While data sculptures date back from the 1990s, the very first sculptures were Venus figurines: A Venus figurine is any Upper Paleolithic statuette portraying a woman with exaggerated physical features. The oldest ones are about 35,000 years old. Right image: modern versions. Also see V.S. Ramachandran on the peak shift principle in art. Sources: Wikipedia article on Venus figurines. Left image from ancient-origins.net, right images from Mari Shiranui's flickr page and heldenshop.de.

An orrery is a mechanical model of the solar system. The left image shows the Antikythera, the oldest known orrery. The middle image shows a virtual reconstruction. The right image shows a contemporary orrery. The Antikythera mechanism is an ancient analog computer designed to predict astronomical positions and eclipses. It was recovered in 1900–01 from the Antikythera wreck, a shipwreck off the Greek island of Antikythera. The instrument was designed and constructed by Greek scientists and has […]

The first terrain/city models date back from the 16th century and were created for military purposes. Left image: a plan-relief of Bayonne, created by Sébastian Vauban (1633–1707), a famous fortification engineer of King Louis XIV. Right image: a plan-relief of Grenoble from 1848. These scale models were highly prized for the tactical advantage they brought, and they were also shown around for dissuasive purposes. “Il y a un relief de Namur dans les Tuileries, je vous demanderai d'avoir la […]

During the 18th century, instrument maker George Adams built and sold solid 3D geometric models as educational complements to the 2D images found in Euclid's Elements of Geometry. As argued by a 18th-century author: It is almost as necessary as in mechanics, to exhibit the objects, whose qualities are to be taught; and to call in the joint assistance of the hands and eyes. According to the Whipple Museum of the History of Science, authors were already experimenting with paper models soon after […]

Left image: As part of its 2014 exhibition entitled Mind Maps: Stories from Psychology, the London Science Museum showcased this very accurate and intricate papier-mâché brain model from 1900 that shows path of nerve fibers. French physician Louis Thomas Jerôme Auzoux developed this technique around 1820 due to the shortage of human cadavers and wax models to study human anatomy. He was inspired by papier-mâché dolls that were common at the time. His models became popular in schools, […]

Between 1839 and 1853 the French mathematician Théodore Olivier created string models to teach and demonstrate descriptive geometry, some of which could be manipulated. He was a student of French mathematician Gaspard Monge, who invented descriptive geometry and was already illustrating his ideas with rudimentary string models. Photo above: intersection of two cylinders. Sources: Nicholas Mee (2013) Strings, Surfaces and Physics. Photo above taken in the Musée des Arts et Métiers in Paris, see […]

In the 19th century, mathematicians became interested in the question how mathematical functions look like. Felix Klein, a German mathematician, had several of such physical models in his lab in Göttingen, and popularized them in America when he brought a boatload to the World's Fair in Chicago in 1893. The photo above shows a model of a Clebsch surface from 1880, designed and presumably built by Adolf Weiler, Klein's grad student. It is kept today at the University of Göttingen. Sources: […]

These three-dimensional maps were carved by inuits from the Ammassalik Fjord in Greenland, and used as eyes-free guides for sailing. The left one shows coastline, the right one shows a sequence of offshore islands. These inuit communities had had no direct contact with Europeans before a Danish explorer met them in 1885 and was shown the wooden maps. Sources: Bill Buxton (2007). Sketching User Experiences. page 36. Wikipedia. Ammassalik wooden maps.

Bronze sculpture showing the phases of the flight of birds, created by French scientist Étienne-Jules Marey in 1887 based on photographs. Étienne-Jules Marey was a pioneer in the study of dynamic phenomena and invented a variety of scientific and medical instruments, photography techniques, and temporal visualization methods. A wealth of information is available about him online. Also see our entry on Peter Jansen's movement sculptures, inspired from his work. Sources: Russel Naughton (2007) […]

Spanish Catalan architect Antoni Gaudí disliked drawings and prefered to explore some of his designs — such as the unfinished Church of Colònia Güell and the Sagrada Família — using scale models made of chains or weighted strings. It was long known that an optimal arch follows an inverted catenary curve, i.e., an upside-down hanging chain. Gaudí's upside-down physical models took him years to build but gave him more flexibility to explore organic designs, since every adjustment would […]

The boundaries of the United States transformed during the 19th century, often through violent means. Mapmaker James Ives created this mechanical map to help people, especially students, visualize these changes. Sources: Leventhal Map Center (2019) Tweet. Boston Rare Maps (2016) Fantastic mechanical map of United States territorial expansion. Video by the Leventhal Map Center.

