特雷莎·埃托爾 約翰·皮奈羅·希爾瓦

引 言

空間句法研究領域以比爾·希列爾（Bill Hillier）、朱利恩·漢森（Julienne Hanson）及其同事于20世紀70年代早期在倫敦大學巴特利特建筑學院開展的開創(chuàng)性工作為基礎。其起源可追溯至題為《人類—環(huán)境范式及其不一致性》的文章[1]，但在文章《空間句法》[2]中首次提到發(fā)展至今日的空間句法的名稱和理論基礎，而此后在《空間的社會邏輯》（The Social Logic of Space）[3]和《空間即機器》（Space is the Machine）[4]這兩本書中則展開了更為詳細的敘述。

空間句法以空間的合成和表現(xiàn)性視覺表征（即所謂的軸向地圖）為基礎，除了能夠解釋人類空間系統(tǒng)，還具有對其社會意義和形式—功能影響的深刻推論能力。軸向地圖由覆蓋整個空間系統(tǒng)的最小軸系—軸線構成。這種表征形成“句法模型”的基礎，在此基礎上進行句法分析，構成了空間系統(tǒng)構形方式從表面上看較為抽象的表征。雖然句法表征有時被批評為簡單化或簡化，但其排除其他城市或建筑特征、現(xiàn)象和事件，而僅僅專注于空間構形，因此可以說恰恰相反，句法表征非常豐富，因為其中涵蓋了對空間信息認知處理的各個方面。

不同于典型的以圖形表征物理現(xiàn)實的方式（如在繪圖或制圖中），句法表征不是旨在再現(xiàn)度量和幾何屬性。相反，在某種程度上，它體現(xiàn)了占據(jù)空間的物理和視覺體驗，即身處城市環(huán)境空間網(wǎng)絡中導航人所經(jīng)歷的連續(xù)度。因此，軸向地圖本身并不描繪視覺障礙物（例如建筑物、樹木等），而是描繪基于持續(xù)視覺感知的空間網(wǎng)絡及其潛在可達性。通過這種方式，空間句法表征并未簡化，反而更加豐富，因其對觀察者（用戶）看到/體驗空間（街道）網(wǎng)絡的方式在認知上沒有惰性，從而引導、創(chuàng)建用戶可能用于導航的構形。句法表征可以說是“具體圖”，因其反映了空間中的具體存在。

句法分析基于嚴格的數(shù)學描述，使用在圖論中開發(fā)的一組算法。在軸向地圖中，頂點或節(jié)點對應于軸線，并且當且僅當相應軸線相交時，兩個頂點相鄰。軸向圖包含有關每條軸線與構成系統(tǒng)的所有其他軸線的連接信息，并可用于分析每條線相對于所有其他線的相對位置。以這種方式獲得的屬性不隨每條線各自的條件而變化，而是隨其在系統(tǒng)中的插入位置（拓撲）而變化。

在空間句法學術界內(nèi)，已經(jīng)創(chuàng)建并測試了幾種句法算法。通過評判每項算法反映（關聯(lián)）城市和建筑現(xiàn)象（例如行人或機動活動、土地使用類型、租金價值）的能力來評估其是否成功。盡管軸向地圖在將模型與實際可測量現(xiàn)象聯(lián)系起來方面具有良好表現(xiàn)，但總是明顯地與城市形態(tài)不匹配，因為一條軸線可以越過幾個區(qū)塊，這有時意味著產(chǎn)生與比較現(xiàn)象大相徑庭的觀點。解決方案是在軸線交叉點處將其打破。由此，今天被認為是代表城市空間最佳方式的線段地圖即誕生于空間句法背景下。然而，這引發(fā)了另一個問題：由于算法基于拓撲深度，當軸線被轉換成線段時會產(chǎn)生深度，這會導致結果不夠理想?？臻g句法學術界解決此問題最常見的方法是線段角度分析[5,6]。該分析計算從一個線段移動到下一個線段的“成本”，但不是從拓撲方面（即每段意味著成本的增量），而是從角度方面（較大的角度對應于較高成本）。因此，在相同方向上移動具有零成本，即模擬軸線的連續(xù)度。如上所述，該程序的理論基礎與在城市環(huán)境中的感知和導航有關。

在空間句法學術界已開發(fā)和測試的所有算法中，有兩個因其分析城市構形的能力脫穎而出：“選擇度”和“整合度”。選擇度（在圖論中稱為“中間中心性”）可以稱之為對潛在通過流量的度量，并且通過計算所有可能的起點/終點（OA）對之間的最小成本（角度；方向的累積變化）路徑來進行測量（將地圖/圖表的每個元素視為可能的起點和終點）。累積較多地在所有起點/終點對之間的最低成本路徑上出現(xiàn)的那些元素，通常將呈現(xiàn)更高的選擇度值（注意，該總和除以可能的行程的總數(shù)）。相反，在所有最低成本路徑上總計累積出現(xiàn)次數(shù)較少的元素將具有較低的選擇度值。

“整合度”（在圖論中稱為“緊密度中心”）是用于分析城市構形的第二個相關算法。該算法衡量中心性程度，通常強調(diào)城市中普通市民稱之為主要街道的空間，也即大部分專業(yè)化商業(yè)的所在地，通常與城市中心的功能概念相關聯(lián)。通常，在軸向地圖上進行整合度分析。但是，由于在線段地圖中使用此算法會有優(yōu)勢，因此必須更新軸向地圖中使用的算法。與“選擇度”的情況一樣，當從對軸向地圖的分析轉移到對線段地圖的分析，而不是從拓撲方面“計算”深度，則要從角度方面進行（其中較大角度意味著更高成本）。

