The Power Behind Physical, 3-D Visualizations

Near the entrance to the Mariposa Grove of Giant Sequoias in Yosemite National Park is an unusual map. Rather than showing either the contours of the terrain (bare ground) or the shape of the surface (treetops and buildings) it’s a three-dimensional model that renders hundreds of mature giant sequoia in full relief, and the remaining surroundings as simple topography, stripped of vegetation.

Photograph of a bronze 3 dimensional model of the mature giant sequoias in Mariposa Grove, Yosemite National Park. Most of the bronze is dark, but the passers-by touching the edges and tops of the tallest trees have worn away the patina, revealing the shiny metal beneath.
Mariposa Grove, Yosemite National Park.
Photo ©2018 Robert Simmon. CC-BY-SA 4.0.

A few steps away is the footprint of a tree, replicated in stone. Dozens of feet across, it conveys the scale of these colossal trees in a way that you otherwise can’t get, even standing next to one.

Photograph of a stone outline of the base of a giant sequoia Mariposa Grove, Yosemite National Park. Dark rock represents the thick bark, while light rocks cut into square blocks and arranged radially represent solid wood.
Mariposa Grove, Yosemite National Park.
Photo ©2018 Robert Simmon. CC-BY-SA 4.0.

Both of these exhibits are examples of physical visualization — data represented in space beyond the constraints of paper or screen. Together, they demonstrate many of the technique’s benefits.

By expanding into an additional dimension, the map allows direct comparison of the size and shape of the most prominent trees. In a flat map, those qualities would have to be encoded with abstract visual parameters (shape, size, color, etc.). This encoding increases the amount of thought and attention required to parse the information in the map. Direct representation leaves more mental bandwidth to explore and understand a visualization, rather than using it on interpreting symbols or abstractions.

Also noticeable are the bright and shiny tips of the most prominent trees — polished smooth by curious visitors. The tactile display draws attention and even encourages direct interaction. People who may have glanced at or totally ignored a traditional map of the grove are drawn to interact with a physical one.

Likewise, the full-size representation of a sequoia’s base encourages engagement, inviting viewers to step into the footprint. This gives a sense of scale that is absent even from the base of a living tree. Our limited stereoscopic vision just isn’t up to the task of evaluating the size of an object that rivals monumental sculpture for size (the largest giant sequoia are roughly the size of the Statue of Liberty). But by stepping into a full-scale representation of a tree’s base, one can better conceive the bulk of a living tree.

Our limited stereoscopic vision just isn’t up to the task of evaluating the size of an object that rivals monumental sculpture for size.

Despite often relying on industrial techniques for their construction, I consider many examples of physical data visualization to be handcrafted because of the thought and attention required to design them. Every detail is intentional, and can be used to better convey the information contained within.

Consider the subtle traces of trails in the bronze map, or the different materials used to indicate a tree’s bark and heartwood in the giant sequoia’s footprint.

Another feature of physical representations of data is the ability to convey three spatial dimensions. I won’t say “without distortion” since we only see in something like “2.5-D” (a term often used to describe vintage games like Doom, where there are x, y, and z coordinates but no overlapping spaces). In general, our brains know how to accurately interpret shapes based on visual stimulus. But any 2-dimensional representation (a screen or sheet of paper) of a 3-dimensional surface will be incomplete.

Breaking Boundaries with Globes & Models

This limitation applies acutely to maps — all maps will distort at least one of these four properties: area, distance, angle, and direction. For large scale maps (maps that show a limited area) these issues are usually moderate, but for small scale maps (those showing a wide area, like a continent or even the entire Earth’s surface) the distortions can get out of hand.

A time-honored solution to the constraints of flat maps is the globe — wrap a map around a sphere and area, distance, angle, and direction are all well preserved (leaving aside the fact that the Earth isn’t quite a sphere).

Globes are created by printing gores — slices of the Earth surface between lines of longitude — that are then pasted onto a substrate. The image below shows 24 gores used in Adolf Henze’s 1891 globe (the “the largest printed globe produced in the 19th century” according to the Rumsey Map Center). Unfortunately they don’t have any photos of an assembled globe made from these gores, but they do have a spiffy interactive 3D render.

Scan of a world map subdivided into 24 gores — 12 for the Northern Hemisphere and 12 for the Southern Hemisphere. Each gore spans 30 degrees of longitude.
World map composed of twelve globe gores, published by Adolf Henze in 1891.
David Rumsey Map Collection, David Rumsey Map Center, Stanford Libraries. CC BY-NC-SA 3.0.

Compare the projection used for the gores with the same map in a geographical projection (a simple grid of latitude and longitude, also known as a Plate Carrée, rectangular, or simple cylindrical projection) shown below. Shapes, angles and distances are all better preserved by the gores, but only after they’ve been assembled in 3D space.

