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. 2015 Oct 6;12(111):20150763. doi: 10.1098/rsif.2015.0763

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© 2015 The Authors.

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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Figure 3. — Growth curve collapse for the cities in the UK and in California. (a,c) Rescaled maximum cluster size as a function of the rescaled threshold for the largest 61 cities in the UK and for the largest 52 cities in California. The dashed curve is (b,d) In order to evaluate the goodness of the collapse of the curves in (a,c), we plot in the horizontal axis the values for the cities in the UK (b) and in California (d) and in the vertical axis, the estimated value via the logistic function Then we calculate the R² value of the resulting points with the dashed curve y = x and we find that R² > 0.99 for both UK and California cities. (e–h) The same methodology as explained for (a–d) is applied for the number of street segments E(τ) for the cities of the UK and California. In this case, we find that the quality of the logistic collapse is given by R² > 0.99 for the UK and R² > 0.98 for California.

Inline graphic — Growth curve collapse for the cities in the UK and in California. (a,c) Rescaled maximum cluster size as a function of the rescaled threshold for the largest 61 cities in the UK and for the largest 52 cities in California. The dashed curve is (b,d) In order to evaluate the goodness of the collapse of the curves in (a,c), we plot in the horizontal axis the values for the cities in the UK (b) and in California (d) and in the vertical axis, the estimated value via the logistic function Then we calculate the R² value of the resulting points with the dashed curve y = x and we find that R² > 0.99 for both UK and California cities. (e–h) The same methodology as explained for (a–d) is applied for the number of street segments E(τ) for the cities of the UK and California. In this case, we find that the quality of the logistic collapse is given by R² > 0.99 for the UK and R² > 0.98 for California.