這兩種句法算法也與“自然活動”的概念有關，即由網(wǎng)格構形本身決定的城市行人活動的比例[7]，并可用于建立空間的“整合度”值及其被理解為隨機活動終點潛力之間的平行關系（到達活動）以及“選擇度”的值與空間被用作其既不作為起點也不作為終點的旅程交叉點的概率之間的平行關系（穿越活動）。

為了說明如何使用空間句法方法論以探索城市擴展如何改變現(xiàn)有空間結構的潛力，我們研究了里斯本市。該分析遵循基于歷史地圖的歷時過程，回溯到舊中世紀城市中心（即市中心）被地震活動大規(guī)模摧毀的日期，此后該地在1755年發(fā)生火災和海嘯。雖然在此次地震前里斯本已延續(xù)了諸多世紀，但從空間結構的角度來看，18世紀的市中心重建已經(jīng)產(chǎn)生了某種類似于“歸零地”的清理情況[8]。地震前的中世紀網(wǎng)格被一個正交網(wǎng)格所取代，該網(wǎng)格合理而實用地重新布置了新的“市中心”區(qū)域。到目前為止，這種結構網(wǎng)格幾乎完好無損（圖1）。

圖1 / Figure 11755年地震后的1758年里斯本市中心重建計劃The 1758 Plan for the reconstruction of the Lisbon downtown after the 1755 earthquake

該研究參考了一套（共8張）里斯本地圖的“重繪地圖”，這8張地圖分別于1785年、1855年、1871年、1911年、1948年、1970年、1997年和2005年（2017年更新）出版，對應了大約230年時間跨度內(nèi)城市演變的不同階段。這些地圖被分解為軸向和線段地圖，因此通過結合軸向和線段角度分析，可以對城市結構演變進行時空分析?？臻g句法工具包（Space Syntax Toolkit）[9]是深度地圖（Depthmap）[10]的前端，用于計算全局和局域尺度下的整合度和選擇度模式，并獲得城市空間中心性條件的一般情況。這些地圖的顏色范圍從藍色到紅色，藍色代表最低值，紅色代表最高值。根據(jù)等間距分類法，在所呈現(xiàn)的類之間進行閱讀。

基于對8個軸向地圖的視覺檢查，即以定性而非定量方式，我們展示了城市增長過程的一般“規(guī)則”。全局尺度分析用于表示城市網(wǎng)格的收斂和分散程度。然后，我們展示了當代城市形態(tài)的一些新興屬性，應用基于不同半徑的局域尺度分析來掌握鄰域尺度上的局域結構。在此基礎上，我們建議對里斯本市的一般結構進行重點澄清。

城市發(fā)展過程的一般規(guī)則

1785年的地圖（圖2）顯示“市中心”正交網(wǎng)格為中心（即城市網(wǎng)格中最綜合的區(qū)域，此地具有更高的整合值），以及對應于舊中世紀區(qū)域（城堡所在地）東部區(qū)域的高強度隔離水平。從方法論的角度來看，這些觀察結果也很重要。一方面，更綜合的區(qū)域與城市網(wǎng)格的幾何中心不對應；另一方面，城堡周圍的區(qū)域幾乎與“市中心”一樣具有中心性，只是隔離程度更高。因為東側與中心的拓撲距離較小，類似的隔離水平僅可在網(wǎng)格西側達到。需要注意的是，河岸是以市中心以東的海灣形式構形，不允許直接的東西向連接，這必然導致產(chǎn)生拓撲距離并因此產(chǎn)生隔離。此外，還要注意在“市中心”區(qū)域內(nèi)，東西軸線和南北軸線之間存在差異。東西線的較低值是缺乏連續(xù)度和連接的結果，在此特定案例中，這是由地形條件造成的。

1855年的地圖（圖3）遵循類似的層次模式。在城市東北部建立的新聯(lián)系對空間結構沒有重大影響。

另一方面，在1871年的地圖上可以清楚地看到已有結構的變化（圖4）。在“市中心”西側立即修建了一條新堤壩，以防止河水淹沒鄰近地區(qū)，并且沿河邊地區(qū)開辟了一條新軸線。此新軸取代了現(xiàn)有軸，并創(chuàng)建了更直接的與南北軸的新連接。這一變化使城市網(wǎng)格西部的整合度值顯著增加。盡管這似乎有點不可思議，但由于構形發(fā)生顯著變化而系統(tǒng)沒有成比例增長，所有整合度值都略有下降（包括所有紅線）。簡單來說，這種現(xiàn)象可以解釋為對整個系統(tǒng)空間整合的再分配和稀釋。

圖2 / Figure 21785年軸向地圖:整合度；全局半徑1785 axial map: Integration; Global radius

圖3 / Figure 31855年軸向地圖:整合度；全局半徑1855 axial map: Integration; Global radius

圖4 / Figure 41871年軸向地圖:整合度；全局半徑1871 axial map: Integration; Global radius

圖5 / Figure 51911年軸向地圖:整合度；全局半徑1911 axial map: Integration; Global radius

圖6 / Figure 61948年軸向地圖:整合度；全局半徑1948 axial map: Integration; Global radius

1911年的地圖（圖5）首次顯示了穿過垂直于河流的兩條“動脈”開口的腹地滲透，將市中心區(qū)與北部和西北部周邊地區(qū)聯(lián)系起來，后者被證明是現(xiàn)代化城市的象征，即現(xiàn)代化藍圖。根據(jù)城市的兩個中心山谷，這些軸按照自然景觀布局。

