Figure 3.

(a) Lacunarity curves of 49 cities (in grey) and the four archetype cities (in colour) shown on a log$(\mathrm{\Lambda })$ vs log(r) plot. The cities with a concave downwards shape in the upper side of the diagonal indicate larger and more aggregated gaps, whereas cities underneath the curve indicate a more uniform dispersed pattern of islets and smaller gaps. (b) Histogram of ${\mathrm{\Lambda }}_{score}$ of 49 cities (mean = 0.04, s.d. = 0.38). (c) Scatter plot of percolation transition range and Lacunarity score. This figure illustrates the classification of cities into the 2 classes based on Lacunarity Score and the type of transition. (d) Scatter plot of Mean Relative Heat Islet Size (A_M) versus ${\mathrm{\Lambda }}_{score}$. Additionally, since the islet-size distribution is heavy tailed, in addition to the A_M, the largest islet size (A_L, as a percentage of the total city area) is indicated using the marker size. The A_M and A_L serve to illustrate the size distribution of the hottest islets occupying the ten percent of the city area.