Model by Alexander Crum Brown (1838-1922) of a half-twist mathematical surface, featuring a non-Euclidean so-called Klein bottle, c. 1900. Sources: Photo from the Science Museum, London, textual description courtesy of Klaus Hentschel. For more, see Klaus Hentschel (2014): Visual Cultures in Science, Technology and Medicine, pp. 96ff. and pl. XIV.

These cams are solid models of bivariate and univariate mathematical functions plotted in cylindric coordinates (left and middle images) and polar coordinates (right image). They were not meant to be visually examined, but were used in mechanical analog computers for aiming battleship guns during WWII. They were also called computing cams. Mechanical fire control aids started to be developed in the 1900s and and were still in use in the late 1980s. During WWII, they could solve multivariate […]

Illustrator and model-maker Roger Hayward (1899-1979) working on a model of the lunar surface for the Griffith Planetarium, 1934. Sources: Kevin Kidney (2009) Mr. Hayward's Moon Model. Photo from Keven Kidney's blog, textual description courtesy of Klaus Hentschel. For more, see Klaus Hentschel (2014): Visual Cultures in Science, Technology and Medicine, pp. 217-226.

A large rotating relief globe showing Ford company's industrial sites around the word, exhibited at the Chicago World's Fair in 1934. Sources: Willard Cope Brinton (1939) Graphic Presentation, p. 160. The Henry Ford Blog (2013) Ford at the Fair. More photos from the Henry Ford Online Collection.

As a response to devastating floods of the Mississippi river in the early 1900s, the US Army Corps of Engineers built a large-scale hydraulic model of the entire river system. The model, 2.5 times the size of Disneyland, allowed them to design better flood control infrastructures and to eventually save millions of dollars. In 1973, the physical model ceased to be used and was replaced by computer models. Nevertheless, mathematical equations still cannot capture all the complexity of river […]

The MONIAC or Phillips machine is a hydromechanical analog computer built to teach basic economical principles using colored water flowing in transparent pipes. The machine was built in 1951 after electrical-engineer-turned-economist William Phillips and his economist colleague Walter Newlyn realized that flows were used as a metaphor to teach economics, but have never been made physical. Phillips is also known for his eponymous curves. Several MONIACs were built, and a working one is […]

A working hydrodynamic model of San Francisco Bay and the surrounding waterways, with tides. It is still open to the public as a demonstration, although it is no longer used for research. Also see our related entry 1949 – Mississippi River Basin Model. Source: Wikipedia U.S. Army Corps of Engineers Bay Model.

The "Great Polish Map of Scotland" is a 50 x 40 m concrete terrain model of Scotland. It was built by a Polish sergeant who stationed in Scotland during WWII and ended up living there. It is claimed to be the world's largest terrain model, although the Chinese built a 900 x 700 m model in 1999. Source: Atlas Obscura. Great Polish Map of Scotland.

Alexander Dewdney is a Canadian mathematician and computer scientist who authored the recreational mathematics column in the Scientific American magazine from 1984 to 1991, after Martin Gardner and Douglas Hofstadter. In 1984, he describes a number of imaginary analog computers he calls "Analog Gadgets", which can in principle solve computing problems instantly. The first one, shown on the left image, uses spaghetti to sort numbers. The second one uses strings to find the shortest path in a […]

In 2006, a mysterious 900x700m solid terrain model with military facilities was discovered by a German Google Earth user next to the Chinese town of Huangyangtan. It was quickly identified as a 1:500 replica of a disputed area in Tibet between China and India 2400km away, with perfectly matching orientation. Chinese authorities claimed the model was built 7-8 years earlier as a tank training facility. It is unclear whether the right image represents the same model. Sources: Newswatch (2011) The […]

A 90 cm tall Clebsch bicubic surface hand made in resin and fiber. It includes all lines lying inside the surface. Also see our entry 1880 – Klein’s Mathematical Plaster Models for an earlier version made of plaster. Sources: Cayetano Ramirez. obratano.com (alternative website) Cayetano Ramirez (2006) Creation process for the transparent Clebsch surface.