城市組織的致密化是通過圍繞這兩個軸進行一系列干預來實現(xiàn)的，此類干預將集成核推向北方，同時與外部保持強大聯(lián)系，并使新興的變形網(wǎng)格成形。城市結構向西的擴張保持了周邊特征，也被低整合度值轉化，而未對當時的空間構形產(chǎn)生明顯影響。

1948年的地圖（圖6）顯示了兩個結構性南北軸線的北部擴展，并顯示了集成核如何沿這些軸線擴展，并與外部保持很強的聯(lián)系。在東北部山谷中確定的軸線變得至關重要，其在城市中心附近的區(qū)段人口密集。然而，此軸線的擴張相比城市中心區(qū)北部山谷的擴張程度較輕。

網(wǎng)絡的東西向擴展雖然在外圍，但增加了核心的整合度（在地圖上顯示為紅色結構）。從現(xiàn)在開始，關鍵集成核的形狀就像變形的輪胎花紋邊緣。然而，由于城市的地形，連接到這些邊緣的長半徑不會在焦點處向內(nèi)完全會聚，以形成堅固的內(nèi)部中心。變形網(wǎng)格致密化需要建造新的住宅區(qū)才能實現(xiàn)，并伴隨網(wǎng)絡向北和東北的擴展。

從現(xiàn)在開始，城市進入了一個動態(tài)擴張時期，從而推動了戰(zhàn)略基礎設施的發(fā)展。這一增長包括開辟了幾條“動脈”，房地產(chǎn)開發(fā)商和私營建筑商推動的住宅區(qū)和其他設施的建設，以及從1940—1970年開展的大規(guī)模公共運營。

1997年的地圖（圖7）顯示了城市結構的規(guī)模越來越大、城市網(wǎng)格的密集化以及新城市網(wǎng)格的多樣化?！笆兄行摹眳^(qū)域第一次大大降低了其中心性特征。全局集成核首先偏向北方，然后略微漂浮到西側和東側，并進一步向東北方向漂移。

這種擴張和重新定位的模式符合希列爾[4]所描述的“中心性悖論”，因為天然屏障的存在限制了邊緣到中心鏈接的效果。

圖7 / Figure 71997年軸向地圖:整合度；全局半徑1997 axial map: Integration; Global radius

圖8 / Figure 82017年軸向地圖:整合度；全局半徑2017 axial map: Integration; Global radius

如2017年地圖（圖8）所示，1997年之后發(fā)生的主要變化是已有結構的東北向擴張，此前一處廢棄和貧困的海濱因世博會（1998年世博會）在當?shù)嘏e辦而改造為混合功能類開發(fā)項目。該世博會展覽區(qū)成為城市的新交匯點和長廊區(qū)。然而，從整個城市空間結構來看，此地的作用微不足道，不會導致自1948年以來已建立的中心移位或增長。

城市結構向西的擴展保持了周邊特征，也是由低整合度值轉化而來，對空間構形沒有結構性影響。城市網(wǎng)格的逐步致密化過程也減少了周邊區(qū)域的隔離程度，同時提高了中心核心整合度。

集成核的規(guī)模增加并且其結構得到加強（雖然并不顯著），向北略微移動，大大降低了市中心的中心性。然而，中心核心與城市其他部分之間缺乏結構連續(xù)度，表現(xiàn)為與城市網(wǎng)格連接為一體的中心軸和局域軸之間缺乏連續(xù)度。

第2部分：城市形態(tài)的新興屬性

對這些地圖的歷時分析表明，里斯本的拓撲中心性在18世紀地震后由有些不規(guī)則的網(wǎng)格模式演變?yōu)楦€性的結構和變形的網(wǎng)格，這是由于19世紀末在兩個南北軸上建立了更深的腹地滲透。城市結構的北擴推動了南北軸線而不利于東西軸線，并推動集成核向北推進，促使城市活動遠離海濱地區(qū)。南北軸既是里斯本城市轉型過程中的里程碑，也對20世紀發(fā)展起來的新城市擴張起到支持作用。盡管這些結構軸具有戰(zhàn)略性特征，但似乎該城市已經(jīng)發(fā)展成為各種城市網(wǎng)格的獨特大雜燴。對當前城市地圖（2017年地圖）局域空間結構的分析將證實這一假設。

圖9 / Figure 92017年線段地圖:選擇度—半徑1（r1）1分鐘/80m距離2017 Segment map: Choice - radius 1 minute1 (r1) 1 minute / 80 meters distance

圖10 / Figure 102017年線段地圖:整合度—半徑3（r3）3分鐘/240m距離2017 Segment map: Integration - radius 1 minute3(r3) 3 minutes / 240 meters distance

圖11 / Figure 112017年線段地圖:選擇度—半徑3（r3）3分鐘/240m距離2017 Segment map: Choice - radius 1 minute3 (r3) 3 minutes / 240 meters distance

圖12 / Figure 122017年線段地圖:選擇度—半徑10（r10）10分鐘/800m距離2017 Segment map: Choice - radius 1 minute10 (r10)10 minutes / 800 meters distance

圖13 / Figure 132017年線段地圖:整合度—半徑10（r10）10分鐘/800m距離2017 Segment map: Integration - radius 1 minute10(r10) 10 minutes / 800 meters distance

