Printing Data: Using 3D printing technology to turn population data into statistical sculpture

Dr Jon Minton, University of Glasgow


We live in a three dimensional world – of x, y and z – as well as a complex, social world. But in our analysis of social phenomena, we too often restrict ourselves to just to the two dimensions of x and y. Much of this restriction in modes of analysis is due to the technology we’ve been used to working with: extruded two dimensional planes such as papyrus, canvas, paper and monitor screens. But the determinants of many forms of social patterning and change are inherently at least three dimensional, and by exploring such patterns we can better understanding the complex interactions that exist between any two factors in influencing a third. Without such understanding, we risk misunderstanding and misrepresenting the fabric of the social world into which we are stitched, of not recognising how the rich pageant of lived experiences have changed, of how what was typical becomes rare, what is rare was once typical, and how social life is likely to change over many years and decades.

An inherently three dimensional representation of complex social change is the Lexis surface, which can be thought of as a map of ‘temporal space’. Instead of longitude, we have the year in which events occur, and instead of latitude, we have the ages of human populations for whom such events have occurred. Such events range from living (reaching a given age in a given year) to dying, to everything in between, such as getting married, getting a house, getting a driving licence, completing a qualification, being convicted of a crime, and so on. Within this temporal space, the rates of amounts of these events, occurring at each distinct combination of age and year, can be thought about as a ‘height’ over a continuous age-year surface. Visualising and understanding these surfaces is key for understanding a great many forms of important social patterns and change.

Map-makers have long developed solutions for representing a three dimensional surface on a two dimensional plane – contour lines, colours and shades can all be used to convey the sense of topographic change over a spatial plane, and without such representations large scale movements of human populations would be much more challenging. But though maps can convey a sense of changing height, and thus stop armies marching over ravines, and hill walkers trying to walk into cliffs, the visceral sense of how a surface’s height and features can only be conveyed through three dimensional representations: physical models and sculptures.

Map-makers’ methods can be applied to produce maps of population data as much as topographic data, and such approaches can reveal important insights into complex patterns of population change and population difference. However, the visceral sense of these data surfaces, the deep intuition about how things change with place, with population, with age and over time, can only be conveyed by seeing such three dimensional surfaces as three dimensional objects. For this reason I have turned over 40 data surfaces into 3D printed data sculptures.


Using data primarily from the Human Mortality Database and the Human Fertility Database , but also using data from the Scottish Government, I have produced a series of what I call ‘Lexis cubes’ since 2015, funded primarily from the University of Glasgow’s Chancellor’s Fund scheme. Using the statistical programming language R, the process for producing the instructions for 3D printing was fairly straightforward. The event, rate or risk of interest – population size, mortality rate, fertility rate or conviction rate – was calculated for each of many different countries, and each gender, for all available years and most available ages. These rates by age and year were then rearranged to form matrices of cells, whose row position represented their year, column position their age, and value the ‘height’ of the surface at each age-year coordinate. These matrices were then used to produce stereolithography (STL) files, a long series of three dimensional coordinates used by 3D printers as instructions for where to place new layers of molten plastic onto existing layers, or by computer-aided manufacture (CAM) lathes, as instructions for where to excise material from rectangular blocks of wood or other solid materials. In either case, additive manufacture using 3D printing or subtractive manufacture using lathes, the result is the same: a physical representation of three dimensional population data.

Given that R is a programming language, and programs are good at automating processes, producing the instructions, the STL files, for dozens or hundreds of different populations only takes fractionally more time than producing them for just one or two populations, and these files, along with the code used to make them, have been made available online. Selecting any STL file produces a computer-generated representation of the data, which can be interacted with online, allowing users to assess whether that particular data sculpture can be, and should be, printed. By clicking on the ‘download’ button from the same web addresses, or by downloading the whole collection and viewing the files directly, the STL files themselves can be seen, saved, and sent to a 3D printer, along with additional instructions about the physical dimensions of the object to produce.

So far, most 3D data sculptures made have been produced using a company based in London, 3DPrintUK, which uses a high-end 3D printer to fuse together powdered nylon in fine layers. The resolution produced by this printer, its capacity to print fine details on the surfaces of the Lexis cubes, to reproduce sharp edges and ridges on these surfaces that otherwise may be unprintable, and the general durability of the finished products, have all been excellent. The majority of the objects produced have been with a diameter of an 8 cm cube, small enough to fit on the palm of a hand while large enough for subtle features, such as the changing texture of the surface, to be easy to see. Some additional surfaces, allowing comparison between two or more populations’ Lexis surfaces, have also been produced in other dimensions to allow side-by-side comparisons.

Uptake and Impact

The statistical sculptures have travelled the world – from Austria to Australia – and been exhibited at over a dozen events for the general public and specialist quantitative social science researchers alike. At a recent gathering of data visualisation experts in Rostock, Germany, they attracted the attention of Periscopic, a specialist data journalism company based in the US, most famous for producing a shocking and affective depiction of premature mortality caused by gun violence; Nikola Sander, whose paper with Guy Abel in Science introduced circular and interactive flow maps as a means of understanding complex process of migration throughout the globe; and Ralf Ulrich, a professor of Public Health based in the University of Bielefeld. Intrigued and inspired by the approach, Prof Ulrich, with the support of Puentes Zegarra, developed a 3D sculpture for showing population projections for the population of Berlin, from 1991 to 2030. Like a conventional population pyramid, male and female population sizes by age appear on opposite sides of a common axis, but unlike standard, flat population pyramids the object has depth to represent time, allowing patterns of cohort ageing and migration to be observed as well. (Aesthetically, the semi-symmetric quality of this sculpture is reminiscent of a Christmas tree!)

As well as being exhibited for many audiences, the 3D sculptures have also been blogged about for the International Journal of Epidemiology, providing more detailed and widely accessible description and discussion about how the approach can be used to understand complex patterns of population change. Recently, the same data, concept and approach used to produce the 3D printed objects have formed the basis of a successful application for funding to develop both academic and commercial applications of virtual reality technology – such as Oculus Rift – for pedagogic purposes. Just as the physical data sculptures allow complex data visualisation to be a tactile as well as simply visual experience, so virtual reality will allow users to be immersed in these data landscapes on a much larger scale. Combined with maps of Lexis surfaces, physical data sculptures and virtual reality technology allow for the physical qualities, and social implications, of such data surfaces to be understood and experienced as never before.

Dr Jon Minton was a Research Associate on the AQMeN Urban Segregation and Inequalities research strand. For more information about this work, visit the AQMeN Research WordPress site. You can also follow Jon on Twitter via @JonMinton