRUDJHWDQNV¶*XVKHKHWDOS7KHUHLVDVLQJOHODUJHZLQGRZRQWKH
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Figure 13. Annotated plan, the Walsh House.
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a bush-­like structure with most access branches VWHPPLQJ IURP WKH H[WHULRU >)LJXUH @ :LWK
only one, non-­trivial loop, this is less permeable than the other four plans. The loop goes from the exterior, to the hallway, then the foyer, the dining area and the living area, before returning WRWKHRXWVLGH7KHJDUDJHDQGEHGURRPFDQ
also only be accessed by way of the exterior, so they almost operate as separate pavilions, much OLNHWKHVWUXFWXUHRIWKH6LPSVRQ/HHKRXVHHYHQ
Figure 14. JPG, with exterior as carrier, for the Walsh House.
though they are contained in the same volume. There are also several short branching points in WKH FRQ¿JXUDWLRQ OHDGLQJ WR WKLV KRXVH EHLQJ
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the least integrated conform to the set of deepest spaces in the plan. The H*UHVXOWRILVLQWKH
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shallow trees, none of which -­ the mathematics suggests -­ are strongly determined. However, a visual inspection does not completely support this result;; ignoring the garage loop, the plan is for several VHSDUDWHSDYLOLRQVXQGHURQHURRIRQHRIZKLFKKDVDVLQJOHORRSWKURXJKWKHSXEOLFDUHDV>7DEOH
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Examining the Relationship Between Topology and Geometry
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Table 6. Summary of JPG results for the Walsh House.
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tions and programmatic differences might produce divergent results. However, when a set of multiple inequality genotypes -­ for similarly sited and designed houses -­ are compared, it is thought to be more OLNHO\WRSURGXFHDFRQVLVWHQWUHVXOW)RUWKH¿UVWVWDJHRIWKHSUHVHQWFRPSDULVRQWKHVSDFHVLQWKH
¿YHKRXVHVDUHVHTXHQFHGLQDFFRUGDQFHZLWKWKHWKHRU\RILQWLPDF\JUDGLHQWV$QLQWLPDF\JUDGLHQW
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WKHEDVLVIRUVHYHUDOGHVLJQSDWWHUQV:KLOHQHYHUQXPHULFDOO\GHVFULEHG$OH[DQGHUibid.LGHQWL¿HVD
OLQHDUVHTXHQFHWKDWFRPPHQFHVZLWKSXEOLFSODFHVIR\HUVKDOOZD\VDQGOLYLQJURRPVDQGHQGVZLWK
SULYDWHRUXWLOLWDULDQVSDFHVVWRUHURRPVEDWKURRPVDQGVHUYLFHDUHDV,QWKLVVHQVHWKHLQWLPDF\
gradient is a type of inequality genotype, loosely derived from social mores of the era.
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Journal of Space Syntax, Volume 2, Issue 2, Pages 223-­246, 2011
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for several utility and service areas to the right of the chart. The results for the remaining three houses KDYHVRPHVLPLODULWLHVWRWKLVSDWWHUQDOWKRXJKOHVVSURQRXQFHG)XUWKHUPRUHDVSUHYLRXVO\QRWHGD
QXPEHURIKRXVHVIHDWXUHFRXQWHULQWXLWLYHUHVXOWV)RUH[DPSOHWKHUHDUHXQH[SHFWHGO\KLJKi results IRUWKHODXQGU\LQWKH0DJQH\+RXVHDZDONLQUREHLQWKH6LPSVRQ/HH+RXVHDQGWKHWRLOHWDQG
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,IDQDYHUDJHUHVXOWIRUHDFKSURJUDPIXQFWLRQLVFDOFXODWHGIRUWKH¿YHKRXVHVHIIHFWLYHO\
producing a partial statistical genotype, it can then be compared with the anticipated result derived from intimacy gradient theory;; which is one possible explanation for the level of integration of do-­
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OLQHDVWKHRWKHU:LWKLQWKLVUDQJHWKHi values for intermediate levels were generated by an equal division.
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son between the statistical genotype and the intimacy gradient it is clear that there is slightly less GLIIHUHQWLDWLRQEHWZHHQWKHLQWHJUDWLRQOHYHOVRIVSDFHVLQ0XUFXWW¶VKRXVHVWKDQDQWLFLSDWHGLQWKH
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Figure 17. Statistical genotype comparison between early and late career houses and their trends.
Journal of Space Syntax, Volume 2, Issue 2, Pages 223-­246, 2011
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cutt’s design practice that has at least partially reduced the importance of social structure in shaping the geometry of design.
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the number, the less the level of formal complexity. Architecture tends to fall into the range between DQG%RYLOO/RUHQ]
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geometry is only considered by implication. That is, certain values developed for topology imply WKDWWKHUHLVQRWDVWURQJDQGFRQVLVWHQWFRQ¿JXUDWLRQDOSDWWHUQLQ0XUFXWW¶VKRXVHVDQGVRVRPHWKLQJ
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correlation between form and spatial pattern developed in the paper is not compelling evidence that JHRPHWU\VKDSHVWRSRORJ\7KHLVVXHLVWKDWDV+LOOLHUSREVHUYHVµ>D@UFKLWHFWXUDOUHDOLWLHV
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systems – these priorities have produced a consistent set of formal solutions. This is not to suggest WKDW0XUFXWWLVFRQWUDU\WRKLVRZQVWDWHGLQWHQWOHWWLQJIRUPGRPLQDWHKLVFRQFHUQVIRUFOLPDWHRU
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and control access to habitable areas. The habitable areas, like bedrooms and living rooms, are typi-­
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thoroughfare, generating the abnormally high integration result that was previously noted. There are PDQ\PRUHLQVWDQFHVRIWKLVDSSURDFKWRSODQQLQJLQWKH¿YHKRXVHVLQWKLVSDSHULQFOXGLQJDQDOPRVW
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architecture. The pattern also explains the tendency in the more recent houses for service areas to be more highly integrated than predicted.
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