可以就各種半徑進行局域分析。出于該解釋性研究的目的，使用80m、240m、400m、800m、1,200m和2,400m半徑，分別對應于表1所示步行時間。此后，將根據(jù)時間而非距離描述半徑值。圖9顯示1分鐘距離內(nèi)的“選擇度”值（r1）。請注意，在此分析半徑范圍內(nèi)，只有歷史悠久的中世紀地區(qū)中心線段才有一定的“選擇度”。這些區(qū)域呈現(xiàn)幾何不規(guī)則的結構，并且線段長度（和街區(qū)大?。┬∮谄骄?。雖然從典型句法分析的角度來看r1作用不大，但在此示范性語境中引人注意，因其代表了穿越活動在極短旅程（80m）中的潛力。考慮到半徑如此之窄，所有長度小于160m的線段都無法提供超出其自身的可達性。唯一具有一定有效能力、在提供差異化可達性（接近度或選擇度）方面能力較為突出的線段對應于長度小于160m的線段。同時，考慮到分析算法的性質(zhì)，長度不是唯一決定因素，因為連接度亦是關鍵因素。因此，該半徑將突出顯示尺寸減小但具有顯著連接度的線段。顯然，這種情況會更頻繁地發(fā)生在城市較舊的地區(qū)，因為那里街區(qū)面積較小。

當分析半徑變?yōu)?分鐘（240m）時，差異是顯而易見的。一些地區(qū)在此規(guī)模上呈現(xiàn)出顯著的整合度（圖10）。此外，其中一些地區(qū)具有明確規(guī)定的核心。還應該指出的是，北部地區(qū)內(nèi)其他較新地區(qū)的整合度變化程度較小，盡管其具有顯著的整合度值。

圖11顯示了基于相同半徑（3分鐘，240m）的“選擇度”值。同樣，只有中世紀的區(qū)域包含在引導本地流動方面能力較為突出的線段。

現(xiàn)在讓我們考慮基于更大半徑（半徑800m/10分鐘）但仍在這些區(qū)域范圍內(nèi)的活動潛力（圖12、圖13）。

最古老的區(qū)域再次在“選擇度”方面突出體現(xiàn)為具有一致的值分布（圖12），而在整合度方面（圖13）則失去相關性。新興結構覆蓋了位于“市中心”區(qū)域和緊鄰區(qū)域的較舊的軸。這種結構保證了兩個中心谷的連接。但是，請注意中世紀地區(qū)現(xiàn)在是如何被顯著地隔離，盡管其地理位置或連接度未變化。

此分析先前支持的觀點是中世紀地區(qū)有自己的結構和明確的層次，這在分析半徑較低時可見。然而，應注意，當半徑較大時（即使仍在步行距離內(nèi)），這些特征會消失（圖14和圖15以及30分鐘半徑）。

圖14 / Figure 142017年線段地圖:選擇度—半徑30（r30）30分鐘/2,400m距離2017 Segment map: Choice - radius 1 minute30 (r30) 30 minutes / 2,400 meters distance

圖15 / Figure 152017年線段地圖:整合度—半徑30（r30）30分鐘/2,400m距離2017 Segment map: Integration - radius 1 minute30(r30) 30 minutes / 2,400 meters distance

半徑30分鐘范圍內(nèi)的“選擇度”值表明該區(qū)域（圖14）幾乎完全不具備活動潛力。雖然這些區(qū)域的隔離變得明顯，但此隔離與此類區(qū)域的地理中心性形成對比（圖15）。這并不意味著這些區(qū)域已經(jīng)失去了任何屬性，但是考慮到整個城市網(wǎng)絡，在半徑較大時的隔離程度意味著這些區(qū)域在某種程度上失去了作為到達活動和穿越活動載體的作用。城市網(wǎng)格的增長并沒有加強這些區(qū)域與其核心的聯(lián)系，因此使其自身閉合。這是一種經(jīng)常出現(xiàn)的現(xiàn)象，可以將城市結構轉變?yōu)橐幌盗胁豢伤甲h且?guī)缀跏桥潘男⌒彤數(shù)噩F(xiàn)實面貌。當基于更大半徑進行分析時，這種現(xiàn)象會加劇。

現(xiàn)階段，我們將澄清這一分析，旨在說明空間句法的方法論，并盡可能地強調(diào)其在城市規(guī)劃和設計中的作用。毋庸置疑，這些街區(qū)應該消除隔離，或者應該進行改造，以在半徑更大時起作用。盡管如此，此分析仍可用于重新考慮其全局整合度狀況，同時保留特定本地特征和優(yōu)勢。此外，應該注意的是，提高整合度并不一定意味著從城市網(wǎng)格的中心點開啟直軸，但這一點最終可以通過一系列小的變化來實現(xiàn)，這些變化重新定義了視覺和物理可達性的一些對齊方式。

圖15顯示了可以視為里斯本市當前中心的區(qū)域。中心核心幾乎完全與城市其他地方分離?？煽吹接膳c城市網(wǎng)格連接為一體的局域結構支持的連續(xù)度軸線。與“選擇度”值（圖14）相比，可以看出，在20世紀初建造的兩個結構軸的南部各區(qū)段普遍作為穿越活動元素。隨著半徑較低時的可達性/移動性增加，這可以解釋市中心區(qū)商業(yè)活動的持續(xù)性（而房地產(chǎn)的主要區(qū)域已經(jīng)向北遷移），同時服務集中度越來越高，從而導致這些區(qū)域周圍出現(xiàn)專業(yè)化趨勢。

通過對里斯本大都市區(qū)（AML）進行簡要分析，可以清楚地看到，其集成中心位于里斯本市，該市大部分區(qū)域與其集成中心相吻合。然而，如圖16所示，在局域半徑（15分鐘）內(nèi)，出現(xiàn)了具有單個可見集成核的多個區(qū)域，從而形成了局域中心。這表明里斯本的自治權有所下降，說明許多此類局域中心有其自身的當?shù)爻鞘猩睢?/p>