Scan of a world map subdivided into gores that has been remapped to a simple cylindrical projection. This map projection represents the Earth’s surface as a rectangle twice as wide as it is high. This progressively distorts shape and area to the north and south of the Equator. Lines of longitude — only hairlines on the original map — widen like funnels near the North and South Poles.
Henze globe reprojected into the geographical projection. Notice how the thin lines of longitude spread as they get close to the North and South Poles.
David Rumsey Map Collection, David Rumsey Map Center, Stanford Libraries. CC BY-NC-SA 3.0.

A final advantage of a globe over a flat map — there are no edges! Sail as far as you want, you won’t fall off.

Mapping the surface of the Earth onto a plane is hard enough. Mapping a complex of tunnels and subterranean mining claims beneath a mountain in desolate western Nevada is another challenge altogether. This particular scenario was faced by the owners and operators of the Comstock Lode mines, a rich silver and gold deposit located beneath Virginia City, Nevada. Knowing the exact location of the mine workings was critical for construction of the tunnels, safety of the workers, and (of course) to ensure the claim owners profited.

To get a sense of the challenge of interpreting a three-dimensional network in the two dimensions of paper, take a look at the following two maps. The first is a cross-section through Mount Davidson, showing the vertical location of ore veins and shafts, paired with a top-down view of mining claims. 

Map of mining claims in the Comstock Lode, Virginia City, Nevada. Across the top of the map is a cross-section delineating the depth of claims, while the main body of the map uses colored polygons to indicate the areal extent of claims.
Map of the Comstock Lode and the Washoe Mining Claims in Storey & Lyon Counties, Nevada.
Image from the Barry Lawrence Ruderman Map Collection, courtesy Stanford University Libraries.

The second is a top-down view of the complex of tunnels deep within the earth, with colors indicating depth.

Scan of a map spanning two pages of a book showing mine tunnels (called "drifts") in the Comstock Lode. Color is used to indicate depth, with the result that areas with many overlapping tunnels look like tangled spaghetti.
Horizontal Map Virginia Mines Workings, Comstock Lode.
David Rumsey Map Collection, David Rumsey Map Center, Stanford Libraries. CC BY-NC-SA 3.0.

Having trouble re-creating a mental map of these tunnels? Yeah, me too. And I suspect the original engineers who built these tunnels had similar issues, so they built a model, which is now located at the The Way It Was Museum in Virginia City. In this model spatial relationships which are nearly impenetrable on paper come to life.

Photograph of a scale model housed at the Way It Was Museum in Virginia City, Nevada. The tunnels are abstracted as straight, colored lines, much like most subway maps. Prints of vintage photographs above the model show the city in its heyday, while photos and drawings behind the model show miners at work.
Close-up photograph of the Comstock Lode model, showing brightly-colored tunnels. The Sutro Tunnel, which carried water away from the deepest shafts, is featured prominently.
An exact scale model of the northern end of the famous Comstock Lode, the portion lying directly beneath Virginia City. This model shows all the principal mine shafts, crosscuts, drifts, winzes and inclines.
Photos taken in The Way It Was Museum by a friendly librarian.

3D Models of Abstractions & Microcosms

The examples I’ve shown so far have all been one form of map or another, but multi-dimensional data doesn’t need to be spatial, and physical visualizations aren’t limited to representing places.

This visualization of electricity usage in the city of Manchester (known as a “load model”) shows three abstract variables. Each card represents the amount of electricity consumed in Manchester, England every 30 minutes over 24 hours. Look closely and you can see that each day is carefully annotated with details like min and max temperature, times for sunrise and sunset, and details of the weather.

Photograph of "Electricity generated or demanded in Manchester, 1951–1954." This type of visualization is known as a "load model", which represents power consumption in three dimensions. Each day is represented as a piece of cardboard, with the top edge of the cardboard cut away to form a column chart with the height of each column representing electricity demand over 30 minutes. The daily cards are stacked tightly together, so the tops create a 3-dimensional surface that indicates power usage over several years.
Electricity generated or demanded in Manchester, 1951–1954.
Via Science Museum. CC-BY-SA 4.0.

Stacked together, the cards transform from a two dimensional representation to a three dimensional one, adding a day of year axis to time and power (in Megawatts). This allows viewers to see seasonal patterns of energy use in addition to the rhythms of night and day. (Thanks to Valentina D’Efilippo for making me aware of this amazing model.)

Sometimes, a physical representation of data isn’t meant to communicate, but is an essential part of the interpretation of experimental results. For example, crystallographers — scientists who study the arrangement of atoms in matter — used models to unravel the structure of complex organic molecules like penicillin, insulin, and DNA.

