Related papers: Scaling and Universality in City Space Syntax: bet…
Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their…
We address the role of multiplicative stochastic processes in modeling the occurrence of power-law city size distributions. As an explanation of the result of Zipf's rank analysis, Simon's model is presented in a mathematically elementary…
Zipf's law can be used to describe the rank-size distribution of cities in a region. It was seldom employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf's law…
We present a broad, phenomenological picture of the distribution of the length of open space linear segments, $l$, derived from maps of 36 cities in 14 different countries. By scaling the Zipf plot of $l$, we obtain two master curves for a…
The rank-size regularity known as Zipf's law is one of scaling laws and frequently observed within the natural living world and in social institutions. Many scientists tried to derive the rank-size scaling relation by entropy-maximizing…
Zipf's law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city…
A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon…
The encoding of cities into non-planar dual graphs reveals their complex structure. We investigate the statistics of the typical space syntax measures for the five different compact urban patterns. Universal statistical behavior of space…
Urban scaling and Zipf's law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about…
The rank-size distribution of cities follows Zipf's law, and the Zipf scaling exponent often tends to a constant 1. This seems to be a general rule. However, a recent numerical experiment shows that there exists a contradiction between the…
A new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random phenomena such as cities. Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world…
In this article, I conduct a textual and contextual analysis of the empirical literature on Zipf's law for cities. Building on previous meta-analysis material openly available, I collect full texts and bibliographies of 66 scientific…
Scaling properties of language are a useful tool for understanding generative processes in texts. We investigate the scaling relations in citywise Twitter corpora coming from the Metropolitan and Micropolitan Statistical Areas of the United…
Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms and urban growth is one of the most eminent transformative processes. We analyze global land cover…
Two fundamental issues surrounding research on Zipf's law regarding city sizes are whether and why this law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf's law holds in a…
The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a…
The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most…
Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of…