該地圖還突出強調(diào)了里斯本市為主要局域中心的地位。圖17描繪了全局半徑的算法，顯示了具有最大到達活動潛力的路徑。應該注意的是，突出顯示的線條如何與AML的高速公路和其他結構可達性相一致。此外，在此層面上，里斯本的位置似乎并沒有顯得特別突出。然而，通過更詳細的分析可以發(fā)現(xiàn)，與其他中心不同，基于全局半徑的這些選擇度元素與基于局域半徑的選擇度元素以及局域和全局半徑整合度突出元素一致。這種空間一致性是一項基本特征，揭示了有關城市群功能和韌性的一個非常重要的因素：協(xié)同作用，其通過以下互連實現(xiàn)：①各種類型的活動，即分別通過整合度與選擇度算法表征的到達活動和穿越活動；②每種活動各自不同的空間范圍（半徑）。

圖16 / Figure 16里斯本大都市區(qū)—線段地圖:整合度—半徑15（r15）15分鐘/1,200m距離Metropolitan Area of Lisbon - Segment map: Integration - radius 1 minute15 (r15) 15 minutes / 1200 meters distance1 minute

結 語

該分析完全依賴于城市構形，并突出城市主要結構及局域子結構，以及與構形本身直接相關的主要和局域循環(huán)軸。但是這種分析方法本身效用有限。事實上，該算法缺乏證據(jù)，即尚未采用適用于空間使用，并可用于評估句法（理論）模型實際適應性的“真實”算法。

沒有有效的城市交通系統(tǒng)，城市就無法生存?；顒訉θ藗兊纳钪陵P重要，是當今城市宜居性和效率的關鍵組成要素。大多數(shù)城市正在努力實現(xiàn)的宜居性以及與之相應的城市經(jīng)濟健康狀況都取決于其適應和管理流動性的能力。為實現(xiàn)此目標，城市設計師再也不可忽視城市交通系統(tǒng)與城市構形的相互作用。

獲得實證性證據(jù)后，句法分析即可為戰(zhàn)略中長期目標的短期決策提供信息。通過識別在引導活動方面具有最大潛力的線段，可以整改城市構形以響應需要客流量的商業(yè)活動的需求。此外，如果特定區(qū)域內(nèi)的交通流量應處于較低水平，則可以通過更改構形來實現(xiàn)。同樣，有關區(qū)域在整合度（及其使用）方面的理論潛力知識可用于規(guī)劃和管理城市空間，以強調(diào)或減輕這一特征，而無論其是否對城市運作有影響。此外，句法方法論還可以用于預測構形變化的影響，從而促進城市規(guī)劃和城市設計策略的實施。

圖17 / Figure17里斯本大都市區(qū)—線段地圖:選擇度—全局半徑Metropolitan Area of Lisbon - Segment map: Choice -global radius 1 minute

Understanding Urban Changes Through Space Syntax:The Case of Lisbon

Teresa V. Heitor, Jo?o Pinelo Silva

Introduction

The space syntax research field is grounded on the pioneering work of Bill Hillier, Julienne Hanson and colleagues, developed in the early 1970's at the Bartlett School of Architecture,University College London. Its origins can be traced back to the article entitled “The man-environment paradigm and its inconsistencies”(Hillier, 1973). But it was the article “Space Syntax” (Hillier et al., 1976) that fi rst mentioned the name and theoretical basis that was to be developed with space syntax, later detailed in the books The Social Logic of Space (Hillier and Hanson, 1984) and Space is the Machine (Hillier,1996).

Beyond its interpretive capacity of human spatial systems and on insightful inferences of their social meaning and form-function impact, Space Syntax is supported on a synthetic and expressive visual representation of space, the so-called axial map. The axial map consists of the smallest set of axes - axial lines - covering the whole spatial system. Such representation forms the basis of the “syntactic model”, and it is on this basis that the syntactic analysis is performed,constituting an apparently abstract representation of how spatial systems are con fi gured. Although it is sometimes criticized as simplistic, or reductive, by excluding other urban or architectural features, phenomena and occurrences, focusing exclusively on the spatial con fi guration, it can be argued that syntactic representations are, on the contrary, extremely rich as they arguably embed aspects of the cognitive processing of spatial information.

Unlike the typical efforts of graphical representation of a physical reality (as in drawing or mapping), the syntactic representation does not aim at reproducing the metric and geometric properties. Instead, to a certain extent, it embodies the physical and visual experience of occupying the space, i.e. the continuity experienced by those who navigate the spatial network which is the urban environment. Thus, the axial map does not portray visual obstacles per se (such as buildings, trees, etc.), but rather the spatial network and its potential accessibility based on continued visual perception. In this way, rather than reductionist, space syntax representations are rich because they are not cognitively inert to the way the network of spaces (streets) is seen/experienced by the observer (user), leading to the creation of a configuration that the user might use to navigate. Syntactic representations can be described as “embodied diagrams”, as they re fl ect the bodily presence in the space.

Syntactic analysis is based on rigorous mathematical descriptions using a set of algorithms developed within the graph theory. The axial graph of an axial map is a graph in which the vertices or nodes correspond to the axial lines and two vertices are adjacent if and only if the corresponding axial lines intersect. The axial graph contains information about the connection of each axial line with all the others that constitute the system and allows to analyzing the relative position of each line in relation to all the other lines. In this way, the properties obtained do not vary with the individual conditions of each line,but with their position (topological) in the system where it is inserted.

