There are three fundamental issues about geographic space or the Earth’s surface: How it looks, how it works, and what it ought to be. In terms of how it looks, there are two laws governing geographic forms or urban structure: scaling law and Tobler’s law. Scaling law is available across all scales ranging from the smallest to the largest, and it states that there are far more small things than large ones in geographic space. Tobler’s law is available at one scale, and it states that more or less similar things tend to be nearby or related. Geographic forms or urban structure (how it works) changes nonlinearly, so they are unpredictable essentially. In terms of what it ought to be, there are two design principles that help make better built environment: differentiation and adaptation, in line respectively with the scaling law and Tobler’s law. In this presentation, I will use two concepts of natural cities and natural streets to demonstrate the ubiquity of scaling law, and further argue how to make built environment more living or more sustainable based on the two design principles. Linked to these two concepts are the two tools we developed:

Axwoman for topological analysis of large street networks (http://giscience.hig.se/binjiang/axwoman/), and head/tail breaks for scaling analysis of geographic features (https://en.wikipedia.org/wiki/Head/tail_Breaks). I will further elaborate why GIS representations such as raster and vector fail to capture the living structure of geographic space or the Earth’s surface, and present a topological representation that is truly multiple scales – multiple scales in one representation.