Dutch artist Peter Jansen creates sculptures of moving characters by merging successive snapshots into a single monolithic object. These are not physical visualizations as they do not display data, but the technique could certainly inspire the creation of physical visualizations for complex temporal data. The idea of merging time slices is reminiscent of the pioneering work of Étienne-Jules Marey in the 1880s on chronophotography. See our entry on Marey's movement sculptures. Source: Peter […]

A commercial offer for a set of 10 plush distributions. Although not formally physical visualizations, they could in principle encode actual data. Source: web shop

Top: Tele-present water by David Bowen is an actuated surface controlled by wires and servo-motors that replicates sea wave patterns measured in real time in a remote location. Bottom: Underwater is a larger-scale version created by the same author. Sources: David Bowen (2011) Tele-present water series. David Bowen (2012) Underwater series.

Everardo Reyes-Garcia from Université Paris 13 turns video sequences into space-time shapes that can be 3D printed. The sculpture above represents 5 seconds of the opening theme of Game of Thrones. Also see our entry on Peter Jansen's sculptures. Source: Everardo Reyes-Garcia (2013) Motion Structures.

Mount Saint Helens is an active volcano located in the north-west of the United States. In an eruption in 1980, the upper section of the volcano was destroyed, reducing the peak's elevation from 2950 m to 2549 m. This two-part 3D printed model of Mount Saint Helens visualizes the dramatic change that occurred over a very short period of time. The digital data for 3D printing and the white and red model were prepared by Drew Thompson, the green model was printed by Jeppe Vestergaard. Sources: […]

This table created by the furniture design company Duffy London is a geological cross-section of the sea shown with layered wood and glass sheets. Designer Christopher Duffy got the idea while visiting a glass factory and noticing that glass sheets darken as more layers as added, as does the sea. You can have this piece of furniture at home for £9,800. Sources: Duffy London (2014) Abyss Table. Nina Azzarello (2014) Duffy London layers the abyss table to look like ocean depths.

Andrew Chard, an award-winning graduate student in architecture at Oxford Brookes, created this multi-layered wooden map where layers can be individually pulled out and rearranged. According to the object's legend, this map shows different cities on top of each other so that people can compare their structure. There is not much information available online but Andrew explained to us by e-mail: It was so long ago that I wouldn’t be able to remember the scale or locations I am afraid. Apart from […]

Kohei Nakajima and his colleagues argue that soft bodies are hard to control from a robotics perspective, but precisely because of their complex dynamics they can be used as information processing devices for solving hard computational problems. In a recent article they explain how they send inputs to a motor that wiggles a silicon tentacle, and read the system's output by sensing the arm's posture. I'm not entirely sure what's being calculated exactly, but the idea seems quite compelling. Also […]

Artist Ren Ri uses beeswax as his medium for making geographical maps and a bee colony as the builder. This original project results in beautiful data visualizations collaboratively crafted by a human and a bee colony! Here's how it works: Because a colony will follow the queen bee and build a hive based on the pheromones that she releases, Ri is able to move the queen such that the others in the colony act accordingly. More details on the project can be found on the Flowing Data blog [1]: The […]

Paper models of terrain/landscape. Mapquest Elevation API is used to gather the elevation isolines and the paper layers are cut on a blade cutter machine. Source: Peter's DIY Blog

Scientists keep using solid models to help them better understand complex 3D data (here, an astrophysical simulation): They say this provides even more insight into what’s going on. “The ability to hold and inspect the 3-D printed models provides a new perspective on the WWIR’s geometry and an improved sense of the scale of the different structures,” they say. In particular, they say the model allows them to appreciate just how large the shockwave is compared to the stars and the distance […]

Jewelry made with data from the US Geological Survey. Source: Courtney Reckord.

Christian Freksa, a professor of Cognitive Systems at the Department of Informatics at the University of Bremen, shows how a shortest route can be computed by 3D-printing the route network using flexible material, and then pulling apart the start and end nodes. The tight portion of the network immediately gives the shortest route. The right image shows an earlier version using strings. This idea was first proposed by mathematician George Minty in 1957, in a short letter to the editor of the […]