Several syntactic measures have been created and tested by the space syntax community. The success of each measure was evaluated by its ability to re fl ect (correlate with) urban and architectural phenomena, such as pedestrian or motorized movement, type of land use, rent values.Regardless of its good performance in terms of linking the model to real measurable phenomena, the axial map has always made evident a mismatch with urban morphology in the sense that an axial line can extend over several blocks,which sometimes means very different from the point of view of comparative phenomena.The solution was to break the axial lines at their intersections. Thus, the segment map was born in the context of Space Syntax, being accepted today as the best way to represent the urban space. However, this creates a further problem:since the algorithms are based on the topological depth, when an axial line is transformed into segments, depth is generated, which has an undesirable effect on the results. The answer to this problem, most commonly used by the spatial syntax community, is the angular analysis of segments (Turner, 2001, Turner, 2007). This analysis calculates the ‘cost' of moving from one segment to the next, not in topological terms(where each segment implies an increment of cost), but in angular terms (for which larger angles correspond to higher costs). Thus, moving in the same direction has zero cost, i.e., the continuity of the axial line is simulated. The theoretical foundation for this procedure relates to the perception and navigation in urban environment,as mentioned above.

Of all the measures developed and tested by the spatial syntax community, two stand out for their ability to analyze urban con fi gurations: “Choice”and “itegration”. Choice (called “Betweenness Centrality” in graph theory) can be described as a measure of potential passing traf fi c and is measured by calculating the least cost (angular; accumulated change of direction) path between all possible origin/destination (OA) pairs (in which each element of the map/graph is considered as possible origin and destination. Those elements that cumulatively belong to the lowest cost paths between all source/destination pairs will most often present higher values of choice (note that this sum is then divided by the total number of possible trips). On the contrary, elements that cumulatively meet less frequently on the sum of all least cost paths will have lower choice values.

“Integration” (called “Closeness Centrality” in graph theory) is the second relevant measure for the analysis of urban configurations. It is a measure of the degree of centrality and usually emphasizes those spaces in the city that the common citizen would call the main streets, where a large part of specialized commerce is located,often associated with the functional concept of an urban centre. Typically, integration analysis was done on the axial map. However, since there would be an advantage in using this measure in the segment map, the algorithm used in the axial map had to be updated. As in the case of “choice”,when one moves from the analysis of the axial map to the analysis of the segment map, instead of “counting” the depth in topological terms, this is done in angular terms (where larger angles imply higher cost).

These two syntactic measures are also related to the concept of “natural movement”, i.e. the proportion of urban pedestrian movement determined by the grid con fi guration itself (Hillier et al. 1993) and allow allow establishing a parallelism between the value of ‘integration' of a space and its potential to be understood as a destination in random movements (to-movement) and between the value of ‘choice' and the probability of a space to be used as a crossing point in such journeys in which it is neither origin nor destination (through-movement).

With the aim of illustrating the use of spatial syntax methodology to explore how the expansion of the city can transform the potential of,the existing spatial structure, we study the city of Lisbon. The analysis follows a diachronic process, grounded on historical maps, back to the date when the old medieval city center -downtown - was massively destroyed by seismic activity, followed by a fire and a tsunami in 1755. Although the history of Lisbon extended many centuries before this earthquake, the eighteenth-century downtown reconstruction has generated some sort of “ground zero” clearing situation from the point of view of the spatial structure (Heitor et al. 1999). The pre-earthquake medieval grid was replaced by an orthogonal grid that rationally and pragmatically reordering the new ‘downtown' area. This structural grid remains almost intact up to now.

Jo?o Pinto Ribeiro, “Planta topográfica da Cidade de Lisboa arruinada também segundo o novo Alinhamento dos Architectos Eugénio dos Santos e Carvalho e Carlos Mardel”, (Topographic plan of the ruined city of Lisbon also under the new alignment of architects Eugénio dos Santos e Carvalho and Carlos Mardel) n.d., copy.The study has involved the ‘cartographic redrawing' of a set of eight maps of Lisbon published respectively in 1785, 1855, 1871, 1911, 1948,1970, 1997 and 2005 (updated by 2017) corresponding to distinct stages in the evolution of the city over a time span of about 230 years. These maps were decomposed into axial and segment maps thus allowing a spatio—temporal analysis of the evolution of the urban fabric by combining axial and segment angular analysis. Space Syntax Toolkit (Gil 2015) a front end to Depthmap(Turner 2004) was used to calculate, integration and choice patterns on global and local scales and to obtain a general picture of the city spatial centrality condition. These maps are colored on a scale ranging from blue to red, where blue represents the lowest values and red the highest values. The reading is done between the classes presented, according to Equal Interval classi fi cation Method.

Based on a visual inspection of the eight axial maps, i.e. in a qualitative rather than a quantitative approach, we show the generic ‘rules' of the urban growth process. Global scale analysis is used to represent the degree of convergence and dispersion of the urban grid. We then show some emergent properties of the contemporary urban form. Local-scale analysis at different radii is applied to grasp the local structure at the neighborhood scale. On this basis, we suggest a key clari fi cation of the generic structure of the city of Lisbon.

The Generic Rules of the Urban Growth Process

The 1785 map (Figure 2) shows the “downtown”orthogonal grid as the center, i.e., the most integrated zone of the urban grid (higher values of integration) and the strong level of segregation of the eastern zone corresponding to the old medieval districts, where the Castle is located.These observations are also significant from a methodological point of view. On the one hand the more integrated area does not correspond to the geometric center of the urban grid; on the other hand, the area around the castle is almost as central as the “downtown” but with higher levels of segregation. Similar levels of segregation are only reached at the western side of the grid, as the eastern side presents less topological distance to the center. Noted that the con fi guration of the river bank, in the form of a bay to the east of the downtown, does not allow a direct east-west link, which necessarily creates topological distance and therefore segregation. Also,note that within the “downtown” area there is a differentiation between the east-west axial lines and the north-south ones. The lower values of the east-west lines are a consequence of the lack of continuity and connection, which in this particular case is due to the topographic conditions.The 1855 map (Figure 3) follows a similar hierarchically pattern. The new connections that were established to the northeast of the city do not have significant implications in the spatial structure.

