Urban street networks of unplanned or self-organized cities typically exhibit astonishing scale-free patterns. This scale-freeness can be shown, within the maximum entropy formalism (MaxEnt), as the manifestation of a fluctuating system that preserves on average some amount of information. Monte Carlo methods that can further this perspective are cruelly missing. Here we adapt to self-organized urban street networks the Metropolis algorithm. The “coming to equilibrium” distribution is established with MaxEnt by taking scale-freeness as prior hypothesis along with symmetry-conservation arguments. The equilibrium parameter is the scaling; its concomitant extensive quantity is, assuming our lack of knowledge, an amount of information. To design an ergodic dynamics, we disentangle the state-of-the-art street generating paradigms based on non-overlapping walks into layout-at-junction dynamics. Our adaptation reminisces the single-spin-flip Metropolis algorithm for Ising models. We thus expect Metropolis simulations to reveal that self-organized urban street networks, besides sustaining scale-freeness over a wide range of scalings, undergo a crossover as scaling varies—literature argues for a small-world crossover. Simulations for Central London are consistent against the state-of-the-art outputs over a realistic range of scaling exponents. Our illustrative Watts–Strogatz phase diagram with scaling as rewiring parameter demonstrates a small-world crossover curving within the realistic window 2–3; it also shows that the state-of-the-art outputs underlie relatively large worlds. Our Metropolis adaptation to self-organized urban street networks thusly appears as a scaling variant of the Watts–Strogatz model. Such insights may ultimately allow the urban profession to anticipate self-organization or unplanned evolution of urban street networks.

未经规划或自组织城市的城市街道网络通常表现出惊人的无标度模式。可以在最大熵形式主义（MaxEnt）内将这种无标度表示为波动系统的表现，该波动系统平均保留一定量的信息。可以进一步发展这种观点的蒙特卡洛方法被残酷地遗漏了。在这里，我们适用于自组织的城市街道网络Metropolis算法。通过将无标度作为先验假设以及对称守恒论点，使用MaxEnt建立“达到平衡”分布。平衡参数是缩放比例；假设我们缺乏知识，那么随之而来的大量信息就是大量信息。要设计遍历动力学，我们将基于非重叠步行的最先进街道生成范例分解为交汇处布局动力学。我们的修改使伊辛模型的单旋转翻转Metropolis算法变得让人想起。因此，我们希望Metropolis模拟能够揭示出，自组织的城市街道网络除了在各种规模上保持无标度之外，还会随着规模的变化而发生交叉变化。文学作品主张小世界交叉。在实际的比例指数范围内，伦敦市中心的模拟与最新技术的输出是一致的。我们以缩放比例作为重新接线参数的说明性的Watts-Strogatz相图说明了在现实窗口2–3内的小世界交叉曲线；它还表明，最新的产出是相对较大的世界。因此，我们的大都市适应自组织的城市街道网络似乎是Watts-Strogatz模型的缩放比例变体。这样的洞察力最终可以使城市专业人士预测城市街道网络的自我组织或计划外的演变。