Head/tail breaks

In the field of mapping, which aims to represent a territory through processes like generalization, classification, and symbolization, cartographers have traditionally prioritized geometric aspects such as size and shape, often overlooking topological and semantic dimensions. Fractal geometry, however, takes the opposite approach. It emphasizes topological and semantic relationships, making maps more insightful by highlighting meaningful geographical connections and structures (Jiang 2015:1–2).

To achieve this, the head/tail breaks method is frequently used to divide data or phenomena into hierarchical levels. This method identifies larger objects by repeatedly splitting them around an average value. In each division, the "head" consists of data points above the average, while the "tail" comprises those below it. This makes head/tail breaks particularly powerful for statistical mapping, generalization, and cognitive mapping, as it reveals the underlying hierarchical patterns within the data. Head/tail breaks is closely linked to fractal geometry, whose core principle, as Jiang (2015:3) points out, is that there are "far more small things than large ones". This principle reflects how complex systems are often composed of many small components and just a few large ones.

Mapping can, therefore, be seen as a head/tail break process that helps us generalize, classify, and symbolize data to create more meaningful maps. To illustrate the fractal geometry mindset, the Koch curve is a fitting example (Jiang 2015:3). Each iteration of the curve produces more small details than large ones, showcasing the essence of fractals. As the scale of the curve decreases by a factor of 3, the number of smaller segments increases by a factor of 4, clearly demonstrating the principle of "far more small things than large ones.".

Source: Jiang & Slocum (2020)

Lab 2 head/tail breaks

In the task "lab 2 head/tailbreaks" I learned how to apply the head/tail breaks method in ArcGIS and to compare head/tail breaks classifications with the conventional Jenks natural breaks classification method. The task consisted of three main parts where I was to perform head/tail breaks on point data, line and polygon data and on raster data. The results from this task are illustrated below.

For this part of the task, I classified the point data in ArcGIS Pro through both the head/tail breaks method and the Jenkins method. The points illustrate randomized data created in Excel. The result shows that depending on which data classification method is used, two different maps are created. In the left map produced by the head/tail breaks method, the map looks more vivid and natural while the map on the right produced by the Jenks method looks more unnatural.

The above maps represent the distribution of population density in Kansas City. Like the maps with point data, it appears that the map produced by head/tail breaks represents a more natural population distribution and a fairer representation of reality. The map produced by Jenk's method represents a more unnatural population distribution. This is because the method reduces the differences between high and low population density. This can create the illusion that there are more densely populated areas than there are, which in turn can cause, for example, skewed decisions in urban planning.

The above maps represent Manhattan streets and the number of connections for each street. The map produced with head/tail breaks is more meaningful as it visualizes which street is the most "popular", or in other words, has the most connections. This is a great example of how head/tail breaks can produce more meaningful maps through generalization, classification, and symbology. In the map produced by Jenks' method, this meaningfulness disappears, which can make critical thinking and problem-solving difficult when, for example, planners have to make decisions about road planning.

The above maps represent raster elevation data. The map produced by the head/tail breaks method represents the elevation data in a better way. This is because the method produces more pixels with low height values than high height values. As previously mentioned, the Jenks method minimizes the differences between high and low values, which makes the elevation data look more even which can give a distorted picture of reality. Therefore, raster elevation data illustrated by the head/tail breaks method illustrates the reality in a better way.

References

Jiang., B (2015). The fractal nature of maps and mapping, International Journal of Geographical Information Science, 29(1), 159–174.

Jiang B. and Slocum T. (2020), A map is a living structure with the recurring notion of far more smalls than larges, ISPRS International Journal of Geo-Information, 9(6), 388. Reprinted as the cover story in the magazine Coordinates, August issue, 6–17, 2020.

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