On the other hand, changes in the built fabric are clearly understandable on the 1871 map (Figure 4). A new embankment was immediately built to the west of the “downtown”, to prevent the river from fl ooding the adjacent area, and a new axis was opened along the riverfront. This new axis replaced the existing ones and created new and more directed connections to the north-south axes. This change produced a signi fi cant increase in the integration values of the western part of the urban grid. Although it may seem surprising,all integration values have slightly decreased(including all red lines) due to a significant change of the configuration without a proportional growth of the system. In simple terms, this phenomenon can be interpreted as a redistribution and dilution of the spatial integration of the whole system.

The 1911 map (Figure 5) shows for the fi rst time the hinterland penetration through the opening of two “arteries” perpendicular to the river,linking the downtown area to the northern and north-western peripheral zones, which turned out to be the symbol of a modern city, i.e., the modernization blueprint. These axes were laid out according to the physical landscape, following the city's two central valleys.

The densification of the urban tissue occurs through a set of interventions carried out around these two axes, pushing the integration core towards the north with strong links to the outside and giving shape to an emergent deformed grid.The expansion of the urban fabric to the west maintains a peripheral character, also translated by low values of integration, not imposing distinct impacts on the spatial con fi guration at that time.

The 1948 map (Figure 6) displays the northern expansion of the two structural south-north axes and shows how the integration core has grown to spread out along these axes, with strong links to the outside. The axis de fi ned in the North-Eastern valley becomes essential, being densely populated in the section near the city's center. However, its expansion became secondary in relation to that of the Northern valley, in the central area of the city.

The eastern and western expansion of the network, although peripheral, increased the integration level of the core (on the map seen as the red structure). From now on the key integrators shape like the rims of a deformed wheel pattern.However, due to the topography of the city,the long radials linking to those rims do not fully converge inward at a focal point to create a robust internal hub. The densification of the deformed grid entails the construction of new residential areas and is accompanied by the expansion of the network towards the north and northeast.

From now on the city entered a period of dynamic expansion which drove the development of strategic infrastructures. This growth included the opening of several “arteries” and the construction of residential areas and other facilities promoted by real estate developers and private builders as well as large-scale public operations,carried out from the 1940's up to 1970's.

The 1997 map (Figure 7) shows the increasing size of the urban fabric and the densi fi cation of the urban grid as well as the diversity of new urban grids. For the fi rst time, the “Downtown”area has substantially reduced its character of centrality. The global integration core has biased fi rst towards the north, then marginally fl oated to the west and east sides and further towards the northeast.

This pattern of expansion and relocation corresponds to “the paradox of centrality” as described by Hillier (1996) since the possibility of the effect of forming an edge to center links is limited by the presence of natural barriers.

As illustrated in the 2017 map (Figure 8), the main change that occurred after 1997 corresponds to the Northeast expansion of the built fabric, following the renewal of a derelict and deprived waterfront into a mix-used development which took place by the occasion of the World Exhibition (Expo 98). The exhibition area became the city's new meeting point and a promenade area. Nevertheless, it has a very insignificant contribution from the point of view of the spatial structure of the city as a whole. It does not entail a displacement or growth of the centre as already established since 1948.

The expansion of the urban fabric to the west maintains a peripheral character, also translated by low values of integration, not having a structural impact on the spatial configuration. This gradual densification process of the urban grid also reduces the segregation of the peripheral areas, while increases the levels of integration of the central core.

Although not significantly, the integration core increases in size and its structure is strengthened,shifting slightly to the north and substantially reducing the centrality of the downtown. However, there is a lack of structural continuation between the central core and the rest of the city,expressed by the lack of continuity between central and local axes connecting the urban grid in an articulated continuum.

Part 2: The Emergent Properties of the Urban Form

The diachronic analysis of these maps revealed that Lisbon's topological centrality evolved after the 18th-century earthquake from a somewhat irregular grid pattern to a more linear structure and deformed grid due to deeper hinterland penetration of two south-north axes built at the end of the 19th century. The northern expansion of the urban fabric, while promoting the South-North axes in detriment to the East-West ones and pushing the integration core towards the north had contributed to moving urban activity away from the waterfront districts. The South-North axes perform both as a landmark in the Lisbon urban transformation process and a support for the new city expansion developed along the 20th century. Despite the strategic character assumed by these structural axes, it seems that the city has evolved into a unique collage of various urban grids. The analysis of the local spatial structure of the current city map (2017 map) will con fi rm this assumption.

Local analysis can be done at various radii.For the purpose of this explanatory study, 80m,240m, 400m, 800m, 1200m and 2400m radii are used, corresponding to walking times as illustrated in Table 1. Hereafter the radii values will be referred to in time and not in distance.Figure 9 shows the “choice” values within 1-minute distance (r1). Note that, at this radius of analysis, only segments at the heart of the historic medieval districts have some degree of“choice”. These districts present a geometrically irregular structure, and the segment length (and block size) is smaller than average. Although r1 is not particularly useful from the standpoint of a typical syntactic analysis, it is interesting in this demonstrative context since it represents the potential of through-movement in particularly small journeys (80m). Considering such a narrow radius, all the segments with less than 160m length do not allow access beyond themselves.The only segments with some effective capacity to stand out for offering a differentiated level of accessibility (proximity or choice) correspond to segments with less than 160m in length. Simultaneously, given the nature of the analytical algorithms, the length is not the only determining factor, being the connectivity the key element.Thus, this radius will highlight segments of reduced dimensions but with signi fi cant connectivity. Obviously, this will occur more often in the older parts of the city, where the size of the block is smaller.

