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The long lots system, also known as the ribbons farming system, is a historical land use pattern, which can be encountered in some specific regions of the world, including in North America, both in the Nouvelle-France, and in the New-Mexico regions. In this paper, we show that, in the late 1990s, the first publications on Constructal Theory, which discussed topics such as urban street patterns or airport systems design, already contained the principles underlying the emergence of the man-made long lots system, but had not yet been linked to land use patterns such as the ribbons farming system. We show that this farming pattern is driven by the Constructal Law. It leads to land use geometries similar, at a human scale, to computer cooling systems. In brief, like many natural designs, the long lots system emerges as a "urge to organize" under local and global constraints specific to the economy of agricultural products trade, and according to the Constructal Law of evolving flow systems. The design of long lots systems can thus be viewed as a historical precursor of the Constructal Design approach, an approach worth considering in the design of sustainable cities.

The parabolic scaling of rank-size distributions is a very common phenomenon in natural or societal systems such as city sizes, petroleum reservoirs, or galactic intensities. Often, the divergence from a log-log linear power-law is explained by the finite size of the system studied. Several distribution functions were also proposed to best fit this kind of distribution, such as the parabolic fractal or the stretched exponential. In order to explain the emergence of this rank-size distribution pattern, we propose instead to consider a generic mechanism of constructal tree-shaped invasion of a territory combined with the constructal rank-size distribution of a growing flow architecture as the mechanism potentially generating a wide variety of parabolically scaling distributions. Simulations of this mechanism were conducted and we showed that it generated shorter and curved distribution tails similar to a parabolic scaling. In conclusion, we propose to consider the constructal law as the first principle behind the generation of parabolic scaling of rank-size distributions in natural, societal, and engineered systems.

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