The Spatiotemporal Organizational Order of Living Circle Units Based on the Law of Walking Time-Distance Distributions

The unclear time-distance decay law between supply and demand, which makes it difficult to coordinate their fairness, is a key factor in the disordered spatiotemporal development of supply and demand. In order to advance the standardized renewal of living circles with a people-oriented approach, this paper clarifies the time-distance decay law between supply and demand embedded in residents’ walking time-distance distributions and explores the spatiotemporal organizational order of supply and demand in living circle units aligned with this law. First, 24 sets of walking time-distance distribution data, each showing significant distribution differences, were standardized using a mean-based transformation relative to their own time-distance means, resulting in an observable law of relative time-distance distribution. Subsequently, an explanatory mechanism for the relative time-distance distribution was constructed based on the generation and decay effects of the relative time-distance between standard supply and demand. A functional model was fitted and verified, indicating that the decay law of the relative time-distance follows a negative exponential function with a parameter value of 2.08, and the time-distance threshold has a stable twofold relationship with the time-distance mean. Finally, by drawing an analogy between living circle units and the relative time-distance distribution and taking their standards as the mean time-distance, the study explored the layout relationships among living circle units. The spatiotemporal organizational order for same-level units was characterized by “one form where the time-distance mean and threshold serve as the service radius and influence radius, and another where supply and demand are placed at 0.5 times the time-distance mean inside and outside, respectively”. For different-level units, the order featured “one form where the center of the upper-level spatiotemporal unit is located at the four corners of the lower-level units, with a service radius twice that of the lower-level unit. Another form ensures coordination of service radius differences between upper and lower units through a twofold speed relationship in travel modes, guaranteeing relative fairness in travel time consumption for the same type of supply across different levels”. Additionally, an ideal layout pattern for living circle units was proposed, featuring a “snowflake-shaped” facility layout and a “twice-speed” transfer method. The findings suggest that the 15, 10, and 5 min living circle planning is not merely about the availability of services within their time-distance standards, but about ensuring multifaceted accessibility fairness for residents within these standards.