When the radius of analysis is changed to 3 minutes (240 meters,) the difference is obvious.Several districts present a signi fi cant level of integration at this scale (Figure 10). Also, some of them have a clearly de fi ned core. It should also be noted that other more recent districts in the northern area show a smaller degree of variation of integration, in spite of their significant integration values.

Figure 11 shows the values of “choice” at the same radius (3 min, 240 meters). Again, just the medieval districts contain segments that stand out in terms of their capacity to channel local fl ows of movement.

Let us now consider the potential of movement with a larger radius (radius 800m/10min) but still within the scale of these districts (Figure 12 and 13).

Once again, in terms of “choice”, the oldest districts stand out with a consistent spread of values (figure 12), but in terms of integration(Figure 13) they lose relevance. The emerging structure covers the older axes, positioned in the“downtown” area and in the immediately adjacent areas. This structure guarantees the linkage of the two central valleys. However, notice how the medieval districts now became signi fi cantly segregated, although their geographical location or connectivity did not change.

This analysis has previously supported that medieval districts have their own structure and a well-de fi ned hierarchy, which is visible at lower radii of analysis. However, it is noted that at a larger radius (even though still in walking distance) these features disappear (Figures 14 and 15 and 30-min radius).

The values of “choice” within a 30-min radius,excludes this area almost completely (Figure 14)from having potential for movement. Although the segregation of these areas becomes evident,it contrasts with their geographical centrality(Figure 15). It does not mean that the areas in question have lost any attribute, but the degree of segregation at larger radii means that they somehow lost their role as carriers of both to and through-movement, considering the whole urban network. The growth of the urban grid did not reinforce the connection to their nucleus, thus leaving them closed on themselves. This is a frequent phenomenon that can transform the urban fabric into an inarticulate set of small, almost exclusively, local realities. When the analysis is performed at larger radii, this is exacerbated.

At this stage, we shall clarify that this analysis aims to illustrate the methodology of spatial syntax and to highlight as much as possible of its role in urban planning and design. It is not argued that these neighborhoods should lose their segregation, or they should be transformed to have a structure that works at greater radii.Nevertheless, this analysis can be used to rethink their global integration condition while retaining their particular local features and advantages.Also, it should be noted that increasing integration levels would not necessarily imply the opening of direct axe from a central point of the urban grid, but could eventually be achieved through a set of small changes that redefined some alignements of visual and physical accessibility.

Figure 15 illustrates what can be considered the present center of Lisbon. The central core is almost completely dissociated from the rest of the city. There are axes of continuity supported by local structures that join the urban grid

in an articulated continuum. When compared with “choice” values (Figure 14), it is visible the prevalence of the south sections of the two structuring axes built at the beginning of the twentieth century as the through-movement elements. Along with greater accessibility/mobility at lower radii, this could explain the persistence of commercial activity in the downtown area while the prime area in terms of real estate has already moved up to the north, together with an increasing concentration of services, which has been led to a tendency for specialization around these areas.

A brief analysis of the Metropolitan Area of Lisbon (AML) clearly shows that its integration center is located in Lisbon, mostly coinciding with its integration center. However, as shown in Figure 16, in a local radius (15 min), a diversity of areas with a visible integration core arises, thus forming local centers. This reveals a decrease in the autonomy of Lisbon, suggesting that many of these local centers will have their own local urban life.

This map also highlights the city of Lisbon as the dominant local center. Figure 17 depicts the measurement of the global radius, showing the pathways with the greatest potential for to-movement. It should be noted how the lines highlighted coincide with AML's motorways and other structuring access. Also, at this level,Lisbon does not seem to present a particularly prominent position. However, a more detailed analysis allows one to detect that, unlike the other centers, these elements of choice of the global radius coincide with elements of choice at the local radius, as well as prominent elements of local and global radius integration. This spatial coincidence is a fundamental characteristic,revealing a very important factor for the functioning and resilience of urban agglomerations -synergy - achieved through the interconnection of: a) various types of movement, namely to and through-movement, respectively represented through the measures of integration and choice;b) various spatial ranges (radii) of each type of movement.

Final Remarks

This analysis relies exclusively on the city's configuration and highlights the city's primary structure as well as local substructures, main and local circulation axes which are directly related to the con fi guration itself. But this analysis per se has a limited utility. In fact, there is a lack of evidence, i.e., “real” measures of space usage have not yet been collected, which will allow to evaluating the practical aptitude of the syntactic(theoretical) model.

Cities cannot survive without an effective urban mobility system. Movement is absolutely critical to people's lives and is a key component of the livability and ef fi ciency of our cities today. The livability that most cities are striving for, and accordingly the health of the city's economy,is dependent on its ability to accommodate and manage mobility. To this end, urban designers can no longer afford to ignore how it interacts with the urban con fi guration.

When completed with empirical evidence, the syntactic analysis can inform short-term decisions with strategic medium- to long-term objectives. The identi fi cation of those segments with the greatest potential for channeling movement allows for the rectification of the urban configuration to respond, for instance, to the needs of commercial activity, which requires footfall.Also, if traf fi c fl ow should be kept low in a specific area, it is possible to achieve that through changes in the configuration. Similarly, knowledge of the theoretical potential of areas in terms of integration (and their use) allows planning and managing urban space in order to emphasize or mitigate this characteristic, whether or not it has implications for the functioning of the city. Moreover, the syntactic methodology also affords predicting the impact of changes to the configuration, which facilitates the implementation of both urban planning and urban design strategies.