Left panel: sum of the length of the street segments of a given class as a function of time expressed in meters. Right panel: growth rate for the sum of the length of the street segments of a given class as a function of time expressed in meters/year.

<p>Left panel: sum of the length of the street segments of a given class as a function of time expressed in meters. Right panel: growth rate for the sum of the length of the street segments of a given class as a function of time expressed in meters/year.</p

The greenbelt surrounding London and the actual extension of London as calculated with the method introduced in the paper.

<p>The extensions of London's street network which appear to violate the green belt boundary are in fact filling in highly fragmented interstitial areas not included in the green belt.</p

In the left panel, we show the street intersection growth and the population growth for London as a function of time. To appreciate the correlations between the two phenomena we normalised both measures to unity. In the right panel, we show the variation of street intersections during time as a function of the number of intersections . This represents a strong violation of Gibrat's law.

<p>In the left panel, we show the street intersection growth and the population growth for London as a function of time. To appreciate the correlations between the two phenomena we normalised both measures to unity. In the right panel, we show the variation of street intersections during time as a function of the number of intersections . This represents a strong violation of Gibrat's law.</p

Street intersection density surfaces in the GLA area from 1786 to 2010.

<p>Street intersection density surfaces in the GLA area from 1786 to 2010.</p

Top-left panel: Street length distribution as measured in the GLA area in 1786 with exponential fit (). Top-right panel: Street length distribution for London as defined by the Jenks' algorithm about one century apart with lognormal fit ( for 1786, 1880, 2010). Middle-left panel: Parcel area distribution for the network generated by motorways, A and B roads in the 1965 GLA area with exponential fit (). Middle-right panel: Parcel area distribution for London with lognormal fit ( for 1786, 1880, 2010). Bottom-left panel: Total street length as a function of the number of intersections for the GLA area with allometric fit (). Bottom-right panel: Total street length as a function of the number of intersections for London with allometric fit ().

<p>Top-left panel: Street length distribution as measured in the GLA area in 1786 with exponential fit (). Top-right panel: Street length distribution for London as defined by the Jenks' algorithm about one century apart with lognormal fit ( for 1786, 1880, 2010). Middle-left panel: Parcel area distribution for the network generated by motorways, A and B roads in the 1965 GLA area with exponential fit (). Middle-right panel: Parcel area distribution for London with lognormal fit ( for 1786, 1880, 2010). Bottom-left panel: Total street length as a function of the number of intersections for the GLA area with allometric fit (). Bottom-right panel: Total street length as a function of the number of intersections for London with allometric fit ().</p

Number of occupied squares at scale for the intersection density maps and measurement of the fractal exponent .

<p>Left panel: For the GLA. Right panel: For the density <i>core</i> we define as <i>London</i>.</p

Left panel: Street intersections inside a 10 km side square in the non-urbanized area of the GLA in 1880. Right panel: Street intersections inside the same square in 1990.

<p>Left panel: Street intersections inside a 10 km side square in the non-urbanized area of the GLA in 1880. Right panel: Street intersections inside the same square in 1990.</p

The street network in the GLA (Greater London Area) from 1786 to 2010.

<p>Different road colours correspond to different road classifications (red A roads and motorways, blue B roads, gray minor roads).</p

Left panel: the average length of the street segments in London's urban core as a function of the number of vertices. The fitting function is a line, , (adj. ). Right panel: the total length of the network as a function of the number of vertices, fitted by Eq.4 ().

<p>Left panel: the average length of the street segments in London's urban core as a function of the number of vertices. The fitting function is a line, , (adj. ). Right panel: the total length of the network as a function of the number of vertices, fitted by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069469#pone.0069469.e076" target="_blank">Eq.4</a> ().</p

Our definition of London's street network, as the urban core of the GLA area derived using the Jenks clustering algorithm.

<p>Our definition of London's street network, as the urban core of the GLA area derived using the Jenks clustering algorithm.</p