X-ray crystallography is an essential technique used to determine the arrangement of atoms within molecules. The process involves beaming x-rays, which have a wavelength similar to the size of a single atom, through a crystal. Since the atoms in the crystal are arranged in a regular pattern, the x-rays diffract (just like ocean waves will diffract around a pier or visible light waves will diffract through a narrow slit) as they pass through it. This creates a pattern of amplified and attenuated x-rays which is then captured on film. By recording these patterns taken from different orientations of the sample, a crystallographer can calculate the pattern of “electron density” in a crystal, which corresponds to the molecular structure.

During World War II, Dorothy Hodgkin led a team of crystallographers investigating the structure of penicillin. X-ray diffraction patterns were deciphered slice by slice, with each atom represented by concentric rings of electron density — the more rings, the heavier the atom. (See Modeling the Structure of Penicillin for an excellent animation showing the process.) Hodgkin drew the contours onto sheets of clear acrylic, which she then stacked to create a 3D model of the crystal (below). The groundbreaking research earned her the 1964 Nobel Prize in Chemistry.

Three dimensional model of the structure of penicillin constructed with stacked sheets of clear plastic. Electron density of individual atoms is represented by concentric rings hand drawn in black ink. Heavier atoms are larger than lighter atoms, with a larger number of rings. The overall effect is to give an impression of each atom as a somewhat nebulous blob.
Model of the Structure of Penicillin, Dorothy Hodgkin, Oxford, c.1945.
© Museum of History of Science, University of Oxford. CC BY-SA 3.0.

A more conventional representation of molecular structure is the ball-and-stick model (below, again by Hodgkin). Also a form of data physicalization, these models identify each atom and represent the bonds between them, at the cost of portraying atoms as solid spheres. In reality, atoms are fuzzy blobs of probability. A characteristic I find better represented by the hand-drawn electron density model.

Ball and stick model of the structure of penicillin. Atoms are represented by plastic spheres (colors distinguish elements from one another), and atomic bonds are represented by thin steel rods. Behind the model are three drawings of electron density arranged at right angles. The blobby electron density diagrams contrast sharply with the hard balls.
Molecular model of penicillin by Dorothy M Crowfoot Hodgkin, England, 1945.
©The Board of Trustees of the Science Museum. CC BY 4.0.

Another application for data physicalization is as a means to preserve delicate samples. The Harvard Natural History Museum’s collection of glass flowers (the official name is “The Ware Collection of Blaschka Glass Models of Plants”) is one such example. These exquisitely sculpted models capture ephemeral objects — flowers in bloom, a blighted apple — in a durable form that’s able to be handled and examined long after the original specimens have decayed.

Close up photograph of a model of a rhododendron flower on display at the Harvard Museum of Natural History. Despite being made of glass the model is lifelike. The flower petals are light pink while the leaves (out of focus due to the depth of field of the photo) are green.
Glass flower model on display at the Harvard Museum of Natural History.
Photo by angela n. via Flickr. CC BY 2.0.

Even something as abstract as a statistical concept can be captured by physical models. The Eames’ Mathematica exhibit (currently installed in the Boston Museum of Science, New York Hall of Science, and Henry Ford Museum) includes a giant bean machine (also known as a Galton Board) that creates a real-life binomial distribution through balls bouncing off pegs and into narrow columns. Each column functions as a concrete histogram or bar chart, the more balls, the higher the column. Even though the fine details of each run differ, the overall shape — a bell curve — is re-created every time.

Photograph of the back of a child framed by a red bell curve painted onto clear glass. The smooth bell curve is superimposed on individual columns (each divided by glass) partially filled with black balls. The combined columns form a coarse histogram that largely follows the idealized shape of a normal distribution.
Binomial distribution from Charles & Ray Eames’ Mathematica exhibit at the Museum of Science, Boston.
Photo by Matt Cottam via Flickr. CC BY-NC-ND 2.0.

Despite the utility of conventional data visualization, there’s something uniquely powerful about data made tangible. Information presented in a concrete way invites viewers to interact with the data in ways that many visualizations on paper or screen do not. Viewers are free to change perspective to reveal something hidden, or pick out an interesting detail to examine more closely. Interactivity that is inherent in data physicalization needs to be deliberately added to 2D visualizations. I suspect that is a big part of the appeal of scrollytelling (another medium that takes a surprising amount of manual work to do well), and an avenue of exploration in virtual reality.

A downside of data physicalization is the expense of creating physical objects, both in material and time. On the other hand, the expense compels creators to think carefully about their work, which is a key ingredient in crafting compelling data viz.

NOTE: This is a reprint from the original article that ran here.

Robert Simmon is a pioneering designer and visualizer renowned for his work in cartography and science communication. With decades of experience at Planet and the NASA Earth Observatory, he transforms satellite data into captivating imagery. Robert’s work has appeared on the front page of the New York Times, the cover of National Geographic, and he crafted the iconic Blue Marble featured on the original Apple iPhone. His expertise in data visualization, remote sensing, and the use of color has left a lasting impact on the field. He is currently freelancing and open to full-time opportunities.