A Fractal Perspective on Scale in Geography

TL;DR

This paper advocates for a fractal geometric perspective to better understand and address scale-related issues in geography, challenging traditional Euclidean views and emphasizing the importance of scale-dependent and fractal properties of geographic features.

Contribution

It introduces fractal geometry as a paradigm shift in geographic analysis, providing new methods to handle scale issues like the MAUP and spatial heterogeneity.

Findings

Fractal geometry explains the scale dependence of geographic features.

Scale issues like the MAUP are inherent and manageable within a fractal framework.

Topological and scaling analyses improve understanding of spatial heterogeneity.

Abstract

Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution, and the modifiable areal unit problem (MAUP). This paper argues that the confusion and frustration mainly arise from Euclidean geometric thinking, with which locations, directions, and sizes are considered absolute, and it is time to reverse this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we introduce topological and scaling analyses based on street-related concepts such as natural streets, street blocks, and natural cities. We further contend that spatial heterogeneity, or the fractal nature of geographic features, is the first and foremost effect of two spatial properties, because it is general and universal across all scales. Keywords: Scaling, spatial heterogeneity, conundrum of length, MAUP, topological analysis